A Scientific Theory of Truth

(This is part 7 of a series about the scientific method.)

The over-arching theme of this series is that science can serve as a complete worldview, that it can answer deep philosophical and existential questions normally associated with philosophy or religion.  I gave a small example of that in the last installment where I showed how the scientific method can be deployed to answer a fun philosophical riddle.  Here I want to show how it can tackle a much deeper question: what is truth?

Note that what I mean by "truth" here in this chapter -- and only this chapter -- is not scientific truth, but philosophical truth.  Remember, I have already disclaimed the idea that science finds philosophical or metaphysical truth.  It doesn't, it finds good explanations that account for observations, which are valuable because one of the properties of a good explanation is that it has predictive power.  But a good explanation is not necessarily true in the philosophical sense.  Newton's theory of gravity, for example, turns out to be completely wrong from a philosophical point of view, but it is still useful because it makes accurate predictions nonetheless.

The word "truth" is sometimes used in science as a shorthand for "theory that is sufficiently well established and makes sufficiently accurate predictions under a sufficiently broad range of circumstances that we proceed as if it were the (philosophical) truth even though we know it's not."  When I want to emphasize that I am referring to philosophical or metaphysical truth I will capitalize it.  Science seeks (and finds!) lower-case-t truth, not upper-case-t Truth.

But this does not mean that (upper-case-t) Truth is beyond the realm of scientific inquiry!  Remember, the scientific method is to find the best explanation that accounts for all of your observations, and one of your observations (if you are a normal human) is a constant stream of overwhelming evidence that there is lower-case-t truth out there, and the obvious explanation for that is that there is upper-case-T Truth out there, and the former is somehow a faithful reflection of the latter.  Furthermore, what we know about lower-case-t truth can put constraints on upper-case-T truth.  Science might not be able to tell us what the Truth is, but it can tell us with very high confidence what it is not.

So how do we use the scientific method to tackle a philosophical problem?  We can't do it directly because "What is Truth?" is not a properly framed scientific question.  Scientific inquiry must begin with a Problem, something we observe that cannot be explained by current theories.  "What is Truth?" is not a valid Problem statement because Truth is not something we observe.  To start a scientific inquiry we have to somehow transform this into a question about something we can observe.

Fortunately, there is a general way of doing this for philosophical questions: we can observe that people wonder about what Truth is!  We can further observe that people have some intuitions about what Truth is (or at least what truth is), and that some of these intuitions are common across a wide swath of humanity, to the point where someone who does not share these intuitions can be considered mentally ill.  For example, here are some things that are widely regarded as true:

All triangles have three sides.

The sun rises in the east.

The sky is blue.

Humans are mortal.

And here are a few examples of statements that are widely regarded to be not true, a.k.a. false:

Some triangles have four sides.

The sun rises in the west.

The sky is green.

Humans are immortal.

We can now advance a some hypotheses to explain these observations:

1. There is a metaphysical Truth out there, and that out intuitions are somehow in contact with this Truth.
2. Our intuitions about truth are illusions.  There are no actual truths.  What we call "truth" is nothing more than a social construct into which we are indoctrinated.  (If you think this sounds ridiculous, believe me, I sympathize.  But this is actually a hypothesis that is taken seriously in some academic circles.  It's called post-modernism.)

Before we go on to discuss the relative merits of these hypotheses (though I guess I've already tipped my hand here), let's consider some more examples:

1. Richard Nixon had eggs for breakfast on the morning of January 1, 1962.
2. Coffee tastes good.
3. The United States is a Christian nation.
4. Gandalf was a wizard.
5. Love is a many-splendored thing.
6. Die Erde ist Rund.
7. This sentence is false.
8. Given a line and a point not on that line, there is exactly one line passing through the given point parallel to the given line.

Each of these examples is meant to illustrate a different subtlety with the notion of "truth".  The first one is either true of false, i.e. there is an actual fact of the matter regarding whether or not this statement is true, but that fact is almost certainly beyond our reach.  We can know that this statement is either true or it is false, but almost certainly we can't know which.

The second example is completely different.  It is an example of a subjective claim.  There is no "actual fact of the matter" with regards to the taste of coffee.  Some people like it, some don't.  Note that you can transform a subjective claim into an objective one by binding it to a particular person: "Coffee tastes good" is subjective, but "I think coffee tastes good" or "coffee tastes good to me" is objective.

The third example is harder to characterize.  At first glance is might appear to be a subjective claim, a matter of opinion analogous to the flavor of coffee.  But consider "Israel is a Jewish state", or "Saudi Arabia is a Muslim state."  Surely those are objectively true?  Surely there is more truth to them than "Israel is a Muslim state" or "Saudi Arabia is a Jewish state"?  I won't say anything more about this example right now, but keep it in the back of your mind because it will become important later in this series.

The fourth example is actually controversial, at least among philosophers.  If you polled ordinary people on the street you would probably find pretty overwhelming agreement that this statement is true, especially when contrasted with, say, "Gandalf was an orc."  But some philosophers argue that any statement about Gandalf cannot be true because Gandalf doesn't actually exist, and non-existent things can't have properties.  So it cannot be true that Gandalf was a wizard, but neither is it true that he was not a wizard.  He simply wasn't anything.  Personally, I think this is ridiculous, and I would not even mention it but for the fact that this point of view was advanced in all seriousness by someone whose views I otherwise hold in the highest regard.

To me, the answer is pretty obvious: the sentence "Gandalf was a wizard" does not mean that Gandalf was an actual wizard in actual physical reality.  It means that within the context of the fictional world created by J.R.R. Tolkien, Gandalf was a wizard.  Or, if you really want to be strict about it, "J.R.R. Tolkien wrote that Gandalf was a wizard", which is clearly true.

The fifth example appears superficially to be a factual claim, but it isn't.  It's poetry.  I included it to show that there is something about factual claims that transcends mere syntax.

The sixth example is German for "the earth is round."  This example makes a similar point to the one before: the process of deciding whether or not a statement is true, or even of deciding whether or not it even makes sense to say that it is true or false, is not a simple one.  There is no straightforward procedure that you can apply to a string of letters to decide these things.

The seventh example is the famous Liar Paradox.  Superficially it appears that this sentence should be either true or false, but either possibility leads immediately to a contradiction.  Another interesting example, which is not considered nearly as often but which I think is equally interesting, is the opposite: "This sentence is true."  It can be true, or it can be false, and both possibilities are internally consistent.

This is also the case for the last example, which is the famous Euclid's fifth postulate.  Intuitively it seems like it should be true, and it also seems like it should be provable from some simpler assumptions, but humans searched in vain for such a proof for two thousand years before realizing that whether or not to consider this statement true or false is an arbitrary choice, and either choice leads to interesting and useful results.

The main point I'm trying to make here is that truth is complicated.  The road to truth winds through the vagaries of natural language and subjective experience, takes a few twists and turns through prejudice and personal opinion, before finally arriving...well, somewhere.  My personal experience is consistent, at least superficially, with the hypothesis that there is an objective reality "out there" which I share with other conscious beings.  Specifically, I am something called a "human being" living on the surface of something called a "planet" which I share with other human beings who do things like eat and sleep and build computers and write blog posts.  If you don't accept that, then I'd be interested to know how you account for what you are doing right this very moment as you read this.

For now, though, I am just going to assume that this is the case.  This is an example of engaging in Step 2 of the scientific method.  The first step is to identify a Problem.  In this case, the Problem is to account for the fact that humans profess to believe, sometimes vehemently, that certain things are true and other things are false.  It's possible that this is because all humans other than me are NPCs in a simulation, and I'm the only truly conscious being in the universe.  (This is called solipsism.)  It's hard (though not impossible) to refute solipsism, but here I'm not even going to try.  I'm just going to assume it's false, and that all my fellow humans really are what they appear to be.

So here is the actual hypothesis I am willing to defend, my proposed answer to the question of "What is 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.

Notice that I have introduced two new words here: "proposition" and "idea".  I don't want to get into too much detail about these just now.  My purpose here is not to present an academically rigorous argument, merely to illustrate in broad brushstrokes how the scientific method can be used to attack problems that are often regarded as outside of the scope of scientific inquiry.  I will get much more precise about this later in this series, but for now just assume that "idea" means what it is commonly taken to mean: some vaguely identifiable thing that exists in someone's mind which can be somehow transferred into another person's mind.  This transferability is the defining characteristic of an idea; it is what distinguishes ideas from other things that might exist in someone's mind, like emotions or self-awareness.

Despite the fact that the idea of an idea (!) is pretty common, it is actually very hard to demonstrate.  I can't show you an actual idea.  All I can show you is a rendering or representation of an idea through some physical medium like writing or speech or dance or music.  So, for example, I can write:

The earth is round.

That looks like an idea, but appearances are deceiving.  What you are looking at is not something inside my brain (which is where ideas live) but patterns of light emitted from your computer screen, which, needless to say, is not part of my brain.  The marks you see on the screen get translated by your brain into an idea, but the marks and the idea are not the same thing.  The idea is the thing that ends up in your brain after seeing the marks, which in this case your brain interprets as letters and words.  Compare with:

Die Erde ist Rund.

or

地球は丸い

Those are completely different marks on the page, but they all denote the same idea, namely, that the earth is round.  That idea is a proposition because it maps onto things in objective reality, namely a planet called (in English) "earth" and a physical property called (again, in English) "round".  And that proposition is true because that thing actually has that property.

Note that evaluating the truth of statements on my theory is a two-step process.  The first step is mapping a rendering or a representation of an idea, which here will almost always be marks on a computer screen, onto an actual idea, and the second step is mapping that idea onto reality.  The importance of the first step cannot be overstated.  It is capable of cutting huge swathes through the philosophical underbrush.  Many seemingly intractable philosophical problems fall before it.

Take the example of "Gandalf was a wizard."  That string can reasonably be interpreted in two different ways, one of which is true, and the other false.  It can be taken to mean, "Gandalf was a real person in the real world, and he was a wizard" or it can be taken to mean, "Gandalf, the fictional character in J.R.R. Tolkein's 'Lord of the Rings' was, within the context of that fictional world, a wizard."  Disagreements over the truth of "Gandalf was a wizard" are nothing more than quibbles over this particular ambiguity of the English language.

The example of "all triangles have three sides" can be resolved similarly.  The word "triangle" means "a shape with three sides" and so this statement really means "All shapes with three sides have three sides."  Which is pretty obviously true, and also not very interesting.

A more interesting example is "The United States is a Christian Nation."  This turns on what is meant by the ambiguous phrase, "Christian nation."  It might mean that the United States is a Christian theocracy, which it is not (at least not yet).  It might mean that the United States was intended to be a Christian theocracy, which it also was not.  Or it might mean that the majority of the people living in the United States self-identify as Christian, which is true.  Again, disagreements over this are disagreements over the meanings of words, not good-faith disagreements over actual facts.

Good-faith disagreements over actual facts are very rare in science.  This is one of the reasons that scientific disagreements are almost invariably settled without resorting to violence, which is in very stark contrast to other methods that humans have tried.

As an exercise, see how far you can get following this line of thought to attack the Liar Paradox, i.e. "This statement is false."  I'll give the answer to that in a future installment because this one is getting too long.  But as a hint, here are two incorrect answers.

Most people upon seeing this puzzle for the first time think that the resolution has something to do with the self-referential nature of the phrase "this statement".  That's not the case.  It's straightforward to construct a similar paradox without any self-reference.  Here is one way:

The following sentence is false.
The preceding sentence is true.

We can even stop playing fast-and-loose with the distinction between strings and propositions simply by giving names to strings:

S1: "The proposition denoted by string S2 is false."
S2: "The proposition denoted by string S1 is true."

And we can even do the same thing without labels by using a clever trick called Quining, which consists of filling in the details of a string that looks something like, "The string that you get when you follow this procedure ... is false", where the ellipses are filled in with instructions such that the string that you get when you follow those instructions are the exact string that you started with.  It's quite a neat trick, and it's the foundation of Godel's famous incompleteness theorem, wherein he constructs a string that essentially says, "This proposition denoted by this string cannot be proven by standard mathematics."

So self-reference is not the problem.

A second possibility is that the liar string does not denote a proposition.  Just because a sentence bears a superficial resemblance to a proposition doesn't mean it actually is one.  "Love is a many-splendored thing" bears a superficial resemblance to "love is an emotion", but the latter denotes a proposition while the former does not.  In order to be a proposition on my theory, an idea has to refer to objective reality somehow because truth is determined by correspondence to reality.  The words "love" and "emotion" refer to things in reality, but "many-splendored thing" does not; it's just a poetic rhetorical flourish.

No such problems are immediately evident in the Liar Paradox sentence.  It refers to an idea, and ideas are part of reality, and so we cannot reject it as a proposition on the grounds that it does not refer to reality.

I'll give you one final hint: the resolution of the liar paradox involves discharging a tacit assumption about propositions which turns out not to be true according to the definition of truth I've advanced here.  If you think you know the answer, put it in the comments.  (Note that I have comment moderation turned on.  This blog has been around for twenty years and it attracts a lot of spambots.)

In closing, I want to reiterate that the main point here is not to resolve the liar paradox (that's just a fun puzzle that happened to come up) nor any other hard philosophical problem, but merely to show how the scientific method can be applied to such problems.  Philosophers have been puzzling over what truth is for millennia; I can't provide an academically rigorous answer in 2500 words.  The best I can hope for is to show that these questions are not beyond the scope of scientific inquiry.

But stay tuned.  There's more to come.