(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.
48 comments:
3 is prime
@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?
Thanks 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.
>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:
Ah. 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.
_/|
@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.
Like 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
@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.
You'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
@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)
>> 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)
One 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)
You 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
@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.
No, 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
In 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
Of 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
@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
I 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:
> that's change, not progress
Just out of curiosity, what would progress look like on your view?
Antecedent to Ontology
@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
@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
However, 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.
> 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
@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
>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.
No. 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
> 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
>> 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."
> 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
Obviously that should have been 1860, not 1960.
Abstract Ideas
>> 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
Readers interested in the Liar Paradox might find this blog post of interest:
This post is lying to you.
> 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
>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
@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.
> 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.
> 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
@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
@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
>> 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.
> 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
@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...
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.
> 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
@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".
That'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
@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
Yes, 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:
>> 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.
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