(Part 8 in a series on the scientific method)
In the last installment I advanced a hypothesis about what truth is, which is to say, I suggested a way to explain the broad consensus that appears to exist about truth. That explanation was: there is an objective reality "out there", and true statements are those that in some sense correspond to the actual state of affairs in that objective reality. This was problematic for statements like, "Gandalf was a wizard" because Gandalf doesn't actually exist in objective reality, but that was accounted for by observing that the actual meanings of sentences in natural languages often goes beyond the literal.
But there is one aspect of truth that is harder to account for, and which would appear at first glance to be a serious shortcoming of my theory: math. Most people would consider, for example, "1+1=2" or "7 is prime" to be true despite the fact that it's hard to map those concepts onto anything in objective reality. I can show you "one apple" or "one sheep", but showing you "one" is harder. The whole point of numbers, and mathematics and logic in general, is to abstract away from the physical. Numbers qua numbers do not exist in the real world. They are pure abstraction, or at least they are supposed to be. Mathematical truth is specifically intended not to be contingent on anything in the physical world, and so it would seem that my theory of truth fails to capture mathematical truth.
Some philosophers and religious apologists claim that it is therefore impossible to ground mathematical truth in objective reality, that the existence of mathematical truth requires something more, some ethereal realm of Platonic ideals or the Mind of God, to be the source of such truths. It's a plausible argument, but it's wrong. Mathematical truth can be understood purely in terms of objective reality. Specifically, mathematics can be viewed as the study of possible models of objective reality. In this installment I will explain what I mean by that.
There are a lot of different examples of (what is considered to be) "mathematical truth" but let me start with the most basic: elementary arithmetic. These include mundane truths about numbers, things like "two plus three equals five" or "seven is prime." It would seem at first glance that numbers used in this way don't refer to anything in objective reality. I can show you two of something but I can't show you "two" in isolation.
There is an easy answer to this: numbers in common usage are not nouns, they are adjectives. The reason I can't show you "two" without showing you two of something is the same reason I can't show you "green" unless I show you a green thing. Adjectives have to be bound to nouns to be exhibited, but that doesn't mean that "green" does not exist in objective reality. It does, it's just not a thing. Green is a color, which is a property of things, but it is not itself a thing. Likewise, "two" is not thing, it is a quantity, which is a property of (collections of) things. And the reason that two plus three equals five is that if I have two things and I put them together with three other things the result is a quantity of things to which English speakers attach the label "five". Likewise "seven is prime" can be understood to mean that if I have a quantity of things to which English speakers attach the label "seven" I cannot arrange those things in a complete, regular rectangular grid in any way other than the degenerate case of putting them all in a line.
But this explanation fails for straightforward extensions of the natural numbers, like negative numbers or irrational numbers or imaginary numbers. I can show you two apples, and I can explain addition and subtraction in terms of putting groups of apples together and taking apples away, but only for positive numbers. I cannot explain "three minus five equals negative two" in terms of starting with three apples and taking five away because that is just not physically possible. Likewise I cannot show you a square with a negative area, and so I cannot explain the square roots of negative numbers in terms of anything physical (at least not easily).
There are two more cases where the numbers-are-adjectives theory fails. The first is truths that involve generalizations on numbers like "There are an infinite number of primes." That can't be explained in terms of properties of physical objects because we live in a finite universe. There are not an infinite number of objects, so if numbers are meant to describe a quantity of a collection of actual physical objects, then there cannot be an infinite number of them either.
Finally, there are a lot of objects of mathematical study beyond numbers: manifolds, tensors, vectors, functions, groups, to name just a few. Some of these areas of study produce mathematical "truths" that are deeply weird and unintuitive. The best example I know of is the Banach-Tarski "paradox". I put "paradox" in quotes because it's not really a paradox, just deeply weird and unintuitive: it is possible to decompose a sphere into a finite number of parts that can be reassembled to produce two spheres, each the same size as the original. That "truth" cannot be explained in terms of anything that happens in objective reality. Indeed, the reason this result seems deeply weird and unintuitive is that it appears to directly contradict what is possible in objective reality. So the Banach-Tarski "paradox" would seem to be a counter-example to any possible theory of how mathematical truth can be grounded in objective reality. And indeed it is a counter-example to the idea that mathematical truths are grounded in actual objective reality, but that is not news -- we already established that with the example of negative numbers and imaginary numbers.
I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality. To defend this hypothesis I need to explain what a "model" is, and what I mean by "possible" in this context.
A model is any physical system whose behavior correlates in some way with another physical system. An orrery, for example, is a model of the solar system. An orrery is a mechanical model, generally made of gears. It is the actual physical motion of the gears that corresponds in some way to the actual physical motion of the planets.
Mathematics is obviously not made of gears, but remember that mathematics is not the model, it is the study of (possible) models (of objective reality). So the study of mechanical models like orreries falls under the purview of mathematics. Mathematics obviously transcends the study of mechanical models in some way, but you may be surprised at how closely math and mechanism are linked historically. Math began when humans made marks on sticks (or bones) or put pebbles in pots to keep track of how many sheep they had in their flocks or how much grain they had harvested. (These ancient roots of math live on today in the word "calculate" which derives from the latin word "calculus" which means "pebble".) And mathematics was closely linked to the design and manufacture of mechanical calculating devices, generally made using gears just like orreries, right up to the middle of the 20th century.
There is another kind of model besides a mechanical one: a symbolic model. Mathematics has its roots in arithmetic which has its roots in mechanical models of quantities where there was a one-to-one-correspondence between marks-on-a-stick or pebbles-in-a-pot and the things being counted. But this gets cumbersome very quickly as the numbers get big, and so humans came up with what is quite possibly the single biggest technical innovation of all time: the symbol. A symbol is a physical thing -- usually a mark on a piece of paper or a clay tablet, but also possibly a sound, or nowadays a pattern of electrical impulses in a silicon chip -- that is taken to stand for something to which that mark bears no physical resemblance at all. The familiar numerals 0 1 2 3 ... 9 are all symbols. There is nothing about the shape of the numeral "9" that has anything to do with the number it denotes. It's just an arbitrary convention that 9 means this many things:
@ @ @ @ @ @ @ @ @
and 3 means this many things:
@ @ @
and so on.
Not all symbols have straightforward mappings onto meanings. Letters, for example, are symbols but in general they don't mean anything "out of the box". You have to assemble letters into words before they take on any meaning at all, and then arrange those words into sentences (at the very least) in order to communicate coherent ideas. This, too, is just a convention. It is not necessary to use letters, and not all languages do. Chinese, for example, uses logograms, which are symbols that convey meaning on their own without being composed with other symbols. And symbols don't have to be abstract either. Pictograms are symbols that communicate meaning by their physical resemblance to the ideas they stand for.
Mathematical symbols work more like logograms than letters. A mathematical symbol like "3" or "9" or "+" generally conveys some kind of meaning by itself, but you have to compose multiple symbols to get a complete idea like "3+2=5". Not all compositions of symbols result have coherent meanings, just as not all compositions of letters or words have coherent meanings. There are rules governing how to compose mathematical symbols just as for natural language. "3+2=5" is a coherent idea (under the usual set of rules) but "325=+" is not.
There is a further set of rules for how to manipulate mathematical symbols to produce "correct" ideas. An example of this is the rules of arithmetic you were taught in elementary school. The result of manipulating numerals according to these rules is a symbolic model of quantities. There is a correspondence between strings of symbols like "967+381=1348" and the behavior of quantities in objective reality. Moreover, manipulating symbols according to these rules might seem like a chore, but it is a lot easier to figure out what 967+381 is by applying the rules of arithmetic than by counting out groups of pebbles.
It turns out that manipulating symbols according to the right rules yields almost unfathomable power. With the right rules you can produce symbolic models of ... well, just about anything, including, but not limited to, every aspect of objective reality that mankind has studied to date (with the possible exception of human brains -- we will get to that later in the series).
Mathematics is the study of these rules, figuring out which sets of rules produce interesting and useful behavior and which do not. One of the things that makes sets of rules for manipulating symbols interesting and useful is being able to separate string of symbols into categories like "meaningful" and "meaningless" or "true" and "false". Sometimes, for sets of rules that produce models of objective reality, "true" and "false" map onto things in objective reality, and sometimes they are just arbitrary labels.
The canonical example of this is Euclid's fifth postulate: given a line and a point not on that line, there is exactly one line through the given point parallel to the given line. For over 2000 years humans believed that to be true and were vexed when they couldn't find a way to prove it. It turns out that it is neither true nor false but a completely arbitrary choice; you can simply choose whether the number of lines through a point parallel to a given line is one or zero or infinite. Any of those three choices leads to useful and interesting results. As a bonus, some of them turn out to be good models of some aspects of objective reality too.
Another way of looking at it is that mathematics looks at what happens when you remove the constraints of physical reality from a set of rules that model that reality. More often than not it turns out that when you do this, what you get is a system that is useful for modeling some other aspect of reality. Sometimes that aspect of reality is something that you would not have even suspected to exist had not the math pointed you in that direction.
An example: arithmetic began as a set of rules for counting physical objects. You cannot have fewer than zero physical objects. But you can change the rules of arithmetic to behave as if you could have fewer than zero objects by introducing "the number that is one less than zero" a.k.a. negative one. Even though that concept is patently absurd from the point of view of counting apples or sheep, it turns out to be indispensable when counting electrical charges or keeping track of financial obligations. So is it "true" that (say) three minus five equals negative two? It depends on what you're counting. Is it "true" that there are an infinite number of primes? It depends on your willingness to suspend disbelief and imagine an infinite number of numbers even though most of those could not possibly designate any meaningful quantity of physical objects in our finite universe. It the Banach-Tarski paradox "true"? It depends on whether or not you want to accept the Axiom of Choice. (And if you think the AoC seems "obviously true" then you should read this.)
There are many examples of alternatives to the usual rules of numbers that turn out to be useful. The most common example is modular arithmetic, which produces useful models of things like time on a clock, days of the week, and adding angles. Another example is p-adic numbers, which are like modular arithmetic on steroids. It is worth noting that in modular arithmetic, some arithmetic truths that are often taken as gospel turn out not to be true. For example, in base 7, the square root of two is a rational number (not just rational but an integer!).
Philosophers and religious apologists often cite mathematical "truths" as somehow more "pure" than empirical truths and our ability to perceive them to be evidence of the existence of God or some other ethereal realm. Nothing could be further from the (empirical!) truth! In fact, all mathematical "truths" are contingent, dependant on a set of (mostly tacit) assumptions. Even the very concept of truth itself is an assumption!
With that in mind, let us revisit the liar paradox, to which I promised you an answer last time. I'll use the two-sentence version since that avoids technical issues with self-reference:
1. Sentence 2 below is false.The puzzle is how to assign truth values to those two sentences. The reason it's a puzzle is that there are two tacit assumptions that people bring to bear. The first is the Law of the Excluded Middle: propositions are either true or false. They cannot be both, and they cannot be neither. A simple way to resolve the paradox is simply to discharge this assumption and say that propositions can be half-true, and that being half-true is the same as being half-false.
2. Sentence 1 above is true.
The second tacit assumption that makes the Liar paradox paradoxical is the assumption that the truth values of propositions must be constant, that they cannot change with circumstances. This is particularly odd because everyday life is chock-full of counterexamples. In fact, the vast majority of propositions that show up in everyday life depend on circumstances. "It is raining." "I am hungry." "It is Tuesday." The truth values of those all change with circumstances. Obviously, "It is Tuesday" is only true on Tuesdays. Why cannot the truth values of the Liar paradox do the same thing? We can re-cast it as:
1. At the moment you contemplate the meaning of sentence 2 below, it will be false.The truth values then flip back and forth between true and false as you shift the focus of your contemplation from one to the other. Note that both of these solutions can also be applied to the "this sentence is true" version, where all three of "true", "false" and "half-true/half-false" produce consistent results (though of course not at the same time).
2. At the moment you contemplate the meaning of sentence 1 above, it will be true.
Finally, note that we can also attack the Liar paradox experimentally by building a physical model of it. There are many ways to do this, but any physical mechanism that emulates digital logic will do. You could build it out transistors or relays or Legos. All you need to do is build an inverter, a device whose output is the opposite of its input. Then you connect the output to the input and see what happens.
In the case of a relay, there is enough mechanical delay that the result will be flipping back and forth. It will happen fast enough that the result will sound like a buzzer, and indeed back in the days before cheap transistors this is often how actual buzzers were made. If you build this circuit out of transistors then the outcome will depend a lot on the details, and you will end up with either an oscillator or a voltage that is half-way between 1 and 0.
If you put two inverters in series and connect the final output to the initial input you will have built a latch, which will stay at whatever condition it starts out in. This is how certain kinds of computer memory are made.
The modeling train runs in both directions. This will become important later when we talk about information. But that will have to wait until next time.
3 is prime
ReplyDelete@Ron:
>Mathematical truth can be understood purely in terms of objective reality.
Then later you write:
>So the Banach-Tarski "paradox" would seem to be a counter-example to any possible theory of how mathematical truth can be grounded in objective reality. And indeed it is a counter-example to the idea that mathematical truths are grounded in actual objective reality, but that is not news -- we already established that with the example of negative numbers and imaginary numbers.
So ... mathematics cannot be understood purely in terms of objective reality?
>Specifically, mathematics can be viewed as the study of possible models of objective reality.
"Possible models of objective reality" are abstract objects. Mathematics is abstract.
Just where do stand on abstract objects? Do abstract objects exist in and/or before particular things (realism), or are they only concepts of the mind (conceptualism), or they don't exist and are just language words (nominalists)?
>It turns out that manipulating symbols according to the right rules yields almost unfathomable power. With the right rules you can produce symbolic models of ... well, just about anything, including, but not limited to, every aspect of objective reality that mankind has studied to date (with the possible exception of human brains -- we will get to that later in the series).
Are you sure? Every aspect of objective reality?
>But you can change the rules of arithmetic to behave as if you could have fewer than zero objects by introducing "the number that is one less than zero" a.k.a. negative one. Even though that concept is patently absurd from the point of view of counting apples or sheep, it turns out to be indispensable when counting electrical charges or keeping track of financial obligations.
Don't need negative numbers for either of those things.
>Mathematics is the study of these rules, figuring out which sets of rules produce interesting and useful behavior and which do not. One of the things that makes sets of rules for manipulating symbols interesting and useful is being able to separate string of symbols into categories like "meaningful" and "meaningless" or "true" and "false". Sometimes, for sets of rules that produce models of objective reality, "true" and "false" map onto things in objective reality, and sometimes they are just arbitrary labels.
Is this you viewing mathematics as formalism, the philosophy of mathematics takes it as holding that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than playing ludo or chess are normally thought to have?
It's hard to tell, in the end, what you think mathematics is, and what mathematical truth is.
>Is it "true" that there are an infinite number of primes? It depends on your willingness to suspend disbelief and imagine an infinite number of numbers even though most of those could not possibly designate any meaningful quantity of physical objects in our finite universe. It the Banach-Tarski paradox "true"? It depends on whether or not you want to accept the Axiom of Choice.
I was expecting this to be an essay of what you believe, not a survey of options.
> mathematics cannot be understood purely in terms of objective reality?
ReplyDeleteThanks for pointing that out, that is definitely something I need to clarify.
The post above is the fourth of fifth draft I wrote on this topic. It has proven to be the most difficult installment yet. It started out being about Turing machines and the Church-Turing thesis, and ended up what you see above. The "Mathematical truth can be understood purely in terms of objective reality" claim is a leftover from an earlier draft. I should probably just take it out and put it in the next chapter.
> Just where do stand on abstract objects?
If you put a gun to my head and force me to choose one of your labels I'll take conceptualism. But I would say that mathematical objects exist in the ontological category of ideas, just like wizards. The difference between math and fiction is not as great as most people think. The only difference is the strictness of the rules that govern their construction.
> Are you sure? Every aspect of objective reality?
Pretty sure, yeah. But I will grant that at this point this is an unsubstantiated claim, and I need to make that clearer too. So thanks for keeping me honest here.
> Don't need negative numbers for either of those things.
True. I guess I should change "indispensable" to "handy".
> Is this you viewing mathematics as formalism
Yes. Again, not as clear as it should be. Math is a game, and some sets of rules turn out to produce models of reality.
> I was expecting this to be an essay of what you believe, not a survey of options.
Why would you expect that? The *whole point* of this series is that what I believe is irrelevant (except insofar as someone has decided that I'm a trustworthy source).
But this essay definitely needs another rewrite. Thanks for the feedback.
4 is even, but I don't believe it.
ReplyDelete>Why would you expect that? The *whole point* of this series is that what I believe is irrelevant (except insofar as someone has decided that I'm a trustworthy source).
It comes from your first installment in this series, when you wrote:
I believe that science provides a *complete worldview* applicable to all aspects of life, not just ones that are commonly regarded as "science-y". Furthermore, I believe that this worldview can be practiced by anyone, not just professional scientists. You don't even have to be good at math (though it doesn't hurt). And I also think that if more people did this, the world would be a better place.
In particular, I believe that science can be applied to answer questions about *morality*, and I claim that if you do this properly the results are *better* than those produced by traditional religions. I also believe that science can provide satisfactory answers to deep existential questions, like what is the meaning of life.
I actually believe that all of these Problems have had some pretty significant dents put into them by the scientific method, much more than is generally appreciated or understood, even among scientists. I've written about all of these things at one time or another, but usually in the context of developing my own ideas about them, and never as a coherent summary that presents the final results in a unified and organized way. I'm going to try to remedy that in the future.
>Math is a game, and some sets of rules turn out to produce models of reality.
The problem you'll have with this view is that mathematics can be used to analyze mathematics itself (meta-mathematics). Meta-mathematics is itself a substantial bit of mathematics, ostensibly committed to an infinite realm of objects which are not, on the face of it, concrete. Tokens of the expressions of the object language game calculus may be finite—ink marks and the like; but since there are infinitely many expressions, theorems and proofs, these themselves must be taken to be abstract types. At best you can achieve no more than a reduction in commitment from the transfinite realms of some mathematical theories, such as set theory, to the countably infinite, but still presumably abstract, realm of arithmetic, wherein the syntax and proof theory of standard countable languages such as those of standard set theory, can, as Gödel showed, be modeled.
> It comes from your first installment in this series, when you wrote:
ReplyDeleteAh. OK, in that context, the answer to your question is that IMHO the question of whether Banach-Tarski is true is comparable to the question of whether or not, say, Batman would win a fight against Superman. Because we live in a quantum world, there are no actual infinities accessible to us, so questions about the properties of infinities are essentially questions about fictional worlds.
> The problem you'll have with this view is that mathematics can be used to analyze mathematics itself
I don't see what that's a problem. Mathematics is a physical process (symbol manipulation). Why would be any more problematic than analyzing any other physical process?
> there are infinitely many expressions, theorems and proofs
But there aren't. Our universe is finite. At worst there are an *unbounded* number of expressions, theorems, and proofs, but unbounded is not infinite.
_/|
ReplyDelete@Ron:
>Because we live in a quantum world, there are no actual infinities accessible to us, so questions about the properties of infinities are essentially questions about fictional worlds.
We encounter the infinite -- and its little buddy, the infinitesimal -- on a daily basis in our lives.
>> The problem you'll have with this view is that mathematics can be used to analyze mathematics itself
>I don't see what that's a problem. Mathematics is a physical process (symbol manipulation). Why would be any more problematic than analyzing any other physical process?
>> there are infinitely many expressions, theorems and proofs
But there aren't. Our universe is finite. At worst there are an *unbounded* number of expressions, theorems, and proofs, but unbounded is not infinite.
Yet the rules of the math game you setup have infinities.
I said you'd have problems.
> We encounter the infinite -- and its little buddy, the infinitesimal -- on a daily basis in our lives.
DeleteLike when?
> Yet the rules of the math game you setup have infinities.
I don't recall setting up any rules for any math game.
> I said you'd have problems.
Problems (with a capital P) are inevitable in science. Identifying a Problem is the first step in the scientific method, remember? That's how science makes progress.
To Infinity, And Beyond
ReplyDelete@Ron:
>Like when?
Vertical things. The walls of your house. They have an infinite slope.
Calculus can be rigorously defined with infinitesimals. Hence if you evaluate a defined integral, you have just added up an infinite number of infinitesimals.
Computer programming -- the use of infinite loops.
>I don't recall setting up any rules for any math game.
Recall your first installment of this series, which I quote for the second time:
>>Math is a game, and some sets of rules turn out to produce models of reality.
Practicing mathematicians are acting as platonists, but if you bug them about the nature of mathematics, this is "game theory" is what they will gesture towards. They desire to get rid of abstract objects and infinities. Yet it fails because mathematics can be used to analyze mathematics itself, and the abstract objects and infinities come back in this second level analysis.
>That's how science makes progress.
Progress? Science does not progress. That's a myth.
> Vertical things. The walls of your house. They have an infinite slope.
ReplyDeleteYou're looking at them wrong. Try lying on your side.
(Seriously though, that just means that slope is not the right model of verticality because there is nothing actually infinite about it.)
> Calculus can be rigorously defined with infinitesimals.
It can be, but it doesn't have to be. Limits work too.
> infinite loops
"Infinite loop" is not an accurate model of physical reality. No physical computer can actually run in an infinite loop because of the second law of thermodynamics.
> Math is a game
That might have been an unfortunate choice of words on my part. But even if I called it a game, I certainly didn't set up the rules. No one "set up" the rules. It just turns out that manipulating symbols by the right rules produces models of objective reality with enough fidelity to be useful. That's simply an empirical observation. TMs explain that observation.
> Science does not progress.
Then how do you account for the many things that exist today but did not exist 200 years ago? Smart phones. The internet. Antibiotics. Jet airplanes. Space telescopes. Blue LEDs. Why didn't the Romans invent all these things?
Math is not a game
ReplyDelete@Ron:
> It just turns out that manipulating symbols by the right rules produces models of objective reality with enough fidelity to be useful.
You're tiptoeing through a minefield -- as symbols are essentially abstract entities (do not confuse the mark with the symbol).
Then usefulness, or instrumentality, is not a guarantee of truth.
Change is Not Progress (Part 1)
ReplyDelete>> Science does not progress.
>Then how do you account for the many things that exist today but did not exist 200 years ago? Smart phones. The internet. Antibiotics. Jet airplanes. Space telescopes. Blue LEDs. Why didn't the Romans invent all these things?
This is to confuse change with progress.
Smart phones -- which make it easier for you to be scammed by fraudsters, allow companies and the government to track and surveil you, which isolate you from human contact and lead to an increase in mental illness.
The internet -- which facilitates not only government and private companies tracking your activities and eliminating your privacy, but also makes it easier for them to censor you. A medium which enables criminal activity on an unprecedented scale and reduces personal security.
Antibiotics -- which decrease mortality and increase life expectancy, but contribute to an increase in population, and this brings with it the disability of a lowered standard of living, increased hardship, and an aggravated struggle to allow the increased population to simply continue living.
Jet airplanes -- which allow the transport over thousands of miles of explosive bombs to population centers and are a key part of modern total warfare.
Space telescopes and blue LEDs -- increased scientific curiosity has brought both wonders and horrors, and has provided tools for the betterment of living conditions and also for the destruction of life. Tools are neither moral nor immoral, they may be used morally or immorally. Nor does merely the accumulation of facts and knowledge lead to wisdom.
Yardsticks of Progress (Part 2)
ReplyDeleteOne of the greatest myths of Western civilization is the myth of progress. For approximately 300 years Western society has generally believed that progress has taken place, that we are experiencing the results of past progress, and that there is a strong possibility if not inevitability that progress will continue in the future. In other words, people tend to make an evaluation of their present status in terms of progress achieved and to project an expectation of progress to be achieved. Usually there is an element of conscious planning in the myth-expectation aspect of the belief. Progress is a dynamic myth, it is motivational and directional. As a myth it is commonly defined or conceived of as the acquisition of "more of the good".
A number of tests or yardsticks of progress have been proposed (and subsequently abandoned). Various authors suggested that progress could be seen in (a) the increase in population, (b) the increase in life expectancy, (c) the decrease in infant mortality, (d) the increase in literacy, (e) the increase of goods and services, (f) the decrease in crime, (g) the increase in personal security, (h) the spread of scientific curiosity, (i) the refinement of social processes, and, someone wrote in the spring of 1914, (j) the end of wars.
There has been a great increase of goods and services, and in many parts of the world the individual is provided with creature comforts unknown to his grandparents. However, does the possession and use of these creature comforts make the individual morally better? Does the existence of scientifically perfected tools bring about the moral discretion necessary to the moral use of those tools? Does a longer life expectancy and an access to the printed word, per se, make wiser or morally improve (or aid sometimes to intellectually enslave) the individual? In the end, has the wholly conscious, planned, guided manipulation of the human environment for 300 years especially elevated the moral stature of mankind? If it cannot be objectively demonstrated that mankind as a whole is morally better because of this process, then it cannot be objectively demonstrated that progress has taken place. If it cannot be objectively demonstrated that progress has taken place, then there is no reason to assume that the present or continued manipulation of the environment will bring about progress. This is the present appraisal of the idea of progress by many contemporary social observers.
Certainly change has taken place. No one would deny that for many people life is longer, healthier, more pleasant, and more comfortable. No one would deny that the conscious manipulation of our environment has caused many men to be better educated, housed, dressed, fed, transported, and entertained. All of this has been brought about at a price. The price we have paid is apparent to anyone who chooses to reflect on the status of our present situation. But for the sake of argument, let us assume that the price has not been exorbitant, that overall, mankind has gained in well-being, health, comfort, etc. Progress is still not self-evident because none of these gains necessarily demonstrates that man is morally improved. We may be better off, but are we better? The myth of progress has taught people to believe that we would become better, not just better off.
> symbols are essentially abstract entities (do not confuse the mark with the symbol)
ReplyDeleteYou need a better dictionary.
symbol: Something that represents something else by association, resemblance, or convention, especially a material object used to represent something invisible. Alternatively, a printed or written sign used to represent an operation, element, quantity, quality, or relation, as in mathematics or music.
Symbols are physical.
> usefulness, or instrumentality, is not a guarantee of truth.
It is according to my definition of truth.
> This is to confuse change with progress.
Um, no. I consider progress to be change that gives us control over our destiny. Just because we don't always make wise choices doesn't mean that having the ability to choose, being the masters of our own fates, isn't progress.
map ≠ territory
ReplyDelete@Ron:
>Symbols are physical.
You need to read your definition more carefully:
symbol: Something that represents something else by association, resemblance, or convention, especially a material object used to represent something invisible.
You're confusing the map for the territory.
>> usefulness, or instrumentality, is not a guarantee of truth.
>It is according to my definition of truth.
Your definition of truth is the correspondence theory of truth (and has all of its problems).
I really, really, really don't think you want to adopt instrumentality as a guarantee of truth.
>I consider progress to be change that gives us control over our destiny. Just because we don't always make wise choices doesn't mean that having the ability to choose, being the masters of our own fates, isn't progress.
Well, now you just need to demonstrate that you have more control over your destiny than people 300 years ago had.
You're still going to end up as worm food, aren't you? Just checking.
> You're confusing the map for the territory.
ReplyDeleteNo, that would be you confusing a symbol and the thing it represents. The latter can be invisible, not the former.
> Your definition of truth is the correspondence theory of truth
Yes.
> (and has all of its problems).
Like what?
> You're still going to end up as worm food, aren't you?
Eventually. But that's likely to happen a lot later than it would have in the past, and in the meantime I have vastly more options available to me than I would have had in the past. I call that progress.
Big Facts
ReplyDeleteIn your prior essay, A Scientific Theory of Truth, I listed several problems: abstract objects, negative facts, counterfactuals, and synthetic facts.
A true proposition about the non-existence of something cannot correspond to anything because such a proposition is not about anything that exists. Consider the proposition, which I shall label NO UNICORNS: "There are no unicorns." Since NO UNICORNS is true, your correspondence theory predicts that NO UNICORNS corresponds to something. But what can it possibly correspond to? It clearly does not correspond to unicorns, since there aren't any -- and if any unicorns did exist, then NO UNICORNS would be false.
An additional objection is an epistemological one, that the correspondence theory of truth must inevitably lead to skepticism about the external world. We cannot "step outside our own minds" to to compare our thoughts with mind-independent reality. Yet, with your correspondence theory of truth, this is precisely what we would have to do in order to gain knowledge. We would have to access reality as it is in itself, independently of our cognition, and determine whether our thoughts correspond to it. Since this is impossible, since all our access to the world is mediated by our cognition, the correspondence theory makes knowledge impossible. Assuming that the resulting skepticism is unacceptable, the correspondence theory has to be rejected.
A final objection is complicated, known as the "Big Fact" or the "slingshot argument." It's too long to cover in a comment, but the ultimate conclusions are:
1. Different propositions (e.g., "Snow is white" and "Grass is green") might be reduced to the same ultimate fact.
2. This reduction undermines the correspondence theory by suggesting that the multiplicity of facts (each corresponding to different true propositions) collapses into one.
3. If all truths correspond to a single fact, the correspondence theory loses its explanatory power, as it can no longer distinguish between different truths based on distinct facts.
@Ron:
>But that's likely to happen a lot later than it would have in the past, and in the meantime I have vastly more options available to me than I would have had in the past. I call that progress.
Do you have more options? Current society constrains your life choices. You can no longer choose, say, to be a jester employed by a nobleman or monarch to entertain guests during royal court. A typical life pattern today is childhood education, college, work for a company, retire. Options haven't expanded, they are just different.
Furthermore, the world population in 1700 is estimated to be about 600 million people. In the 20th century, 200 million people were killed and murdered through a combination of war, genocide, and criminal actions by communist governments. In the middle of the 20th century, certain people in central Europe were nearly guaranteed to be murdered. The ideals of the Enlightenment did nothing to help them. That 1/3 of the world population in 1700 was killed during the 20th century is not progress, and those killed and murdered certainly did not have more options than people in 1700.
The most damaging thing about the myth of progress is that people assume that it is true.
> A true proposition about the non-existence of something cannot correspond to anything
ReplyDeleteOf course it can. "There are no unicorns" is true if, in point of actual fact, there are no unicorns. It's not that hard.
> the correspondence theory of truth must inevitably lead to skepticism about the external world
That's right, it does. Why do you think that's a problem?
> the "Big Fact" or the "slingshot argument." It's too long to cover in a comment
Here, let me help you.
My position on this is exactly what Wikipedia says: the slingshot argument does not go through if Bertrand Russell's account of definite descriptions is assumed. Which I do. I actually wrote my masters thesis about the problem of referential transparency, which can also be solved in the same way.
> You can no longer choose, say, to be a jester employed by a nobleman
Actually, I can.
> Options haven't expanded, they are just different.
For the price of about a week of minimum-wage labor I can buy a device that gives me access to vastly more information than was contained in the library of Alexandria. This same device provides me with access to news, music, and the ability to communicate with billions of people. For the same amount of money I can travel thousands of miles in a matter of hours. I can go to a market in just about any major city and get food from around the world, including fresh produce year-round. I can heat and cool my house by pushing a button; I don't have to chop wood. I have hot and cold running water that I can even drink without getting sick. Not even kings could boast of these things a few hundred years ago.
Abstract Objects: Can't Live Without Them
ReplyDelete@Ron:
>"There are no unicorns" is true if, in point of actual fact, there are no unicorns. It's not that hard.
Let's copy Ron's Theory of Truth:
Ron's Theory of Truth: Truth is a property of propositions, which are ideas that stand in relation to some circumstance in objective reality (whose existence we have assumed for the sake of argument). If the circumstance corresponding to that proposition actually pertains, then the proposition is true, otherwise it is false.
Under Ron's Theory of Truth, one must make a judgment of a proposition and some circumstance of objective reality. Yet for negative facts ("there are no unicorns"), one cannot make a judgment, for it is not there to be judged. To judge something that is not existing is to judge nothing, and, hence, to judge not at all.
Aside: propositions are abstract objects.
>That's right, it does. Why do you think that's a problem?
So now you're an Idealist?
>My position on this is exactly what Wikipedia says: the slingshot argument does not go through if Bertrand Russell's account of definite descriptions is assumed.
Wikipedia is out of date, as the slingshot has been rearmed, and no theory of descriptions can save you.
Which I do. I actually wrote my masters thesis about the problem of referential transparency, which can also be solved in the same way.
As the third reader of your master's thesis, let me tell you that you have a typo on the third line of page 12 -- "phone sumber".
>Actually, I can.
I'll need to see a job requisition.
For the price of about a week of minimum-wage labor I can buy a device that gives me access to vastly more information than was contained in the library of Alexandria.. . . Not even kings could boast of these things a few hundred years ago.
Sure, we live better than historical kings. But that's change, not progress.
I actually remember when there was no internet. Is life better today that it was back then? No.
> for negative facts ("there are no unicorns"), one cannot make a judgment
ReplyDeleteI can. Watch this: there are no unicorns.
But you do you.
> propositions are abstract objects
Maybe you'd better describe "abstract object" for me. And you might also want to go back and review my theory of ontology.
> So now you're an Idealist?
No, I'm a Scientist. Have been for decades now.
> no theory of descriptions can save you.
Yes, it can.
> we live better than historical kings. But that's change, not progress.
I guess we'll have to agree to disagree about that.
@Publius:
ReplyDelete> that's change, not progress
Just out of curiosity, what would progress look like on your view?
Antecedent to Ontology
ReplyDelete@Ron:
>I can. Watch this: there are no unicorns.
What is the mass of the no unicorn? What is the size of the no unicorn? Where is the no unicorn? Is the no unicorn in the room with you right now?
>Maybe you'd better describe "abstract object" for me.
No one has developed a standard description of abstract objects. There is consensus on several paradigm cases. The only simple description of abstract objects is that they are not concrete objects.
>And you might also want to go back and review my theory of ontology.
It suffers from property dualism and in general is not an ontology, as you just conclude "it's all in your head." But then you have gems like this:
It is not clear how many ontological categories there are beyond brains. Music, fiction, math, law and language are five different OCs that I can come up with just off the top of my head. There are probably more. The boundaries between them are not crisp, and they don't form a hierarchy.
Beyond brains, you say?
But then you say this:
All of them fall into the meta-OC of "mental construct".
Nope, just brains after all.
>No, I'm a Scientist.
You're not Batman?
>I guess we'll have to agree to disagree about that.
Perhaps you could apply your scientific method to the question, "Has there been human progress since the Enlightenment"?
Progress 1
ReplyDelete@Ron:
>Just out of curiosity, what would progress look like on your view?
In short, that "we" become "better," not just "better off."
A little history is in order.
The idea of progress emerged during the Enlightenment. A key figure in popularizing this idea was Marquis de Condorcet with his work, Sketch for a Historical Picture of the Progress of the Human Spirit (ironically written in 1794 while hiding during the French Revolution, and published posthumously in 1795). He argued that expanding knowledge in the natural and social sciences would lead to an ever more just world of individual freedom, material affluence, and moral compassion. He argued the past could be understood in terms of the progressive development of human capabilities, that progress of the natural sciences must be followed by progress in the moral and political sciences, and that social evils are the result of ignorance and error rather than an inevitable consequence of human nature. Condorcet believed that there was no definition of the perfect human existence and thus believed that the progression of the human race would inevitably continue throughout the course of our existence. He envisioned man as continually progressing toward a perfectly Utopian society.
Some Enlightenment thinkers were less optimistic, envisioning only a gradual moral improvement of humanity. However, they generally agreed that by controlling and manipulating their environment, humans could morally improve themselves and create a society closer to the ideal envisioned by humanitarian idealists.
In the 18th and 19th centuries, many proponents of progress advocated for social reforms to speed up the development of a more perfect society and moral individuals. These reforms ranged from increased education for women to universal male suffrage, changes in voting districts, tariff repeals, national self-determination, and the formation of a multinational federation. While not all proposals were accepted, the belief in progress grew stronger, with a widespread commitment to manipulating the environment to achieve this ideal.
In the 19th century, Herbert Spencer argued that progress was not just an optimistic ideal but an inevitable law, supported by Darwin's concept of evolution. According to Spencer, society could be confident that progress was real and morally beneficial. However, this idea faced criticism. Some scholars argued that history did not show a linear progression from worse to better and that if progress were inevitable, human efforts to achieve it would be unnecessary. This led to a rethinking of progress, viewing evolution as a means for humans to adapt and choose paths that offered the best chances for moral improvement. Progress, according to this view, required value judgments about the changes it brought.
This created a new problem: if progress was not inevitable, what evidence was there for its occurrence, and why should it continue? The myth of progress provided an optimistic outlook, but it became increasingly clear that belief in progress needed a scientific basis. Progress had to be measured. Various tests were proposed, such as population growth, increased life expectancy, reduced infant mortality, higher literacy rates, more goods and services, decreased crime, increased personal security, scientific curiosity, and improved social processes.
Progress 2
ReplyDeleteHowever, after two world wars, a global depression, and numerous smaller conflicts and revolutions, these tests were abandoned. None of them conclusively showed moral improvement, and some contradicted objective facts. While advancements like lower infant mortality and longer life expectancy were generally positive, they also brought challenges such as overpopulation and its associated hardships. Increased personal security was debatable, considering the potential for modern warfare. Crime rates had not decreased, and social processes had not necessarily refined. Literacy alone did not ensure a desire to read valuable literature, and knowledge accumulation did not guarantee wisdom. Scientific curiosity had led to both benefits and horrors, providing tools for better living and for destruction. The increase in goods and services improved many lives, but it did not necessarily make individuals morally better. Longer life expectancy and access to information did not inherently lead to wisdom or moral improvement. Over 300 years of conscious environmental manipulation did not objectively demonstrate moral progress.
While there have been many changes, and people are better educated, housed, dressed, fed, transported, and entertained, this came at a cost. Reflecting on the current situation in 2024, the price is evident. Even if we assume the cost was not too high and that humanity has generally gained in well-being, health, and comfort, progress is not self-evident because these gains do not necessarily mean moral improvement. We may be "better off," but are we "better"? The myth of progress taught that we would become "better," not just "better off." The ultimate goal of progress has always been moral betterment.
That is why progress is a myth.
ReplyDelete> What is the mass of the no unicorn?
You are playing word games.
> No one has developed a standard description of abstract objects.
Ah. So "abstract objects" are like pornography too. You can't define them but you know them when you see them. Oh, wait, you can't see abstract objects? Hm, that seems like a problem.
Here, let me help: is there a difference between an "abstract object" and an "idea"? If not, start using "idea" instead. It's less typing.
> It suffers from property dualism
No, you have missed the point. Existence is not a property of things, it is a property of *substrates*. If a thing exists, it's not because that thing has "popped into existence", it's because something *else* has *arranged* itself in a certain way, because something *else* is in a certain *state*. Material objects and ideas are both arrangements/states of atoms, and atoms are states of the wave function. There is no dualism. It's the exact opposite in fact.
> Beyond brains, you say?
That was an oversight on my part. I've fixed it. The text now reads:
[O]nce you get beyond the basics (QM -> atoms -> chemistry -> life -> brains -> ideas) things get very complicated. It is not clear how many ontological categories there are beyond ideas.
> Perhaps you could apply your scientific method to the question, "Has there been human progress since the Enlightenment"?
You can't tackle that question scientifically without defining "progress", otherwise it becomes (as it is here) a quibble over terminology.
> In short, that "we" become "better," not just "better off."
OK, but what counts as "better"? There is a general trend towards increased tolerance. Slavery, homophobia, xenophobia, are nowhere near as fashionable as they once were. That looks "better" to me.
> two world wars, a global depression
Ah, because we never had wars or economic downturns before the enlightenment. Got it.
> people are better educated, housed, dressed, fed, transported, and entertained, this came at a cost
Well, duh, there are always tradeoffs. That's just the Way Things Are. But there's a reason that "tradeoff" is a riff on "trade", because some tradeoffs change things in such a way that actually make things better. Finding those, or even deciding what they are, is not easy. But the correct response is not just to throw up your hands in despair and decide that the situation is hopeless because suffering is part of God's Plan or some such nonsense.
Abstraction: scientific theories
ReplyDelete@Ron:
>You are playing word games.
I'm trying to apply the procedure you gave for determining truth:
Ron's Theory of Truth: Truth is a property of propositions, which are ideas that stand in relation to some circumstance in objective reality.
If the proposition is "There are no unicorns", I need you to present the circumstance of objective reality of "no unicorns" so that I can perform the correspondence test.
If you cannot produce the objective reality of "no unicorns," then your theory of truth is incomplete.
Aside: propositions are abstract objects.
>Ah. So "abstract objects" are like pornography too. You can't define them but you know them when you see them.
No, it just means abstraction and abstract objects are complicated. Why would you assume them to be simple? There are different ways one can draw the abstract/concrete distinction. These include: the way of example (which is simply to list the paradigm cases of abstract and concrete objects in the hope that the sense of the distinction will somehow emerge); the way of conflation (i.e., identifying abstract and concrete objects with some already-known distinction); the way of negation (i.e., saying what abstract objects are by saying what they are not, e.g., non-spatiotemporal, non-causal, etc.); and the way of abstraction (i.e., saying that abstract objects are conceptualized by a process of considering some known objects and omitting certain distinguishing features).
Oh, wait, you can't see abstract objects? Hm, that seems like a problem.
Why do I need to "see" them? Can you see love, hope, and charity?
>Here, let me help: is there a difference between an "abstract object" and an "idea"? If not, start using "idea" instead. It's less typing.
This is conceptualism. You are limited to this (or to nominalism) because your mind has as an axiom of materialism, so you are locked into these kinds of explanations, even when evidence and paradoxes challenge it.
If everyone stopped thinking about the Pythagorean Theorem, and all books and writings around it were destroyed, would the Pythagorean Theorem cease to exist?
>> It suffers from property dualism
>No, you have missed the point.. . . There is no dualism.
The very first question in your 31 Flavors of Ontology is by yours truly were I quote you:
You are a computational process, reified as an arrangement of electrical impulses in a human brain. Because we do not yet know how to copy software out of brains the way we can out of computers, you (the software process) are tightly bound to your brain. And because we do not yet know how to replace all other parts of the human body, your brain is tightly bound to your body, and that is why you (the computational process) feel a particular kinship with your body. But nonetheless, you and your body are not only distinct, they exist in different ontological categories. Your body is a material object. You (the thing that is reading these words) aren't.
... and then I ask:
>So the brain has physical properties (structure, blood flow, temperature,...) and mental properties (thinking, memory, intentionality, imagination,...)?
... and you reply:
Yes.
That's property dualism.
The Myth of Progress
ReplyDelete>You can't tackle that question scientifically without defining "progress", otherwise it becomes (as it is here) a quibble over terminology.
Then apply your scientific method first to define "progress."
If you can't do that, you're betraying your original thesis in A Clean Sheet Introduction to the Scientific Method, in which you said:
I believe that science provides a *complete worldview* applicable to all aspects of life, not just ones that are commonly regarded as "science-y". Furthermore, I believe that this worldview can be practiced by anyone, not just professional scientists.
>OK, but what counts as "better"?
I have an answer for that, and it doesn't involve better technology.
>There is a general trend towards increased tolerance.
Not really. If anything, it's been backsliding recently.
>Slavery, homophobia, xenophobia, are nowhere near as fashionable as they once were.
At this moment, there are more people enslaved that there were in 100 years of the African slave trade.
Xenophobia has hardly decreased, as reflection of the events of the past few years will demonstrate.
>That looks "better" to me.
You don't only believe the myth of progress, you organize your life around it: the present is an inferior condition of what the future will be. It's embedded in the belief structure in how you view the world, it is the narrative story that how you imbue existential meaning to the world. You adhere to it with your life, not just your mind.
>> two world wars, a global depression
>Ah, because we never had wars or economic downturns before the enlightenment. Got it.
You're just reinforcing the point I made. If we had wars and economic downturns before and after the Enlightenment, where is the progress?
If fact, after the Enlightenment, it got worse. No progress there. World War 2 killed more people than all prior wars combined, and the Enlightenment provided the technology and the ideas that propelled the horrors of that war.
>some tradeoffs change things in such a way that actually make things better. Finding those, or even deciding what they are, is not easy.
There is no directionality in scientific knowledge and technological development. It can make the human experience better or worse. The Myth of Progress is that there is a directionality, that the human experience will be made better.
The data shows no progress. But enjoy your iPhone.
>But the correct response is not just to throw up your hands in despair and decide that the situation is hopeless because suffering is part of God's Plan or some such nonsense.
What is the correct response? Does it involve a sober, rational assessment of the data? Or do you reject the data because it disproves the myth you've organized your life around and you cannot tolerate the cognitive dissonance?
Also - God wants you to live life, and live it to the fullest. Our situation is not hopeless because our Lord Jesus Christ came down to Earth to instruct us, then saved us from death and separation from God by his death and resurrection.
"Be not afraid! For we are an Easter people, and our song is Hallelujah!"
-- Saint JohnPaul II the Great
> If you cannot produce the objective reality of "no unicorns," then your theory of truth is incomplete.
ReplyDeleteNo. My theory is not contingent on my being able to actually "produce the objective reality" (whatever that means). If there are no unicorns, then "there are no unicorns" is true, and if there are unicorns, then it is false. I don't have to actually "produce" anything. It's entirely possible that we might simply be unable to determine whether or not it's true. There might be unicorns somewhere in the universe, I just don't know.
> propositions are abstract objects
> love, hope, and charity
OK. It seems a little weird to lump all these together because propositions are ideas, love and hope are emotions, and charity is an action (so yes, I can see charity). But fine, whatever.
> your mind has as an axiom of materialism
No, it's not an axiom. It's just that materialism suffices to explain everything I observe.
> you are locked into these kinds of explanations, even when evidence and paradoxes challenge it
What evidence and paradoxes? The only thing I've seen from you is word-play about the mass of non-existent objects and fuzzily defined phrases like "abstract object".
> If everyone stopped thinking about the Pythagorean Theorem, and all books and writings around it were destroyed, would the Pythagorean Theorem cease to exist?
Yes.
> That's property dualism.
OK, if you want to take the fact that I divide states into two categories and attach different labels to them and call that "property dualism" that's fine. But then "property dualism" is not something that my theory "suffers from", it's just a label that you've chosen to attach to it. Attaching a label to something in and of itself says nothing about the merits of the thing you are labeling.
What you call "mental properties" *are* physical properties. It is nonetheless possible to distinguish them, and it is sometimes a distinction worth making. But it's it's only "dualism" to the same extent that distinguishing between, say, academic skills and athletic skills is dualism.
> Then apply your scientific method first to define "progress."
Why? I'm not making a scientific claim here, just stating my opinion.
> At this moment, there are more people enslaved that there were in 100 years of the African slave trade.
Both slavery and xenophobia were once much more prevalent than they are today. Slavery was once practiced openly, legally. Nowadays the slave trade has been driven underground. While far from ideal, I still think that's better than having legal chattel slavery out in the open.
> Xenophobia has hardly decreased, as reflection of the events of the past few years will demonstrate.
I'll have to concede that one, though I can't help but observe that the overwhelming majority of the people at the vanguard of this new wave of xenophobia self-identify as Christians and are not exactly enthusiastic advocates of science.
> If we had wars and economic downturns before and after the Enlightenment, where is the progress?
Here.
Segmentation Fault
ReplyDelete> My theory is not contingent on my being able to actually "produce the objective reality" (whatever that means).
It's right there in your theory!
Ron's Theory of Truth: Truth is a property of propositions, which are ideas that stand in relation to some circumstance in objective reality (whose existence we have assumed for the sake of argument). If the circumstance corresponding to that proposition actually pertains, then the proposition is true, otherwise it is false.
>If there are no unicorns, then "there are no unicorns" is true, and if there are unicorns, then it is false.
The proposition is "There are no unicorns."
What is the circumstance in objective reality you compare it to?
Think of it this way -- you have a null pointer error. Consider this short C code:
// Ron's Theory of Truth in C
#include
#include
int main() {
char *str1 = "There are no unicorns.";
char *str2 = '\0';
// Attempting to compare str1 with str2 (NULL)
if (strcmp(str1, str2) == 0) {
printf("The proposition is TRUE\n");
} else {
printf("The proposition is FALSE\n");
}
return 0;
}
>No, it's not an axiom. It's just that materialism suffices to explain everything I observe.
No, you explain everything you observe by applying the axiom of materialism.
>fuzzily defined phrases like "abstract object".
It's hardly a criticism to call a concept "fuzzily defined," given that everything is fuzzily defined. Try to define "chair."
Try living without abstract objects for a week.
>OK, if you want to take the fact that I divide states into two categories and attach different labels to them and call that "property dualism" that's fine. But then "property dualism" is not something that my theory "suffers from", it's just a label that you've chosen to attach to it. Attaching a label to something in and of itself says nothing about the merits of the thing you are labeling.
The fact that acts of categorization are interest-relative does not entail that categories themselves have no objective validity. Being pet lovers with a penchant for zoology, we count dogs and cats as belonging to different categories, even though we can imagine a society whose inhabitants are uninterested in pets or scientific classification in which these animals were not so classified, but lumped together into one amorphous category of animals –- "cogs," say. But this does not entail that there is no objective difference between dogs and cats, or that this classification is no more reflective of objective reality than would be an obviously artificial classification of all physical objects into those that are inside my office and those that are outside of it. Some classifications, however interest-relative our reasons for making them, clearly reflect objective features of reality.
What you call "mental properties" *are* physical properties. It is nonetheless possible to distinguish them, and it is sometimes a distinction worth making.
That's exactly what a property dualist believes.
Confirmation Bias
ReplyDelete>> Then apply your scientific method first to define "progress."
>Why? I'm not making a scientific claim here, just stating my opinion.
Are you saying your scientific method is impotent to determine the truth or falsity of the proposition, "There been human progress since the Enlightenment"?
>> At this moment, there are more people enslaved that there were in 100 years of the African slave trade.
>Both slavery and xenophobia were once much more prevalent than they are today.
Are you paying attention? Your response to my statement "At this moment, there are more people enslaved that there were in 100 years of the African slave trade."
So, no, those things were not more prevalent in the past -- they are more prevalent now.
>Slavery was once practiced openly, legally. Nowadays the slave trade has been driven underground. While far from ideal, I still think that's better than having legal chattel slavery out in the open.
So progress is that while there are more slaves today, you feel better about it. How many slaves work for you?
>Here.
An excellent example of how strong the myth of progress has taken hold of humanist atheists, how science and enlightenment ideals must drive progress in society, towards a perfected human and a Utopian society. So Pinker cherry picks his data and chooses statistical metrics which back his belief -- it just has to be true, so he would find nothing but confirmation.
> The proposition is "There are no unicorns."
ReplyDelete> What is the circumstance in objective reality you compare it to?
The absence of unicorns. Obviously. You are trying to make this much more complicated than it actually is.
> No, you explain everything you observe by applying the axiom of materialism.
It's not an axiom. It's a hypothesis, and it is falsifiable. It just hasn't been falsified.
If you have evidence that falsifies materialism, by all means share it. Otherwise STFU.
> Try to define "chair."
Ah, chairs. What is it with you Christian apologists and chairs?
The reason you need to define "abstract object" and I don't need to define "chair" is that you used "abstract object" as part of an argument:
"Practicing mathematicians are acting as platonists, but if you bug them about the nature of mathematics, this is "game theory" is what they will gesture towards. They desire to get rid of abstract objects and infinities. Yet it fails because mathematics can be used to analyze mathematics itself, and the abstract objects and infinities come back in this second level analysis."
I haven't used "chair" as part of any argument. As soon as I do, you can insist that I define it. Not before.
> Try living without abstract objects for a week.
As soon as you tell me what distinguishes an "abstract object" from an "idea" I will give it a shot.
> The fact that acts of categorization are interest-relative does not entail that categories themselves have no objective validity.
Sure, but not all categorizations have utility.
You need to re-read this.
> That's exactly what a property dualist believes.
OK, if you say so.
> Are you saying your scientific method is impotent to determine the truth or falsity of the proposition, "There been human progress since the Enlightenment"?
Of course not. But our dispute is not over any objective fact, it's over the meaning of the word "progress", and ultimately over our own personal quality metrics. Science cannot resolve disputes over what different people consider desirable.
> Are you paying attention?
Yes. Are you?
> there are more slaves today
Because there are more *people* today. As a percentage of the population there are fewer slaves today, and vastly fewer *legal* slaves. If you are a black person in the U.S. your odds of being a legal slave have dropped from about 90% in 1960 to 0% today. I call that progress, notwithstanding that there is still a lot of work to be done world-wide.
> about 90% in 1960
DeleteObviously that should have been 1860, not 1960.
Abstract Ideas
ReplyDelete>> What is the circumstance in objective reality you compare it to?
@Ron:
>The absence of unicorns.
How can you compare existence to non-existence? If unicorns don't exist, then they're not in objective reality, and your theory of truth is incomplete.
>If you have evidence that falsifies materialism, by all means share it. Otherwise STFU.
You would reject any evidence that falsifies it. Ronald Reagan could be raised from the dead, knock on your front door, then talk to your for 4 hours, the leave, then a voice could boom in your house, "I am the Lord thy God, I made this happen, now believe!" and you would check yourself into a hospital because you would think you've gone mad.
>Ah, chairs. What is it with you Christian apologists and chairs?
It has nothing to do with Christian apologists. It's an old philosophical example that any definition either over determines the object, or under determines the object.
>The reason you need to define "abstract object" and I don't need to define "chair" is that you used "abstract object" as part of an argument:
Well, no, I challenged you to define a "chair" because you said "abstract object" is "fuzzily defined."
I then said: "It's hardly a criticism to call a concept "fuzzily defined," given that everything is fuzzily defined. Try to define "chair.""
>> Try living without abstract objects for a week.
>As soon as you tell me what distinguishes an "abstract object" from an "idea" I will give it a shot.
Abstract objects are non-physical and non-mental entities that exist independently of our thoughts and perceptions. They are often considered timeless, changeless, and not located in space. Ideas are mental constructs or representations that exist within human minds. They are the products of thinking, imagination, memory, or perception. Abstract objects are often seen as the objective counterparts of ideas, which are subjective and mind-dependent.
>You need to re-read this.
You'd have to pay me to re-read that.
>Because there are more *people* today. As a percentage of the population there are fewer slaves today, and vastly fewer *legal* slaves. If you are a black person in the U.S. your odds of being a legal slave have dropped from about 90% in 1860 to 0% today. I call that progress, notwithstanding that there is still a lot of work to be done world-wide.
Ah, you found your metric to justify the myth of progress -- slavery per capita. If progress is lowering slavery per capita, then we could have avoided the Civil War by just having more babies. Grow the population to get that slavery per capita number down.
Yet the Atlantic slave trade, which you consider an existential evil, involved the forced transport of 12 to 15 million Africans to the Americas over a period of 300 years. Today, right now, there are 50 million enslaved people. That's greater than the population of Canada. Yet you claim that as progress, as none of those slaves are living around you.
The most damaging thing about the myth of progress is that people assume it is true.
FYI
ReplyDeleteReaders interested in the Liar Paradox might find this blog post of interest:
This post is lying to you.
ReplyDelete> How can you compare existence to non-existence? If unicorns don't exist, then they're not in objective reality, and your theory of truth is incomplete.
That is literally nonsense. One does not "compare existence to non-existence", one ascertains whether or not a thing exists. Actually, one ascertains whether the existence of a thing explains observations or not. Objective reality itself is a thing that explains many (but not all) observations. The actual existence of objective reality is very much debatable, as you will see when I finally get around to talking about quantum mechanics.
> You would reject any evidence that falsifies it.
That is manifestly untrue.
> I challenged you to define a "chair" because you said "abstract object" is "fuzzily defined."
> I then said: "It's hardly a criticism to call a concept "fuzzily defined," given that everything is fuzzily defined. Try to define "chair.""
Your ability to produce examples of fuzzily defined things does not show that everything is fuzzily defined. Also, fuzziness is a continuum, not a dichotomy.
> Abstract objects are non-physical and non-mental entities that exist independently of our thoughts and perceptions.
Ah, now we are getting somewhere. I deny the existence of abstract objects as you have defined them. Can you demonstrate that I'm wrong?
> Ah, you found your metric to justify the myth of progress -- slavery per capita. If progress is lowering slavery per capita, then we could have avoided the Civil War by just having more babies. Grow the population to get that slavery per capita number down.
It's not just the raw numbers, it's humanity's attitude towards slavery that has fundamentally changed. In 1860 there were a lot of people (almost exclusively Christians BTW) who openly advocated for slavery. Here's a quote from the Declaration of Causes of the Seceding States:
"...all white men are and of right ought to be entitled to equal civil and political rights [emphasis in the original]; that the servitude of the African race, as existing in these States, is mutually beneficial to both bond and free, and is abundantly authorized and justified by the experience of mankind, and the revealed will of the Almighty Creator, as recognized by all Christian nations..."
People literally fought and died for that idea. I think you'd have a hard time finding even a single person willing to openly support it today. IMHO, that's progress.
(BTW, you can play the numbers game in the opposite direction too and observe that you can eliminate all sin by eliminating all people. You don't even have to kill them, just sterilize everyone. In 100 years you would have no slaves. But that's obviously not the right answer.)
Abstract objects: can't live without 'em
ReplyDelete>Your ability to produce examples of fuzzily defined things does not show that everything is fuzzily defined. Also, fuzziness is a continuum, not a dichotomy.
Sure, but it demonstrates your criticism of abstract objects as being "fuzzily defined" isn't a good one.
>Ah, now we are getting somewhere. I deny the existence of abstract objects as you have defined them. Can you demonstrate that I'm wrong?
You first have to tell me your Theory of the World, or your theory of discourse. For example, a platonist theory of the world believes universals exist.
You appear to be a conceptualist about abstract objects, that they are just concepts in the mind.
As a conceptualist, several aspects of abstract objects will challenge you:
If abstract objects are merely ideas in individual minds, how do different people share the same abstract concept? For example, if the number "2" is just an idea, how is it that different people across time and space can refer to and understand the exact same concept of "2"? How can abstract objects have a consistent, shared existence across different minds if they are purely mental constructs?
Conceptualism implies that abstract objects, being mere ideas, are subjective and dependent on human minds. However, many abstract objects seem to possess objectivity and necessity (e.g., "2 + 2 = 4"), which suggests they exist independently of any particular mind.
Conceptualism asserts that abstract objects like numbers or mathematical truths are ideas in human minds. However, mathematical truths seem to hold universally, even in a hypothetical universe without any conscious beings.
For a conceptualist, logical laws, like the law of non-contradiction, are dependent on human minds. But logical consistency is required for any rational thought, including the thought that conceptualism might be true. If logical laws are mere ideas, then they are not necessarily true in all cases, which undermines the very basis of rational thought, including the argument for conceptualism.
If abstract objects depend on minds for their existence, how were minds created? Minds depend on abstract concepts like logic and identity to function, so those concepts must exist prior to or independently of minds. How can abstract objects be both dependent and prior to minds?
Proslavery Thought Today
ReplyDelete@Ron:
> In 1860 there were a lot of people (almost exclusively Christians BTW) who openly advocated for slavery.
What's the point of "almost exclusively Christians BTW"? Why put that in?
Abolitionists were also almost exclusively Christians. So why mention Christians at all?
>it's humanity's attitude towards slavery that has fundamentally changed.
> I think you'd have a hard time finding even a single person willing to openly support it today.
It's not very hard at all to find people who are proslavery today, nor to find laws that codify slavery on the books today.
Both Boko Haram and ISIS openly justify slavery. ISIS has even used online auctions to sell them to Saudi Arabian buyers.
The 13th Amendment to the US Constitution codifies slavery as legal punishment for convicted criminals. California's Constitution, Article 1, Section 6 allows slavery as a criminal punishment. The very state you live in allows slavery [the people of California have an opportunity to end it this November by voting for Assembly Constitutional Amendment 8]. You pay taxes to support a State government that allows slavery.
Neither the Constitution of Canada nor the Canadian Charter of Rights and Freedoms explicitly mentions or directly outlaws slavery.
Slavery is not a crime in almost half of the countries in the world.
> IMHO, that's progress.
That's change, it's not progress.
ReplyDelete> your criticism of abstract objects as being "fuzzily defined" isn't a good one
Perhaps I should have said, "so fuzzily defined as to render the term devoid of all possible meaning." But you've addressed that by providing a better definition, so that is now moot.
> You first have to tell me your Theory of the World, or your theory of discourse.
You must really not have been paying attention at all.
> You appear to be a conceptualist about abstract objects, that they are just concepts in the mind.
Yes, I'll accept that.
> As a conceptualist, several aspects of abstract objects will challenge you:
Great! Bring it on!
> If abstract objects are merely ideas in individual minds, how do different people share the same abstract concept? For example, if the number "2" is just an idea, how is it that different people across time and space can refer to and understand the exact same concept of "2"? How can abstract objects have a consistent, shared existence across different minds if they are purely mental constructs?
That is an excellent question, and it doesn't have a simple answer. To do it justice I'd need several full posts. But let me start by pointing out that we cannot be 100% certain that people do share the same abstract concepts. All we know is that the hypothesis that they do has a lot of predictive power.
The best I can do to distill the answer down to something that will fit in a comment is to say that the reason this is so is that it has survival value: genes that make brains that act as if they share the same abstract concepts, that can communicate effectively using words like, "Look out, there are two sabre tooth tigers behind you!" have better reproductive fitness than genes that don't make brains with that property.
> Conceptualism implies that abstract objects, being mere ideas, are subjective and dependent on human minds. However, many abstract objects seem to possess objectivity and necessity (e.g., "2 + 2 = 4"), which suggests they exist independently of any particular mind.
Not all ideas are subjective. "2+2=4" for example can be modeled by physical systems that are not human minds. In fact, it was the human mind's attempts to deal with such systems that led to the invention of concepts like "two" and "plus" and "four" in the first place.
> Conceptualism asserts that abstract objects like numbers or mathematical truths are ideas in human minds. However, mathematical truths seem to hold universally, even in a hypothetical universe without any conscious beings.
How could you possibly know that?
> For a conceptualist, logical laws, like the law of non-contradiction, are dependent on human minds.
No, but again this would require a full blog post. (In fact, that one is already on my agenda.) But I'll point you towards the answer with a Socratic answer to your next point:
> But logical consistency is required for any rational thought
why?
> If abstract objects depend on minds for their existence, how were minds created? Minds depend on abstract concepts like logic and identity to function, so those concepts must exist prior to or independently of minds. How can abstract objects be both dependent and prior to minds?
Minds are not a thing, they are an activity, a process, like "sunrise" or "eclipse" or "election". Minds are a thing that brains do. Again, it's a product of evolution: genes that build brains that are capable of hosting minds have better reproductive fitness relative to those that don't.
ReplyDelete> What's the point of "almost exclusively Christians BTW"? Why put that in?
Because I happen to know that you're a Christian apologist, and slavery is a touchy subject. But you're right, I probably shouldn't have brought it up. It just middies the waters. My apologies.
> It's not very hard at all to find people who are proslavery today, nor to find laws that codify slavery on the books today.
> Both Boko Haram and ISIS openly justify slavery. ISIS has even used online auctions to sell them to Saudi Arabian buyers.
OK, maybe my view is colored by the fact that I live in the U.S. That is definitely not progress. But my guess is that neither Boko Haram nor ISIS have the volume that antebellum slave traders had, so there's that.
> The 13th Amendment to the US Constitution codifies slavery as legal punishment for convicted criminals.
That's true. That there is a lot of work yet to be done does not change my view that (much of) the work that has been done is progress.
BTW:
> Ah, you found your metric to justify the myth of progress -- slavery per capita.
Not that I'm accepting that assessment of my position, but do you have a better idea? Finding the right quality metric is really hard, and I'm open to suggestions.
Teleology
ReplyDelete@Ron:
>Not that I'm accepting that assessment of my position, but do you have a better idea? Finding the right quality metric is really hard, and I'm open to suggestions.
You need to first ask: why would you expect progress?
Choose
ReplyDelete@Ron:
>You must really not have been paying attention at all.
You need to decide if your worldview is materialism, physicalism, scientism, psychologism, and conceptualism:
Materialism
Definition: Materialism is the view that the only thing that exists is matter; everything in the universe is made up of physical substance. Mental states, consciousness, and other phenomena are ultimately reducible to material or physical processes.
Key Ideas: Materialists believe that everything, including thoughts, emotions, and consciousness, can be explained in terms of material interactions. There is no immaterial substance, such as a soul or spirit.
Physicalism
Definition: Physicalism is a more modern form of materialism, stating that everything that exists is either physical or supervenes on the physical. This includes phenomena that may not seem physical but are nonetheless dependent on physical processes (e.g., mental states).
Key Ideas: Physicalism allows for the existence of things like consciousness but maintains that these are fully grounded in physical processes (e.g., brain activity). It broadens materialism to include not just matter but also energy, fields, forces, and space-time.
Scientism
Definition: Scientism is the view that the empirical sciences are the most authoritative or the only legitimate way to gain knowledge about reality. It asserts that science, and only science, can provide true knowledge about the world.
Key Ideas: Proponents of scientism may dismiss or downplay other forms of knowledge (e.g., philosophy, religion) as either secondary or irrelevant to understanding reality.
Psychologism
Definition: Psychologism is the philosophical position that psychological processes, such as perception, thinking, and emotion, are the basis for explaining all other phenomena, including logic, mathematics, and ethics.
Key Ideas: Psychologism reduces phenomena like logic and knowledge to psychological states or processes, claiming that these fields can be understood by studying the human mind and its operations.
Conceptualism
Definition: Conceptualism is the view that universals (general concepts or properties) exist, but only within the mind as mental concepts. It is a middle ground between realism (which asserts that universals exist independently of the mind) and nominalism (which denies the existence of universals).
Key Ideas: In conceptualism, while universals don't exist outside the mind in a physical or metaphysical sense, they still have real existence in the cognitive realm. Concepts are not arbitrary but are grounded in our experiences of the world.
Evolution is not directed
ReplyDelete>> If abstract objects are merely ideas in individual minds, how do different people share the same abstract concept?
>That is an excellent question, and it doesn't have a simple answer. To do it justice I'd need several full posts. But let me start by pointing out that we cannot be 100% certain that people do share the same abstract concepts.
That's a problem for you, as abstract objects are objective, universal, and independent of individual psychology.
>The best I can do to distill the answer down to something that will fit in a comment is to say that the reason this is so is that it has survival value: genes that make brains that act as if they share the same abstract concepts, that can communicate effectively using words like, "Look out, there are two sabre tooth tigers behind you!" have better reproductive fitness than genes that don't make brains with that property.
Evolution, by its nature, explains the development of physical organisms and cognitive capacities through natural selection. However, abstract objects are not physical entities and are not subject to evolutionary forces. The number "2" or the truth "2 + 2 = 4" exists independently of whether humans have evolved to recognize them. Evolution might explain why we developed the capacity to to understand abstract objects, but it does not explain the existence of the objects themselves.
In addition, evolutionary processes are primarily concerned with survival and reproductive success, not with producing creatures that have access to objective truths about abstract entities. Evolution favors cognitive faculties that enhance an organism's ability to navigate its environment successfully, not necessarily ones that lead to accurate beliefs about non-empirical truths like those found in mathematics or logic. If the concept of abstract objects evolved purely through evolutionary pressures, how would you explain why our understanding of these objects is so precise and reliable, especially since the knowledge of abstract objects (e.g., advance mathematics or logic) often seems irrelevant to survival? Evolution might lead to useful heuristics, but it is unlikely to lead to the discovery of necessary, universal truths about abstract objects.
>Not all ideas are subjective. "2+2=4" for example can be modeled by physical systems that are not human minds. In fact, it was the human mind's attempts to deal with such systems that led to the invention of concepts like "two" and "plus" and "four" in the first place.
Numbers aren't based on physical systems, they're based on the abstract concept of sets.
0 = ∅
1 = {∅}
2 = {∅,{∅}}
3 = {∅,{∅},{∅,{∅}}}
.
.
.
>> Conceptualism asserts that abstract objects like numbers or mathematical truths are ideas in human minds. However, mathematical truths seem to hold universally, even in a hypothetical universe without any conscious beings.
>How could you possibly know that?
Our knowledge about abstract objects is superior to concrete objects. A block, a stone, or an apple on a desk are extremely complex, deeply mysterious, and we don't have a very good account of it. We're familiar with it, but we don't really understand it. Yet we can give extremely accurate and precise accounts about the nature of the empty set, or a point, or a line. Abstract existence is what we really understand.
>> But logical consistency is required for any rational thought
>why?
Are you asking why the laws of logic are needed to perform rational thought?
>Minds are not a thing, they are an activity, a process, like "sunrise" or "eclipse" or "election".
Yeah, whatever. If the mind process depends on abstract concepts like logic and identity to function, those concepts must exist prior and independently of minds. How can abstract objects be both dependent and prior to minds?
> > we cannot be 100% certain that people do share the same abstract concepts.
ReplyDelete> That's a problem for you
Why? The hypothesis that the ideas in people's heads correspond to each other somehow has tremendous explanatory and predictive power. In fact, the recognition that people might not share the same abstract concepts is itself tremendously powerful. It allows you to recognize misunderstandings, which can be a very useful skill.
> abstract objects are not physical entities and are not subject to evolutionary forces
Sez you. I still claim that "abstract objects" as you have defined them do not exist.
> The number "2" or the truth "2 + 2 = 4" exists independently of whether humans have evolved to recognize them.
Again, sez you. I say that the "truth" of 2+2=4 is contingent on a huge number of tacit assumptions, all of which boil down to empirical observations about certain kinds of physical objects. There are physical situations where 2+2=4 is false (adding velocities, for example).
> In addition, evolutionary processes are primarily concerned with survival and reproductive success, not with producing creatures that have access to objective truths about abstract entities.
Yes, that's true, and the fact that evolution produced brains that can do abstract thinking is an observation that demands explanation. And the explanation is: general computation at its core is actually not that complicated. When you start to put together random things at a certain level of complexity you can hardly avoid building a Turing machine.
> Numbers aren't based on physical systems
The computer I'm reading this on looks pretty physical to me. The funny-looking symbols you've caused it to draw like = and ∅ and { and } look pretty physical to me. How could I see them otherwise?
> Our knowledge about abstract objects is superior to concrete objects.
Maybe yours is. I am not yet persuaded that your "abstract objects" even exist. All the evidence I see is consistent with the hypothesis that your idea of "abstract objects" is a delusion, no different from those who claim to have been abducted by Aliens or seen the Virgin Mary.
> Are you asking why the laws of logic are needed to perform rational thought?
No, read more carefully: I am asking why *logical consistency* is required for rational thought. (BTW, I am asking this Socratically. I already know the answer. But I don't think you do.)
> > Minds are not a thing, they are an activity, a process, like "sunrise" or "eclipse" or "election".
> Yeah, whatever.
If you're going to just casually dismiss my answers without even trying to seriously engage with them, I'm going to stop responding. It takes quite a bit of time and effort to respond to your comments.
> You need to decide if your worldview is materialism, physicalism, scientism, psychologism, and conceptualism:
No, I don't. I am not required to shoehorn my worldview into categories that you have invented.
> why would you expect progress?
I don't. I *observe* it. I also observe (evidence for) historical periods lasting centuries with little progress, so the fact that progress happens at all is actually quite surprising.
Courtesy
ReplyDelete@Ron:
>Why? The hypothesis that the ideas in people's heads . . ..
You're entirely ducking the epistemological question of how abstract objects could be objective and universal while being contingent on minds. That your "hypothesis" might be useful, or instrumental, has no bearing on the truth of your hypothesis.
>And the explanation is: general computation at its core is actually not that complicated. When you start to put together random things at a certain level of complexity you can hardly avoid building a Turing machine.
Computation is not intrinsic to the physics of system, but assigned to it by an observer.
>> Yeah, whatever.
>If you're going to just casually dismiss my answers without even trying to seriously engage with them, I'm going to stop responding. It takes quite a bit of time and effort to respond to your comments.
Sorry, but I get tired of your little gambits to avoid answering hard questions. Yet you're wrong that I didn't seriously engage with your comment -- in fact, I reformulated my question in terms of your "mind as a process" response:
>>If the mind process depends on abstract concepts like logic and identity to function, those concepts must exist prior and independently of minds. How can abstract objects be both dependent and prior to minds?
... and you ducked the question for a 2nd time. Am I to conclude you cannot answer it?
Furthermore, you might extend the same courtesy to me that you are requesting from me. How is "Yeah, whatever" substantially different from "Sez you"?
>Again, sez you. I say that the "truth" of 2+2=4 is contingent on a huge number of tacit assumptions, all of which boil down to empirical observations about certain kinds of physical objects.
Wrong. Pure mathematics is based on a small set of axioms, then built up with theorems and proofs. Mathematical objects are all abstract and have no necessary mapping to physical objects.
>No, read more carefully: I am asking why *logical consistency* is required for rational thought. (BTW, I am asking this Socratically. I already know the answer. But I don't think you do.)
It has nothing to do with me not reading carefully enough, that was about me trying to clarify your question.
I also cannot answer the question unless I know your world view.
>No, I don't. I am not required to shoehorn my worldview into categories that you have invented.
I thought you'd say that. This just reveals you haven't given serious thought to the question. As it is, your answers are consistent with conceptualism. Leave it you to reinvent the worst one.
>> why would you expect progress?
>I don't. I *observe* it.
You observe change and confuse it with progress.
Debate note: I will be travelling on and off this week, then solidly for the next two weeks after that, so replies will likely be delayed.
> You're entirely ducking the epistemological question of how abstract objects could be...
ReplyDeleteNo, I'm not. I am, for the nth time (please pay attention) *denying the existence of abstract objects* as you have defined them. There is nothing more to be said about about them.
> Computation is not intrinsic to the physics of system, but assigned to it by an observer.
Um, no. That is just ridiculous. You're confusing the theory of computation with quantum measurements or some such category error.
> How is "Yeah, whatever" substantially different from "Sez you"?
Because "sez you" is just a colloquial way of saying that your claim is unsupported by any evidence, which is a legitimate response when you advance claims unsupported by evidence. "Sez you" is just easier to type and sounds a little less highfallutin'. (It's also, frankly, an expression of my frustration with you that you keep advancing the *same* unsupported claims over and over.) But "Yeah, whatever" is just an outright dismissal, essentially saying that what I said was so wholly without merit that it doesn't deserve *any* kind of response at all, and closing the door on any possible response. "Sez you" is snarky, but it is also an invitation to respond with actual supporting evidence, e.g. "No, it's not just me, it's also..."
But in this case there is an over-arching consideration which renders this whole point moot:
> > Again, sez you. I say that the "truth" of 2+2=4 is contingent on a huge number of tacit assumptions, all of which boil down to empirical observations about certain kinds of physical objects.
> Wrong. Pure mathematics is based on a small set of axioms, then built up with theorems and proofs. Mathematical objects are all abstract and have no necessary mapping to physical objects.
I don't see how it could have escaped your notice, but this series of posts is not about pure mathematics, it's about the scientific method. Once again you have not been paying attention. I've reiterated that at the beginning of every single post in this series.
> I also cannot answer the question unless I know your world view.
Well, that is what this entire series of blog posts is about. But you pretty clearly don't want to actually understand my world view, you just want to attach a label to it. Well, sorry, no. Languages are theories, and I don't accept yours. My world view is much more nuanced than your labels.
But why do you need to know *my* world view to answer the question? Just answer it according to *your* world view. Surely you're sufficiently clear about *that*?
> You observe change and confuse it with progress.
I observe change and I adjudicate (some of) it as progress according to my personal quality metric.
> I will be travelling
Happy trails.
Scaffolding
ReplyDelete@Ron:
>No, I'm not. I am, for the nth time (please pay attention) *denying the existence of abstract objects* as you have defined them. There is nothing more to be said about about them.
You need to re-read this. The question is not if abstract objects exist, it's what ontological category they are in. You claim they are in the categories of "ideas". I have presented several objections to that categorization, which apparently you have no good response to.
For example:
>>>If the mind process depends on abstract concepts like logic and identity to function, those concepts must exist prior and independently of minds. How can abstract objects be both dependent and prior to minds?
>Um, no. That is just ridiculous. You're confusing the theory of computation with quantum measurements or some such category error.
1. Computation involves symbol manipulation according to syntactical rules.
2. But syntax and symbols are not definable in terms of the physics of a system.
3. So computation is not intrinsic to the physics of a system, but assigned to it by an observer.
Q.E.D.
>I don't see how it could have escaped your notice, but this series of posts is not about pure mathematics, it's about the scientific method.
Yet when you make statements like
> I say that the "truth" of 2+2=4 is contingent on a huge number of tacit assumptions, all of which boil down to empirical observations about certain kinds of physical objects.
That is about mathematics. Hence you might expect the discussion of thise statement to involve the nature of mathematics. Now, if you want me to wait for your post on "Mathematics is just physics" or whatever, fine.
>Well, that is what this entire series of blog posts is about. But you pretty clearly don't want to actually understand my world view, you just want to attach a label to it.
Well, in the first comment I stated, "I was expecting this to be an essay of what you believe, not a survey of options."
To which you replied:
Why would you expect that? The *whole point* of this series is that what I believe is irrelevant
Furthermore, learning can be described as a process of "scaffolding". Prior knowledge acts as a foundation, and one links new information to what they already know. If one can see the connection between new material and what one already knows, a "scaffold" is built up to bridge the gap between the familiar and the unfamiliar.
So don't be surprised if I try to link what you're writing to an existing body of knowledge, as it helps me to understand your writing.
Finally, you're somewhere in the middle of writing out your world view. I can't know it if you haven't completed it.
My world view is much more nuanced than your labels.
Do you really think you've developed anything that hasn't been done before? Time will tell.
>But why do you need to know *my* world view to answer the question? Just answer it according to *your* world view.
Because you've made it a game, and I want to win, as your approval is important to me. To win the game, I need to know the rules.
>I observe change and I adjudicate (some of) it as progress according to my personal quality metric.
So far your metrics (e.g., slavery) haven't demonstrated progress. But enjoy your smart phone.
> The question is not if abstract objects exist, it's what ontological category they are in. You claim they are in the categories of "ideas".
ReplyDeleteThat's right. But you have denied this. So the situation we are in is analogous to one where you are insisting that ghosts are real (and not just hallucinations or delusions), but you refuse to tell me what they are made of. You are advancing a hypothesis, but you are being cagey about the details. That alone is sufficient grounds to reject it, much like if you'd claimed to invent a perpetual motion machine but refused to describe how it worked.
> I have presented several objections to that categorization, which apparently you have no good response to.
We'll have to agree to disagree about whether my responses have been good or not.
> 2. But syntax and symbols are not definable in terms of the physics of a system.
Why not?
> Q.E.D.
Not until you explain why "syntax and symbols are not definable in terms of the physics of a system". Unless you want to argue that computers have some kind of dualistic quality, a literal ghost in the machine, then your claim is manifestly untrue.
> Yet when you make statements like
> > I say that the "truth" of 2+2=4 is contingent on a huge number of tacit assumptions, all of which boil down to empirical observations about certain kinds of physical objects.
> That is about mathematics. Hence you might expect the discussion of thise statement to involve the nature of mathematics.
Yes, of course. That is the reason I wrote an entire blog post about it. You've even commented on it so I know you've seen it.
> The *whole point* of this series is that what I believe is irrelevant
I left out an important qualifier: what I believe is irrelevant *to the question of what is actually true*, i.e. what the underlying nature of reality actually is (or indeed if there even is such a thing as "the underlying nature of reality"). The truth is what it is independent of my (or anyone else's) beliefs. So my beliefs are irrelevant to the question of why (or even if) contradictions are fatal to rational thought. I believe I know the answer, but I might be wrong.
But obviously what I believe is not irrelevant in any absolute sense. It's relevant *to me*, and to those who care about me, and to anyone who believes that I'm a trustworthy and reliable source of information. But I don't believe that you fall into that category. I believe that you believe that my thinking is fundamentally flawed at the deepest levels, and your goal is to somehow persuade me of this. All of your behavior is consistent with this hypothesis.
> So don't be surprised if I try to link what you're writing to an existing body of knowledge, as it helps me to understand your writing.
That's fair, but you have to link it to the right body of knowledge. Not all bodies of knowledge are created equal. So called "philosophical knowledge" in particular needs to be approached with extreme skepticism because a lot of it is the product of ignorance.
> Finally, you're somewhere in the middle of writing out your world view. I can't know it if you haven't completed it.
I'm barely getting started. When I'm done, I'll let you know. (Don't hold your breath.)
> Do you really think you've developed anything that hasn't been done before? Time will tell.
No, at least not much. I think idea-ism might be original with me, and maybe the "zero-worlds" interpretation of quantum mechanics (which I really ought to have called the necker-cube interpretatin) but that's it. Everything else is due to Popper (by way of Deutsch), Darwin, Turing, Einstein, Newton, Bell, Aspect, Dawkins, Aaronson, and a few others.
> your approval is important to me
I don't believe you (see above), but giving you the benefit of the doubt: if you want my approval, you're definitely not going to earn it by turning a Socratic question into a zero-sum game.
Imagine
ReplyDelete@Ron:
> You are advancing a hypothesis, but you are being cagey about the details.
To the contrary, I am not advancing a hypothesis. I am simply arguing that your claim, that abstract objects are ideas, cannot be correct. How, for example, if the mind process depends on abstract concepts like logic and identity to function, those concepts must exist prior and independently of minds. How can abstract objects be both dependent and prior to minds?
>Not until you explain why "syntax and symbols are not definable in terms of the physics of a system".
Though symbol tokens are always physical tokens, "symbol" and "same symbol" (for example) are not defined in terms of physical features. The ascription of syntactical properties is always relative to an agent or observer to treats certain physical phenomena as syntactical.
Consider that we observe a person write down:
X Y
+ Z
======
Z X
The most probable consequence is that we will believe we have observed the person doing addition like 29 + 3 = 32 or 59 + 6 = 65 with the letters representing the respective digits. But these solutions only work in base 10 system we are used to, or in number systems of a higher base. If another observer, who is more accustomed to numbers in base 8, would probably arrive first at one of the interpretations 27 + 3 = 32 or 57 + 6 = 65.
Different observers can interpret one and the same process as different computations. So there is definitely not one computation intrinsic to each computational process. This indicates that computation is not an intrinsic property of physical objects or processes at all. Rather, it depends on the knowledge and imagination of the observer, whether he can discover computation in a given process.
>The truth is what it is independent of my (or anyone else's) beliefs.
Interesting.
> I am not advancing a hypothesis
ReplyDeleteYes, you are:
> the mind process depends on abstract concepts like logic and identity to function
That's a hypothesis.
> "symbol" and "same symbol" (for example) are not defined in terms of physical features. The ascription of syntactical properties is always relative to an agent or observer to treats certain physical phenomena as syntactical.
> Different observers can interpret one and the same process as different computations.
Yes, that's true. That is a legitimate capital-P Problem, and the idea that there are abstract concepts that exist independent of minds or other computational agents is a legitimate hypothesis that you are advancing as an explanation. It happens to be demonstrably wrong, but this is not immediately self-evident.
BTW, the fact that you are advancing a hypothesis is a good thing. It's what you are supposed to be doing. The fact that you don't realize that you're doing it is not so good, but we have to start somewhere. Notice too that here you have finally (albeit obliquely) provided a legitimate definition of "abstract concept": abstract concepts are the hypothetical, non-physical, non-mental entities that allow different agents to agree on the meanings of certain symbols.
If you want a sneak preview of the argument against your position, read this:
https://blog.rongarret.info/2015/03/why-some-assumptions-are-better-than.html
Note that the opening statement of that post, "All reasoning has to start from assumptions," is actually false, but I didn't realize it at the time. But the substance of the post still stands.
BTW:
ReplyDelete>> The truth is what it is independent of my (or anyone else's) beliefs.
> Interesting.
I don't see why. Truth is *by definition* that which corresponds with objective reality. Objective reality is what it is regardless of anyone's beliefs, again, by definition. So the truth being independent of belief is true by definition, which is not very interesting at all.
Semantic Meaning
ReplyDelete>> I am not advancing a hypothesis
@Ron:
>Yes, you are:
When I write, "I am not advancing a hypothesis," it means I am not advancing a hypothesis.
I am simply working to disprove your hypothesis that abstract objects are ideas in human minds.
>>That is about mathematics. Hence you might expect the discussion of these statement to involve the nature of mathematics.
>Yes, of course. That is the reason I wrote an entire blog post about it. You've even commented on it so I know you've seen it.
So then don't say in response, "I don't see how it could have escaped your notice, but this series of posts is not about pure mathematics, it's about the scientific method. Once again you have not been paying attention."
>> Different observers can interpret one and the same process as different computations.
>Yes, that's true. That is a legitimate capital-P Problem, and the idea that there are abstract concepts that exist independent of minds or other computational agents is a legitimate hypothesis that you are advancing as an explanation.
Recall that this little tangent on computation not being intrinsic to the physics of the system began with this exchange:
>> In addition, evolutionary processes are primarily concerned with survival and reproductive success, not with producing creatures that have access to objective truths about abstract entities.
>Yes, that's true, and the fact that evolution produced brains that can do abstract thinking is an observation that demands explanation. And the explanation is: general computation at its core is actually not that complicated. When you start to put together random things at a certain level of complexity you can hardly avoid building a Turing machine.
Hence you are without an explanation, as your naturalistic physics cannot produce a computation.
>If you want a sneak preview of the argument against your position, read this:
That's not going to help you.
The Interesting Part
ReplyDelete>>The truth is what it is independent of my (or anyone else's) beliefs.
> Interesting.
>I don't see why. Truth is *by definition* that which corresponds with objective reality. Objective reality is what it is regardless of anyone's beliefs, again, by definition. So the truth being independent of belief is true by definition, which is not very interesting at all.
Here's why it's interesting. "Facts" and "propositions" are abstract objects, and you've stated they're independent of anyone's beliefs, thereby placing them outside of human minds.
Which contradicts your Conceptualism or Psychologism world view (you won't clarify which, let's go with psychologism).
The problem you're having is that psychologism is impossible to formulate in a coherent way. It cannot possible be correct. Indeed, the very attempt to formulate it presupposes its falsity. When you say, for example, that there are no true propositions independent of this or that particular human mind or collection of human minds, that claim is put forward as if it were itself true independently of the mind of the speaker and of anyone else’s mind. When you say that what we take to be true, and the laws of logic, reflect nothing more than the way that natural selection, economic or cultural forces, or the like contingently molded the human mind, you appeal to claims (about how natural selection and the relevant economic and cultural forces work) that are put forward as if they were true before human minds ever came on the scene. In defending such claims, you appeal to standards of logical argumentation as if they had an objective status that made them normative for all listeners, including those you are trying to persuade to endorse psychologism. And so on.
Now, this is where you reply, given your commitment to naturalism, "Oops, facts and propositions are particles after all." Then you need to find a place to stuff them, so you choose the human brain, because who really understands that anyhow? Then you promise that neuroscientists will figure it out, likely after we're dead.
Blogger Notes
ReplyDeleteFYI, Blogger is looking different than it did in the past.
1. The page that comes up after choosing the "Post a comment" link is formatted in a large, sans serif font (it used to use the same font as the main blog page). The "box" to put in comments is not really a box anymore, just a line (and the "box" cannot be resized like in the past).
2. On the main blog page, with comments displayed -- the formatting gets corrupted about half way through. Namely, after my "The Myth of Progress" comment, all the comment text underneath that is bold format. It's like my Saint JohnPaul II The Great quote had an unclosed bold tag (yet blogger doesn't accept comments with unclosed tags). Now, after my "Scaffolding" comment, the formatting is stuck on bold italic, even the little headers above the comments (example, "Ron said ..." is not in bold italic).
I don't know if you can do anything about it, but I thought I would mention it. Blogger has been static for so long, I'm surprised it changed. I wouldn't expect Google to put in any additional effort into Blogger beyond announcing its cancellation.
Blogger Notes Errata
ReplyDelete>(example, "Ron said ..." is not in bold italic).
correction: example, "Ron said ..." is now in bold italic).
> Blogger is looking different than it did in the past.
ReplyDeleteYes, I know. I had nothing to do with this, it's something Google did. I am just as surprised (and dismayed) by this change as you are.
> I am simply working to disprove your hypothesis that abstract objects are ideas in human minds.
ReplyDeleteLanguages are theories. You introduced "abstract object" into this discussion, that makes it your theory.
> P: That is about mathematics. Hence you might expect the discussion of these statement to involve the nature of mathematics.
>
> R: Yes, of course. That is the reason I wrote an entire blog post about it. You've even commented on it so I know you've seen it.
>
> P: So then don't say in response, "I don't see how it could have escaped your notice, but this series of posts is not about pure mathematics, it's about the scientific method. Once again you have not been paying attention."
You have missed the point. Your definition of "mathematics" is different from mine. I am using "mathematics" to mean a *physical* process of manipulating symbols according to rules, which turns out to be useful for producing scientific models. You are using it to mean something else, something having to do (AFAICT) with "abstract objects", which you still have not defined.
You seem to think that mathematics is some kind of portal to an ethereal realm of "abstract ideas" or something like that. Maybe it is, the burden is on you to demonstrate the necessity of introducing this ethereal realm in order to explain observations, and to explain why it is not adequate to explain mathematics as computation and mathematical objects as ideas.
> your naturalistic physics cannot produce a computation.
Why not?
> That's not going to help you.
Why not?
> "Facts" and "propositions" are abstract objects, and you've stated they're independent of anyone's beliefs, thereby placing them outside of human minds.
Not exactly. I said that *truth* (as I have defined it) is (by definition) independent of anyone's beliefs.
The problem here is that you have redefined the words "fact" and "proposition" by saying that they are "abstract objects". That's not part of my definition of "fact" or "proposition". You cannot challenge *my* theory using *your* definitions. Languages are theories. If you want to criticize *my* theory you have to do it using *my* definitions because those are part and parcel of my theory. If you use *your* definitions you aren't criticizing *my* theory.
> Which contradicts your Conceptualism or Psychologism world view (you won't clarify which, let's go with psychologism).
Um, no, let's not. I don't subscribe to either conceptualism or psychologism. I keep telling you that my world view doesn't fit neatly into anything you will find in the literature. If it did, I'd just point to it and say "I believe that" rather than take the trouble to write all these blog posts.
Again, if you want to criticize my theory, you have to do it on the basis of what I actually say rather than on what you choose to read between the lines.
> The problem you're having is that psychologism is impossible to formulate in a coherent way.
Well, that would be my problem if I subscribed to psychologism. But I don't, so it isn't.
> Now, this is where you reply, given your commitment to naturalism, "Oops, facts and propositions are particles after all."
Um, no.
Languages are what?
ReplyDelete>href="https://blog.rongarret.info/2024/05/languages-are-theories-debunking-new.html">Languages are theories.
Did you notice I didn't comment on that blog post? Let me tell you why: I find it incomprehensible. I have no idea what point you're trying to make, nor why it's interesting, nor why I should care about it. Perhaps a rewrite is in order.
So I have no idea what you mean when you quote and re-quote yourself "languages are theories."
Now, if you mean by "languages are theories" that each language serves as a system that provides categories, descriptions, and rules for interpreting the world, then this is your theory about how the world works. You might call it a world view.
Yet you claim your world view is a work in progress, which is convenient, as you can just counter any argument against you by making up your world view as you go along.
> I have no idea what you mean when you quote and re-quote yourself "languages are theories."
DeleteSorry about that, I wish you had mentioned that earlier. I would have tried to clarify.
> this is your theory about how the world works
Part of it, yes. Except that this idea is not mine, it's Karl Popper's.
> your world view is a work in progress
Science is always a work in progress. That's a feature, not a bug.
> you can just counter any argument against you by making up your world view as you go along
Not really, no, because I am bound by the constraint that what I make up has to be consistent with all observed data. You seem to have forgotten that bit.
Formalism is hopeless
ReplyDelete>You introduced "abstract object" into this discussion, that makes it your theory.
Didn't you have an English class in high school or something where the concept of abstract objects was discussed? Abstract objects are used, referenced, and reasoned about by everyone. They're common knowledge.
>You have missed the point. Your definition of "mathematics" is different from mine. I am using "mathematics" to mean a *physical* process of manipulating symbols according to rules, which turns out to be useful for producing scientific models.
Your view is known as Formalism. It is hopelessly implausible. David Hilbert took a shot at redefining mathematics as formalism.
Hilbert did not take the natural numbers to be mental constructions. Instead, he argued that the natural numbers can be taken to be symbols. Symbols are strictly speaking abstract objects. Nonetheless, it is essential to symbols that they can be embodied by concrete objects, so we may call them quasi-concrete objects. Perhaps physical entities could play the role of the natural numbers. For instance, we may take a concrete ink trace of the form | to be the number 0, a concretely realized ink trace || to be the number 1, and so on. Hilbert thought it doubtful at best that higher mathematics could be directly interpreted in a similarly straightforward and perhaps even concrete manner. However, he thought that higher mathematics is no more than a formal game. The statements of higher-order mathematics are uninterpreted strings of symbols. Proving such statements is no more than a game in which symbols are manipulated according to fixed rules. The point of the ‘game of higher mathematics’ consists, in Hilbert’s view, in proving statements of elementary arithmetic, which do have a direct interpretation.
Hilbert and his students set out to prove the consistency of, e.g., the axioms of mathematical analysis in classical Peano arithmetic. This project was known as Hilbert’s program. It turned out to be more difficult than they had expected. In fact, they did not even succeed in proving the consistency of the axioms of Peano Arithmetic in Peano Arithmetic.
Then Kurt Gödel proved that there exist arithmetical statements that are undecidable in Peano Arithmetic. This is known as Gödel’s first incompleteness theorem. This did not bode well for Hilbert’s program, but it left open the possibility that the consistency of higher mathematics is not one of these undecidable statements. Unfortunately, Gödel then quickly realized that, unless Peano Arithmetic is inconsistent, the consistency of Peano Arithmetic is independent of Peano Arithmetic. This is Gödel’s second incompleteness theorem. Gödel’s incompleteness theorems turn out to be generally applicable to all sufficiently strong but consistent recursively axiomatizable theories. Together, they torpedoed Hilbert’s program. It turns out that higher mathematics cannot be interpreted in a purely instrumental way. Higher mathematics can prove arithmetical sentences, such as consistency statements, that are beyond the reach of Peano Arithmetic.
Later, titans of philosophy -- Wittgenstein, Carnap, Quine, Curry -- would tackle the problem and also fail. W. V. O. Quine, one of the greatest philosophers of the 20th Century, tried to reformulate the theories from natural sciences without making use of abstract entities -- and failed. From this, Quine developed his famous theory of ontological commitment.
Philosophers of mathematics think that formalism is a hopeless position, but hey, you be you.
> Abstract objects are ... common knowledge.
DeleteThat's what I thought too. I thought that "abstract object" was a synonym for "idea". But you have denied this. But you haven't told me what abstract objects *are*, only what they are not.
> Symbols are ... abstract objects.
But symbols are physical. I can *show* you a symbol. But earlier you denied that abstract objects are physical.
> Philosophers of mathematics think that formalism is a hopeless position
Perhaps, but actual mathematicians use proof assistants like Coq regularly nowadays. And their work product -- mathematical papers rendered as PDFs, -- consist entirely of symbols.
What you and the philosophers are missing is that formalism might be unable to unlock Platonic or metaphysical Truth, but it works a treat at producing scientific models.
Abstract is not exotic
ReplyDelete>You are using it to mean something else, something having to do (AFAICT) with "abstract objects", which you still have not defined.
Yeah, me and most everyone else. Mathematicians often study abstract objects as a fundamental part of their work. Abstract objects in mathematics are not physical or concrete entities but are conceptual entities that exist within mathematical thought. Some key examples of abstract objects that mathematicians study are numbers, geometric shapes and figures, sets (including infinite sets), functions, vectors and matrices, groups, rings, fields, topological spaces, logic, formal systems, and abstract graphs.
Now if you don't know what abstract objects are, I could begin a remedial lesson.
>You seem to think that mathematics is some kind of portal to an ethereal realm of "abstract ideas" or something like that.
I haven't made any positive claims about abstract objects. You're importing that from elsewhere.
I am simply endeavoring to demonstrate that your definition of mathematics cannot possibly be correct.
> I haven't made any positive claims about abstract objects.
DeleteYes, that is exactly the problem. You've told me what they are not: they are not physical and they are not ideas. But you haven't told me what they *are*. You've also said that symbols are abstract objects, thereby contradicting yourself when you said that abstract objects aren't physical. So you don't need a "remedial lesson", I just need you to tell me what you actually mean when you use the term.
Metaphorical Cranks
ReplyDelete>> your naturalistic physics cannot produce a computation.
>Why not?
Because computation is not intrinsic to the physics of the system, but assigned by an observer.
>> That's not going to help you.
>Why not?
Systems of material representations (words, pictures, or what have you) are, considered just by themselves, inherently indeterminate, inexact, or ambiguous in their content. Given their physical properties alone, there is no fact of the matter about exactly what meaning they convey.
>The problem here is that you have redefined the words "fact" and "proposition" by saying that they are "abstract objects". That's not part of my definition of "fact" or "proposition". You cannot challenge *my* theory using *your* definitions.
Your theory of truth is what is commonly known as the Correspondence Theory of Truth. Which uses facts and propositions, which are abstract objects. You are not special.
>If you want to criticize *my* theory you have to do it using *my* definitions because those are part and parcel of my theory. If you use *your* definitions you aren't criticizing *my* theory.
You're going to regret writing that.
>Um, no, let's not. I don't subscribe to either conceptualism or psychologism. I keep telling you that my world view doesn't fit neatly into anything you will find in the literature.
You are not special. You are simply replaying the mistakes others have made before you.
>Again, if you want to criticize my theory, you have to do it on the basis of what I actually say rather than on what you choose to read between the lines.
>If you want to criticize *my* theory you have to do it using *my* definitions because those are part and parcel of my theory.
Yeah, no thanks. It's a warning sign of a crank if you're inventing your own terminology.
It just creates too much work to translate your language to prior philosophical work. Then you will disagree with that translation, as you consider yourself a special snowflake.
It reminds me of the journals that banned papers presenting optimization algorithms based on metaphors from nature due to concerns over lack of scientific rigor and contribution. The issue arises from the fact that many such algorithms, like the "firefly algorithm," "bat algorithm," and others, often have limited novelty and merely apply existing concepts under different metaphorical guises. It was too much work to translate them to existing concepts -- and when that task was completed, there was nothing novel in these papers. The papers just repackaged existing methods wither superficial changes based on nature-inspired metaphors.
> Because computation is not intrinsic to the physics of the system, but assigned by an observer.
DeleteSo? Why can't nature produce an observer?
> there is no fact of the matter about exactly what meaning they convey.
And yet somehow I manage to use the word "cat" in my day-to-day life without causing much confusion.
> Your theory of truth is what is commonly known as the Correspondence Theory of Truth.
Yes.
> you're inventing your own terminology
But I'm not. None of the ideas nor the terminology I've presented so far is original with me. If either of us is guilty of "inventing your own terminology" it's you with your vague and self-contradictory use of "abstract object".
observer not
ReplyDelete> Because computation is not intrinsic to the physics of the system, but assigned by an observer.
>So? Why can't nature produce an observer?
I have to make a few clarifications to answer that. First, we are talking about rational observers. Second, you subscribe to the modern scientific view of matter, which lacks any intentionality or teleology.
In that is the case, then it follows directly that nature cannot produce a rational observer.
>And yet somehow I manage to use the word "cat" in my day-to-day life without causing much confusion.
Well, maybe you need to get out more. :-)
More on the indeterminacy of language in the comments on the other post.
P.S. The Blogger formatting issues appear to have spontaneously healed themselves.
> we are talking about rational observers
DeleteSo... you are disqualifying yourself?
(Sorry, if you lob be a fat pitch like that can you really expect me not to swing at it?)
Seriously, though, how do you define "rational" observer? Who gets to decide which observers are rational and which are not?
> The Blogger formatting issues appear to have spontaneously healed themselves.
Happy to hear it.
Everywhere a Sign
ReplyDelete> I thought that "abstract object" was a synonym for "idea".
>You've told me what they are not: they are not physical and they are not ideas. But you haven't told me what they *are*.
Here's an idea for you: abstract objects can be non-spatial, non-temporal, and non-causal. [Note that non-mental is not on this list] Of course, these statements are defining what abstract objects are not; it gets very long and complicated to define what they are. This is usually clarified by examples.
Not every abstract object shares all three of those properties, however. Numbers and other mathematical objects are the typical example for abstract objects that have all three. A fictional story, say Romeo and Juliet, is non-spatial and non-temporal, but it may have causal powers: one may read it and thereby want to read more Shakespeare, or change one's life in some way. Impure sets, such as {Elton John}, is non-temporal and non-causal, but some might suggest it has a location in space (namely, wherever Elton John is located). A musical rhythm is non-spacial and non-causal, yet is temporal, as it is defined by timing.
Propositions are abstract objects. One way to think of a proposition is as the meaning of a sentence. Alternatively, we can say that a proposition is that which is expressed by a sentence on a particular occasion of use. Either way, we can say that, e.g., the English sentence "Snow is white" and the German sentence "Schnee ist weiss" express the same proposition, namely, the proposition that snow is white.
Objects can generally be separated into concrete or abstract (although there are a few that are neither).
Now is your claim is that the nature of abstract object existence is that they are ideas in human minds?
Never mind what I think they are, it's less of a burden on you to just defend what you think they are.
>> Symbols are ... abstract objects.
>But symbols are physical. I can *show* you a symbol.
We often write down marks, or signs to represent abstract mental concepts. So we may write any variation of 𝟐 , 𝟚 , ② , ➋ , 𝍢, 𝍲, 𝍡, 𝍳 or 2 as marks/signs, but they all represent the abstract mental concept of two.
We need to agree on a terminology.
Definition: A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship.
Symbols are the semantic anchors by which symbol manipulating systems are tied to the world. Observe that the meta-statement:
The symbol "|" signifies object y.
if true, specifies semantic information:
* It is wellformed: the statement has a specific syntax.
* It is meaningful: Only in the context where the scratch "|" is actually made deliberately on, e.g., a tally stick or in a rock to mark a well defined occurrence it has a meaning.
* It is truthful.
Example: The sign "0" is the symbol for zero. This statement is wellformed, meaningful, and truthful.
Refer to the Triangle of Reference. Although I like this picture better.
Delete> abstract objects can be non-spatial, non-temporal, and non-causal
What does "non-causal" mean? If it means that they don't cause anything, then they cannot possibly be necessary to explain any observations. They are a textbook example of an IPU (Invisible Pink Unicorn).
> defend what you think they are.
It is not my burden to defend anything about "abstract objects" because I'm not the one who introduced that term into the discussion. You are. I'll defend "idea", and I'll state that I don't believe you can provide any meaningful distinction between ideas and "abstract objects" (which so far you have indeed failed to do). But if you think there is a difference between abstract objects and ideas the burden is on you to say what that difference is. Otherwise, I choose to use "idea" because it's more parsimonious.
> A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship.
Not quite. A symbol does not have to represent anything. It just has to be identifiable as a symbol, and distinguishable from other symbols. The marks used in Linear A are symbols despite the fact that no one has any idea what they mean.
Symbols about nothing
ReplyDelete>Sorry, if you lob be a fat pitch like that can you really expect me not to swing at it?)
That's fine, but to be fair, you should provide me with a coupon that I can redeem in the future to do the same to you.
>Seriously, though, how do you define "rational" observer? Who gets to decide which observers are rational and which are not?
A rational observer will have the properties of consciousness, intentionality, and rationality. Consciousness can be seen as the overarching experience of being aware and experiencing qualia. Intentionality is the "aboutness" of a thought, and it's "directedness" onto an object. Rationality is the ability to grasp concepts, combine them into judgments, and reason from one judgment to another using logical principles.
Humans are presently the only rational observers around.
>> abstract objects can be non-spatial, non-temporal, and non-causal
>What does "non-causal" mean? If it means that they don't cause anything, then they cannot possibly be necessary to explain any observations. They are a textbook example of an IPU (Invisible Pink Unicorn).
Non-causal means exactly that: the object can't cause anything to happen.
Numbers are non-causal. Has two ever caused you to do anything? Could two cause you to do anything? Can "redness" cause you to do anything? No, they can't: they're non-causal.
The IPU is a work of fiction, and hence is abstract. However, recall that I wrote above that non all abstract objects will have all 3 properties. An IPU could be causal if it inspired you to, say, draw a picture of a unicorn.
Why do objects need to be useful to explain observations? Anyhow, numbers and mathematics in general has been highly useful in explaining observations.
>Not quite. A symbol does not have to represent anything. It just has to be identifiable as a symbol, and distinguishable from other symbols. The marks used in Linear A are symbols despite the fact that no one has any idea what they mean.
By my definition (see above), symbols do have to represent something (be meaningful). Hence Linear A has no symbols, it is just signs.
It seems of dubious utility to have symbols that represent nothing. You'd have symbols everywhere, representing nothing. I'm looking at a knot in the wood grain of my desk -- is that a symbol for nothing? There's a little red dot on my right forearm -- is that a symbol for nothing?
Delete> Humans are presently the only rational observers around.
Are you sure?
Leaving that aside, let's return to the original point:
> naturalistic physics cannot produce a computation ... because computation is not intrinsic to the physics of the system, but assigned by a [rational] observer
Why is a "rational observer" necessary? Why are consciousness and intentionality necessary to recognize a computation? Do you not think that I could program a computer to recognize a computation?
And even if I grant that a "rational observer" is necessary to recognize a computation, why could nature not produce the thing that a rational observer recognizes as such?
> Non-causal means exactly that: the object can't cause anything to happen.
Then what observation could a non-causal object possibly be necessary to explain?
> Can "redness" cause you to do anything?
Yes. Under certain circumstances, redness causes me to apply hydrocortisone. In extreme cases it can cause me to seek medical attention.
> The IPU is a work of fiction
It is a very special work of fiction: its defining characteristic is that it cannot be detected, even in principle. I suppose you would call it "non-causal".
> Why do objects need to be useful to explain observations?
Because we're doing science here, and science is about finding the best explanations that account for all observations. Part of being the "best" explanation is not including any unnecessary crap, like IPUs.
> Anyhow, numbers and mathematics in general has been highly useful in explaining observations.
Indeed. So how can you say that numbers are "non-causal"? They "cause" superior scientific explanations.
> By my definition (see above), symbols do have to represent something
Yeah, but this is my blog, and I'm a Lisp programmer, so I believe in unbound symbols.
> It seems of dubious utility to have symbols that represent nothing.
I say FOO to that.
But fine, whatever. When you see a symbol that represents nothing just assume that it represents something but you don't know what it is. (That is actually the case with Linear A.)
> I'm looking at a knot in the wood grain of my desk -- is that a symbol
No. A symbol has to have an *identity* that transcends its physical representation. You have to be able to recognize that FOO and Foo are the same symbol, despite the fact that they look a little different, and that FOO and BAZ are different symbols. FOO and BAZ and BAR and SNOZ are (four distinct) symbols despite the fact that they generally have no meaning.
98% of everything is crap
ReplyDelete@Ron:
>Why is a "rational observer" necessary?
Computation involves symbol manipulation according to syntactical rules, but syntax and symbols are not definable in terms of the physics of a system. Hence if a machine, a system, is said to be computing anything, that judgment is assigned to it by an observer.
>Why are consciousness and intentionality necessary to recognize a computation?
Consciousness and intentionality are needed for rational observers, which are needed to recognize a computation.
>Do you not think that I could program a computer to recognize a computation?
Sure, but you'd just be automating your assignments of syntax and symbols. Observers can use tools.
>And even if I grant that a "rational observer" is necessary to recognize a computation, why could nature not produce the thing that a rational observer recognizes as such?
By your naturalistic model, nature can't produce a rational observer due to the way you've defined "matter."
>> Can "redness" cause you to do anything?
>Yes. Under certain circumstances, redness causes me to apply hydrocortisone. In extreme cases it can cause me to seek medical attention.
That is a particular instantiation of redness, not the abstract concept.
>> The IPU is a work of fiction
>It is a very special work of fiction: its defining characteristic is that it cannot be detected, even in principle.
Can't you smell it? Doesn't he leave hoof prints all over the place? Also, I hear he's pretty chatty.
>I suppose you would call it "non-causal".
Hardly! The IPU causes atheists all over the world to make ignorant and stupid claims about God and religion.
>So how can you say that numbers are "non-causal"? They "cause" superior scientific explanations.
Numbers, given they are non-physical and non-temporal, are not agents with the ability to initiate a process or bring about a certain effect. The number "2" or the set of natural numbers cannot initiate or cause anything to happen by themselves. It's scientists that cause scientific explanations.
>Because we're doing science here, and science is about finding the best explanations that account for all observations. Part of being the "best" explanation is not including any unnecessary crap, like IPUs.
Mathematics (which is abstract) provides the language and framework through which scientific theories are expressed, modeled, and tested. Mathematics allows scientists to express theories with precision and predict phenomena in a quantifiable way.
Also, ahem, scientific theories themselves are abstract objects and have no causal power.
>When you see a symbol that represents nothing just assume that it represents something but you don't know what it is. (That is actually the case with Linear A.)
You might call Linear A has having archaic symbols, or "former symbols." Yet why do that when you can call it what it is - a collection of signs. The scholars studying it have even produced a Signary for Linear A.
Delete> syntax and symbols are not definable in terms of the physics of a system.
Of course they are. In what other terms could they possibly be defined?
>> Do you not think that I could program a computer to recognize a computation?
> Sure, but you'd just be automating your assignments of syntax and symbols. Observers can use tools.
OK, but if I can program a computer to do something then that thing must be definable in terms of physics because computers operate according to the laws of physics.
There *might* be something non-physical going on in the decisions humans make leading up to that programming, but once the programming is done it's all physics from then on.
> nature can't produce a rational observer due to the way you've defined "matter."
Huh??? That makes no sense to me at all. What does my definition of "matter" (or any other word) have to do with what nature can and cannot do? Nature does what it does independent of the words I use to think about it.
> Mathematics allows scientists to express theories with precision and predict phenomena in a quantifiable way.
I don't see a lot of daylight between "allows" and "causes" here.
> You might call Linear A has having archaic symbols, or "former symbols." Yet why do that when you can call it what it is - a collection of signs. The scholars studying it have even produced a Signary for Linear A.
Maybe linguists distinguish between "symbols" and "signs" but I'm a computer scientist and "sign" is not a word that I've ever seen used. AFAICT it's synonymous with what a computer scientist would call an "unbound symbol". It's a poor choice for a technical term because it can be too easily conflated with its common usage as in "street sign".
limits of naturalism
ReplyDelete>syntax and symbols are not definable in terms of the physics of a system.
>Of course they are. In what other terms could they possibly be defined?
Recall that physical properties of symbol do not, and cannot, fix its meaning. The physical arrangement of those symbols do not, and cannot, define syntax.
Syntax and symbols are formal and abstract concepts and have no intrinsic meaning until interpreted by a mind.
>OK, but if I can program a computer to do something then that thing must be definable in terms of physics because computers operate according to the laws of physics.
There *might* be something non-physical going on in the decisions humans make leading up to that programming, but once the programming is done it's all physics from then on.
Sure, the computer can continue to run your program.
Yet, if you and rational observers withdraw from the system, then there is no determinate meaning of what the computer is doing. The physical properties of a system by themselves don't suffice to determine what function it is computing.
Your computer only computes relative to the intentions of the designers and users.
>>By your naturalistic model, nature can't produce a rational observer due to the way you've defined "matter."
>> nature can't produce a rational observer due to the way you've defined "matter."
>Huh??? That makes no sense to me at all. What does my definition of "matter" (or any other word) have to do with what nature can and cannot do? Nature does what it does independent of the words I use to think about it.
Sure, nature does what nature does. Yet can you explain how nature can produce a rational observer (with consciousness, intentionality, and rationality)?
Note you cut off my conditional, "By your naturalistic model," when you quoted me. Given the way you define matter, you can't provide an explanation as to why nature could produce a rational observer. Naturalists inherited from Galileo, Descartes, Boyle, Locke a conception of matter that abstracts away any intentionality or teleology from matter. Matter is instead characterized in mathematical terms, in a purely quantitative rather than qualitative way. Anything that can't be mathematically modeled is relegated to the status of "secondary qualities." That was less of a metaphysical discovery, though, than a methodological stipulation. If you set out to study only those aspects of reality that might be rigorously predictable and controllable, then you are bound to find that those are the only ones you discover.
Now, I have a different world view, and I can provide an explanation as to how nature produces rational observers.
>> Mathematics allows scientists to express theories with precision and predict phenomena in a quantifiable way.
>I don't see a lot of daylight between "allows" and "causes" here.
Then let's rewrite it as "Mathematics provides scientists the tools needed to express theories with precision and predict phenomena in a quantifiable way."
> Recall that physical properties of symbol do not, and cannot, fix its meaning.
ReplyDeleteThat's right.
> The physical arrangement of those symbols do not, and cannot, define syntax.
Did you mean "semantics"? Because syntax absolutely can be fixed by physical arrangement. That's what "syntax" *means*.
> Syntax and symbols are formal and abstract concepts and have no intrinsic meaning until interpreted by a mind.
Do you think a mind is necessary to transcribe DNA into proteins? Where do you think that mind resides? Do you think ribosomes have a mind?
> There *might* be something non-physical going on in the decisions humans make leading up to that programming, but once the programming is done it's all physics from then on.
Whew. I'm glad we can agree on *that*.
> if you and rational observers withdraw from the system, then there is no determinate meaning of what the computer is doing.
You really need to define "determinate" for me because a lot of your argument seems to turn on it, but I can't wring any sense out of it. The dictionary is no help here.
> The physical properties of a system by themselves don't suffice to determine what function it is computing.
Again, I'll cite the transcription of DNA into proteins which produce living organisms: does that process involve a mind? Is it "determinate"?
> Your computer only computes relative to the intentions of the designers and users.
You apparently have not been keeping up with the latest news.
> can you explain how nature can produce a rational observer (with consciousness, intentionality, and rationality)?
Yes, I can, but it's a long story. I'm working up to it. Patience, grasshopper.
> Given the way you define matter, you can't provide an explanation as to why nature could produce a rational observer.
My explanation of how nature produces a rational observer has nothing to do with how I define matter. The production of an rational observer is a *computational* process. It has to do with *information*. Matter is an implementation detail.
> I can provide an explanation as to how nature produces rational observers.
Do tell! Would you like to write a guest post for the Ramblings? Appear as the inaugural guest on my podcast?
>> I don't see a lot of daylight between "allows" and "causes" here.
> Then let's rewrite it as "Mathematics provides scientists the tools needed to express theories with precision and predict phenomena in a quantifiable way."
I don't see how that helps. Tools are causal.
Interest relative
ReplyDelete>> The physical arrangement of those symbols do not, and cannot, define syntax.
> Because syntax absolutely can be fixed by physical arrangement. That's what "syntax" *means*.
"define syntax" -- the rules that define syntax.
>>Syntax and symbols are formal and abstract concepts and have no intrinsic meaning until interpreted by a mind.
>Do you think a mind is necessary to transcribe DNA into proteins? Where do you think that mind resides? Do you think ribosomes have a mind?
>> The physical properties of a system by themselves don't suffice to determine what function it is computing.
>Again, I'll cite the transcription of DNA into proteins which produce living organisms: does that process involve a mind? Is it "determinate"?
As clarified in my comment to your other post, "determinate" relates to semantic determination.
The transcription of DNA into proteins involves copying a segments of DNA into messenger RNA (mRNA) molecules (which may involve RNA splicing as a intermediate step), then protein synthesis via a ribosome performing messenger RNA translation.
Now, life is a very complex chain of events. What is your justification for picking out a starting event, the copying of segments of DNA into mRNA (call this event "A"), and ending with the ribosome performing mRNA translation (call this event "B")? What does event A count as "the beginning" -- rather than, say, the last mitosis event of the cell, or the partial unwinding of the DNA double helix such that one strand can be used for mRNA synthesis? Why does event B represent "the end" of the causal chain -- rather than, say, folding of the protein, or the degradation of the mRNA?
Objectively, as far as the physical world itself is concerned, there is just the ongoing and incredibly complex sequence of causes and effects, which extends indefinitely forward and backward in time well beyond the events we have described. Objectively, that is to say, there is no such thing as "the beginning" or "the end," and nothing inherently significant about any one event as compared to another.
What counts as the "beginning" and "end" points of such a causal sequence, and thus what counts as "the causal sequence" itself considered in isolation from the rest of the overall causal situation, are interest relative. These particular aspects of the overall causal situation have no special significance apart from a mind which interprets them as having it.
Life is just chemistry. As a physical process, it is indeterminate, as there is no objective fact of the matter about which of the alternative possible meanings or contents it possesses -- or as you say, "We can only ever be in possession of a finite amount of data, and that data will always be consistent with an infinite number of potential theories."
>> Your computer only computes relative to the intentions of the designers and users.
>You apparently have not been keeping up with the latest news.
That is not responsive to my statement, but, rather, changing the subject. Do you have anything to challenge my statement that computation is only relative to the intentions of the designers and users?
P.S. This comment marks approximately 300th comment I have posted, since I started saving them in 2017.
Matter and causality
ReplyDelete>> Given the way you define matter, you can't provide an explanation as to why nature could produce a rational observer.
>My explanation of how nature produces a rational observer has nothing to do with how I define matter. The production of an rational observer is a *computational* process. It has to do with *information*. Matter is an implementation detail.
Yeah, I suppose you'll get there. Let me guess, the mind is a computational process of the brain?
We can defer that argument for later.
>> I can provide an explanation as to how nature produces rational observers.
>Do tell! Would you like to write a guest post for the Ramblings?
You already know it -- God created man in his image and to quote Augustine (Gen. ad lit. vi, 12): "Man's excellence consists in the fact that God made him to His own image by giving him an intellectual soul, which raises him above the beasts of the field."
Now, naturalism could redefine the conception of matter and provide an explanation of the emergence of rational observers, but there seems to be little research in this area.
I once offered that I would write a post "Why you should be an atheist" if you would write a post "Why you should be a Christian." I don't know if I could write it today, as the more I research the atheist arguments, the weaker they become. A good summary of my position would be this article: Atheo-Scientism At Twenty by R. Joseph Hoffmann (who is an atheist, with "a soft spot for religion"). I wish I was educated and could write as well as he does.
>Appear as the inaugural guest on my podcast?
You're thinking of starting a podcast?
I would urge you to put a lot of effort into getting excellent sound. This will include choice of microphones and preparing a room that is "dead" to sound (i.e., sound absorbing materials to eliminate reflections). Make sure your microphone doesn't pop Ps.
Don't know how I'd feel being on a podcast. My voice is kind of thin. Needs equalization and a bass boost.
>Tools are causal.
Tool users are causal.
Hammers don't have agency.
> What is your justification for picking out a starting event, the copying of segments of DNA into mRNA (call this event "A"), and ending with the ribosome performing mRNA translation (call this event "B")? What does event A count as "the beginning"
ReplyDeleteI presume you meant "why" and not "what"? It's because the causal chain of the sequence of events that I'm focusing on in order to make my point (that computation, or at least copying information, does not require a rational observer) goes from DNA->RNA->protein.
> Life is just chemistry. As a physical process, it is indeterminate
Wait, what? I thought "determinate" applies to the meanings of words, and yet here you apply "determinate" not to a word but to a physical process.
> Do you have anything to challenge my statement that computation is only relative to the intentions of the designers and users?
Um, yes? The fact that AI could pose an existential threat to humanity? Do you really think that is the *intent* of the people building AI?
> P.S. This comment marks approximately 300th comment I have posted, since I started saving them in 2017.
But who's counting, right?
> You already know it -- God created man in his image
I know the slogan. I don't know what it *means*. I can't even imagine what it could *possibly* mean for an allegedly perfect being whose existence transcends space and time to create a physical mortal fallible being "in his image".
Please don't try to respond to that in this comment thread. It's much too big a topic, and too much of a distraction.
> You're thinking of starting a podcast?
Yes.
> Don't know how I'd feel being on a podcast. My voice is kind of thin. Needs equalization and a bass boost.
Why do you think that matters? Don't you think your words should be judged on substance rather than your tone of voice?
>> Tools are causal.
> Tool users are causal. Hammers don't have agency
Agency is required for something to be "causal"??? That seems like a weird definition. To me something is "causal" if it can be a cause regardless of its position in the causal chain. And the dictionary agrees with me: "Causal: Of, involving, or constituting a cause."
Physical process: no intrinsic meaning
ReplyDelete> It's because the causal chain of the sequence of events that I'm focusing on in order to make my point (that computation, or at least copying information, does not require a rational observer) goes from DNA->RNA->protein.
You are observing the process DNA->RNA->protein and you are assigning it the meaning of "computation" or "copying".
As I said:
Objectively, as far as the physical world itself is concerned, there is just the ongoing and incredibly complex sequence of causes and effects, which extends indefinitely forward and backward in time well beyond the events we have described. Objectively, that is to say, there is no such thing as "the beginning" or "the end," and nothing inherently significant about any one event as compared to another.
What counts as the "beginning" and "end" points of such a causal sequence, and thus what counts as "the causal sequence" itself considered in isolation from the rest of the overall causal situation, are interest relative. These particular aspects of the overall causal situation have no special significance apart from a mind which interprets them as having it.
>> Life is just chemistry. As a physical process, it is indeterminate
>Wait, what? I thought "determinate" applies to the meanings of words, and yet here you apply "determinate" not to a word but to a physical process.
The semantic meaning of the physical process is indeterminate, as it could mean anything. Nothing intrinsic to the physical process gives it meaning. Any meaning can be assigned to it. As you say, "We can only ever be in possession of a finite amount of data, and that data will always be consistent with an infinite number of potential theories."
>Agency is required for something to be "causal"??? That seems like a weird definition. To me something is "causal" if it can be a cause regardless of its position in the causal chain. And the dictionary agrees with me: "Causal: Of, involving, or constituting a cause."
You want to get into Aristotle's four causes? I'm willing to go there.
> Any meaning can be assigned to it.
DeleteNo, that's not true. Yes, a finite amount of data is consistent with an infinite number of models, but that doesn't mean that anything goes. There are still models that are *eliminated* by the data, and others that are eliminated by other considerations, like being indistinguishable from one another (c.f. last-thursdayism).
More than One
ReplyDelete> Any meaning can be assigned to it.
>No, that's not true. Yes, a finite amount of data is consistent with an infinite number of models, but that doesn't mean that anything goes. There are still models that are *eliminated* by the data, and others that are eliminated by other considerations, like being indistinguishable from one another (c.f. last-thursdayism).
Fair enough. Yet to be indeterminate only requires the possibility of more than one meaning could be assigned to it.
Let me rewrite that paragraph for you:
The semantic meaning of the physical process is indeterminate, as no definite meaning can be assigned to it. Nothing intrinsic to the physical process gives it meaning. Multiple meanings could be assigned to it.
> Nothing intrinsic to the physical process gives it meaning. Multiple meanings could be assigned to it.
DeleteThose are not equivalent. The latter is true, the former is false.
Well, then, what intrinsic properties of a physical process give it meaning?
DeleteCorrelations.
DeleteSneaking in a mind
DeleteWell, this is reminiscent of Richard Feynman's story of a painter who assured him that he could make yellow paint by mixing together red paint and white paint. Feynman was incredulous. As an expert in the physics of light, he knew this should not be possible. Yet the guy was an expert painter, with years of practical experience. So, ready to learn something new, Feynman went and got some red paint and white paint. He watched the painter mix them, but as Feynman expected, all that came out was pink. Then the painter said that all he needed now was a little yellow paint to "sharpen it up a bit" and then it would be yellow.
Correlation is an abstract concept that a human mind projects onto systems. It's not an intrinsic process of a physical processes.
Correlation is a human-constructed concept that simplifies and represents how two systems behave in relation to each other. Without a human observer or interpreter, the physical systems would simply exist and interact according to natural laws, without the abstract idea of correlation being applied. It is our minds that create the abstraction of correlation by recognizing patterns, assigning significance to those patterns, and using statistical tools to describe them.
> Correlation is an abstract concept that a human mind projects onto systems.
DeleteNot if the objective-reality hypothesis is true. Then correlation is a real thing.
You will also have a hard time explaining the behavior of non-human minds like dogs, corvids, cetaceans, and great apes, or even ants and termites, without hypothesizing that correlation is independent of human minds.
Humans are special
Delete@Ron:
>Not if the objective-reality hypothesis is true. Then correlation is a real thing.
>You will also have a hard time explaining the behavior of non-human minds like dogs, corvids, cetaceans, and great apes, or even ants and termites, without hypothesizing that correlation is independent of human minds.
Correlation refers to a statistical relationship between two variables. This relationship exists as a formalism, independent of the entities that may experience it. However, the recognition and interpretation of that correlation depends on a human mind.
Even under the objective-reality hypothesis, correlation as a conceptual framework remains something that we, as observers, impose upon data. While physical events may co-occur or influence each other, calling that 'correlation' is a human-created tool to help us understand these patterns.
Animals and non-human minds detect patterns or relationships, but they do not "think" in terms of correlation as humans do. Their behaviors may reflect responses to stimuli and patterns, but labeling these as correlations is still a human abstraction. While the animals experience reality and respond to it, the term "correlation" itself is a product of human cognitive and linguistic systems.
Delete> Correlation refers to a statistical relationship between two variables. This relationship exists as a formalism, independent of the entities that may experience it. However, the recognition and interpretation of that correlation depends on a human mind.
But it manifestly doesn't. All kinds of non-human creatures are able to "recognize and interpret" correlations. They don't do it *symbolically*, but they still do it.
> Even under the objective-reality hypothesis, correlation as a conceptual framework remains something that we, as observers, impose upon data.
No, we don't "impose" anything. We *observe* correlations in data.
> the term "correlation" itself is a product of human cognitive and linguistic systems
Yes, obviously. Humans have linguistic and symbolic reasoning abilities that other animals lack.
No other animal can learn to play chess either. So what?
stimulus response
Delete@Ron:
>But it manifestly doesn't. All kinds of non-human creatures are able to "recognize and interpret" correlations. They don't do it *symbolically*, but they still do it.
You're right that many non-human creatures can detect patterns in their environment -- this is often an instinctual or biological response. However, only humans can recognize and interpret correlations, which are an intellectual process involving the conscious mind. While animals can respond to stimuli based on learned associations, what they do isn't exactly interpretation in the human sense. Human interpretation involves reflective awareness and symbolic thought, where we deliberately assign meaning to relationships between variables. So, while both humans and animals can recognize patterns, only humans engage in the kind of interpretation that involves deeper conceptual understanding.
>No, we don't "impose" anything. We *observe* correlations in data.
Your observe the data, then you impose your interpretation upon that data.
The concept of "correlation" is a tool we use to interpret relationships between variables. It's not something that simply exists in the data independently of our observation. When we say two variables are correlated, we're applying a specific statistical framework that allows us to quantify that relationship. Without this framework, the raw data does not suggest anything by itself -- it's our analysis that reveals these patterns.
>Yes, obviously. Humans have linguistic and symbolic reasoning abilities that other animals lack.
>No other animal can learn to play chess either. So what?
The point I’m making is broader. It's not just that humans have these abilities; it's that our understanding of the world, including concepts like "correlation," is shaped by the frameworks we construct. These frameworks -- statistical, linguistic, or conceptual -- are tools we use to impose structure on the raw data of reality. Other animals, while they may not play chess or use symbolic reasoning like us, don’t need to impose such frameworks to navigate their environments. In this context, "correlation" isn’t an inherent feature of reality but something we create as part of our cognitive and analytical processes.
Delete> The concept of "correlation" is ... not something that simply exists in the data independently of our observation.
It does if the objective-reality hypothesis is true. That's the *whole point* of the objective-reality hypothesis, that the consistency of our observations is *explained* by the actual existence of an objective reality that is independent of our observation.
> When we say two variables are correlated, we're applying a specific statistical framework that allows us to quantify that relationship. Without this framework, the raw data does not suggest anything by itself -- it's our analysis that reveals these patterns.
But, if the objective-reality hypothesis is true, then these patterns reveal properties of objective reality. The causality goes from objective reality to observation, not the other way around. That is what the objective-reality hypothesis *means*.
> The point I’m making is broader. It's not just that humans have these abilities; it's that our understanding of the world, including concepts like "correlation," is shaped by the frameworks we construct.
Yes. Our *understanding* of the world is shaped by these frameworks, but the *actual world* is not.
> These frameworks -- statistical, linguistic, or conceptual -- are tools we use to impose structure on the raw data of reality.
No. The structure is *observed*, not *imposed*.
> Other animals, while they may not play chess or use symbolic reasoning like us, don’t need to impose such frameworks to navigate their environments.
Oh, but they do. Animals need to at some level understand the concepts of "food", "danger", "potential mate", etc. even though they might not have *words* for these things.
> In this context, "correlation" isn’t an inherent feature of reality but something we create as part of our cognitive and analytical processes.
If the objective-reality hypothesis is true, then correlations *are* an inherent feature of reality, and this explains why, for example, dogs understand the concept of "food". In fact, dogs can and often do learn the meanings of *words* like "food", "treat", "walk", "sit", "stay" and many more. They can even learn them in Chinese.
Contradictions
DeleteYou claim that correlations are "inherent" in objective reality if the objective-reality hypothesis is true. However, this position implies that abstract objects, like correlations, exist independently of human thought or perception. But if correlations are not merely cognitive constructs but truly exist "out there," then you are implicitly treating them as real, abstract entities. This is problematic because you reject the independent existence of abstract objects.
If you deny the independent existence of abstract objects, then you must explain how something like a "correlation" -- a statistical relationship, which is an abstract concept -- can exist in reality without human interpretation. You can't have it both ways. Either correlations are cognitive constructs imposed by minds (in which case, they are not inherent in reality), or they are abstract objects existing independently (which you seem unwilling to accept).
You assert that the structure of reality is "observed, not imposed," yet acknowledges that animals or humans need frameworks to make sense of their environments (such as concepts of "food," "danger," etc.). However, by acknowledging this, you are admitting that cognition plays a role in structuring experience, which is more in line with my argument that our understanding of reality is mediated by frameworks. To say that "correlation" is simply an objective feature of reality, without any framework, undermines the complexity of how we interpret and quantify relationships in the world.
You are caught in a philosophical contradiction: rejecting abstract objects while implicitly relying on their existence, and dismissing the role of cognitive frameworks in understanding reality while subtly admitting their necessity. If you reject the independent existence of abstract concepts like correlation, then you should concede that these are mental constructs, not features of reality itself.
> [I]f correlations are not merely cognitive constructs but truly exist "out there," then you are implicitly treating them as real, abstract entities.
DeleteThat depends on what you mean by "real" and "entity". There are things out there in the world (objects) and those things have properties (which are not objects) and those properties have correlations (also not objects).
> This is problematic because you reject the independent existence of abstract objects.
That's right. Properties of objects are not themselves objects, and neither are correlations among those properties.
> If you deny the independent existence of abstract objects, then you must explain how something like a "correlation" -- a statistical relationship, which is an abstract concept -- can exist in reality without human interpretation.
No, I don't. All I have to do is define it operationally, i.e. to tell you how you can determine when there is a correlation, and I can do that. I don't have to commit to the metaphysical status of correlations for them to serve perfectly well as a scientific explanation any more than I have to commit to the metaphysical status of "objects". All I have to tell you about objects for them to serve as scientific explanations is that they are things that exist at particular places at particular times, and that they interact with each other according to certain laws.
> You can't have it both ways. Either correlations are cognitive constructs imposed by minds (in which case, they are not inherent in reality), or they are abstract objects existing independently (which you seem unwilling to accept).
But I *can* have it both ways. I can define correlations in a similar manner to that in which I define objects, and I can use those definitions to explain past observations and make accurate predictions of future observations. That is the only requirement for something to serve as a scientific explanation.
> You assert that the structure of reality is "observed, not imposed," yet acknowledges that animals or humans need frameworks to make sense of their environments (such as concepts of "food," "danger," etc.).
No. I don't acknowledge that they *need* to construct "frameworks" (as you call them), I simply *observe* that they *do* (or at least seem to). There is nothing necessary about it. There are plenty of entities, like rocks and bacteria, that don't do it, so it's manifestly not required.
> cognition plays a role in structuring experience
Well, sure, I guess -- it depends on what you mean by "cognition" and "structuring" and "experince". (Languages are theories!) Mental states that correspond to reality can be beneficial in navigating reality. But those mental states don't *determine* what reality actually *is*. Reality exists, and is what it is, independent of anyone's or any thing's mental states. That is the objective-reality hypothesis.
> To say that "correlation" is simply an objective feature of reality, without any framework, undermines the complexity of how we interpret and quantify relationships in the world.
I have no idea what it can possibly mean to "undermine the complexity" of something. The complexity of something (or lack thereof) is a feature of objective reality -- a thing is either complex or it is not. Nothing anyone says or thinks can "undermine" it any more than they can undermine Mount Everest.
> You are caught in a philosophical contradiction: rejecting abstract objects while implicitly relying on their existence, and dismissing the role of cognitive frameworks in understanding reality while subtly admitting their necessity. If you reject the independent existence of abstract concepts like correlation, then you should concede that these are mental constructs, not features of reality itself.
No, I am not relying on the existence of abstract objects. The only objects in my theory are concrete: electrons, photons, neutrons, and a few other odds and ends. (Or quantum fields if you want to get technical.)
Your argument hinges on defining correlations operationally, which avoids the need for metaphysical commitments. However, the question isn’t merely about utility in scientific explanation but about what that utility presupposes. When you say correlations "exist out there" as features of reality, even operationally, you imply a certain ontological status. Can you explain how something can be "out there" but not an object or an abstraction? If correlations are not objects, abstractions, or cognitive constructs, then in what sense are they real?
DeleteAlso, your dismissal of frameworks as necessary for understanding reality seems problematic. You observe that humans (and presumably other animals) construct them, but why? Wouldn’t that imply that these frameworks are more than incidental? If cognition is a tool that helps us navigate reality, then doesn’t that imply that our mental constructs are at least partly responsible for the way we experience or interpret correlations? And how do you reconcile this with your objective-reality hypothesis, which seems to dismiss any interpretive role of cognition?
In short, I’m curious how you would reconcile your desire to avoid metaphysical commitments with the need to account for the "realness" of correlations while still rejecting abstractions and cognitive frameworks. Isn't there an inherent tension in using correlations as explanatory tools while denying them any ontological or conceptual status?
I don't reject abstractions, I reject abstract *objects*. "Abstraction" is a subset of "idea". The only objects in my theory are the 17 fundamental particles in the Standard Model. There is also space-time. whose ontological status is a bit weird. Everything else is a consequence or an "emergent property" of how these particles arrange themselves relative to each other. When an electron and three quarks arrange themselves in a certain way, I call that a hydrogen atom. When eight electrons and however many quarks do it, that is an oxygen atom. When two hydrogen atoms and an oxygen atom arrange themselves in a certain way, that is a water molecule. And so on through a dozen or so more layers until you get to an arrangement called a neuron, which then arrange themselves to form brains. After that things get complicated. You'll just have to wait for the details (though I'm pretty sure you could actually fill them in yourself if you tried).
DeleteWrong Word, Ron
ReplyDelete@Ron:
>"Abstraction" is a subset of "idea".
Abstraction cannot be a subset of idea because it’s a cognitive process, not a type of idea. Abstractions arise as the result of an operation on ideas -- so we could say ideas may be abstract, but abstraction itself is not a form of idea. It is more accurate to say that abstraction produces a certain kind of idea rather than to say abstraction is a subset of idea.
Or: Abstraction is a verb, not a noun. How's that "wrong word" method tasting to you now, Ron?
>The only objects in my theory are the 17 fundamental particles in the Standard Model. There is also space-time.
When you claim to "reject abstract objects" while affirming only the existence of fundamental particles and space-time, you seem to overlook that your own explanation implicitly relies on abstract concepts. Specifically, when you refer to "the 17 fundamental particles," "space-time," "neutrons," "quarks," and "atoms," you"re not pointing to individual, concrete objects, but rather to types or categories. These terms represent general classes of entities that share certain properties—concepts that are abstract rather than physical.
For example, when you speak of an "electron," you"re not referring to a specific electron in a particular location at a given moment. Instead, you're referring to the abstract idea of what an electron is -- a type of particle that behaves according to a set of rules. These classifications are abstractions, not physical objects. The same applies to terms like "space-time," which refer to a theoretical framework, not to something you can directly observe or interact with as you would with a rock or a tree.
Furthermore, your explanation relies on mathematical structures, such as the "arrangements" of particles that form atoms and molecules. These arrangements aren't physical objects themselves; they're relationships and configurations -- abstract, mathematical entities that describe how particles behave and interact. Thus, while you aim to restrict your ontology to purely physical objects like particles and space-time, you're in fact depending on abstract relationships and classifications to make sense of the physical world. You may fancy yourself the champion of physical reality, but you're depending on abstract structures to even describe how particles interact.
In addition, your theory addresses only a small portion of reality, leaving out major parts: dark matter and dark energy. Even within your Standard Model, some of the entities you include, such as quarks, have never been directly observed (yet there’s a convenient theory to explain why they can never be observed). So, you're leaning on unobservable entities and then confidently declaring them "real." That's called reification and it’s a classic philosophical blunder -- turning abstract mathematical models into things you think exist out there in the real world.
While your intention may be to reject abstract objects, the very structure of your explanation requires an ontological commitment to them, whether in the form of mathematical relationships, types, or theoretical constructs. The boundary between the physical and the abstract in your theory is not as clear-cut as you think.
> Abstraction is a verb, not a noun.
DeleteReally?
"Abstractions arise as the result of an operation on ideas..."
"These classifications are abstractions..."
"If correlations are not ... abstractions..."
Looks like a noun to me.
I am really starting to have my doubts about whether you are actually thinking about what you are saying at all.
> your own explanation implicitly relies on abstract concepts
Sure. A.K.A. ideas.
You keep missing the point. The problem is not what part of speech "abstraction" is. The problem is that you insist that "abstract objects" are neither physical nor mental. So they must be in some other category, but you've refused to tell me what it is or describe it.
> In addition, your theory addresses only a small portion of reality, leaving out major parts: dark matter and dark energy.
Why do you think that is salient? Dark matter and dark energy are currently extant Problems. The identification of Problems is the first step in the scientific method. The existence of Problems is part and parcel of the process.
Also, dark matter and dark energy have no impact on anything that happens here on earth beyond astronomical observations. This is one of the reasons they were only discovered recently, and why it's so hard to make progress explaining them.
> Even within your Standard Model, some of the entities you include, such as quarks, have never been directly observed
Nothing is ever directly observed. Even when you look at something, the feeling you have that you are "directly observing" is an illusion. There are many layers of indirection between you and the thing you're looking at. You aren't seeing the object, you are seeing the light reflected from the object. Are you aren't directly observing the light either, you are observing the electrical impulses emitted from your retina, transmitted by your optic nerve, and processed by your visual cortex.