Friday, October 2, 2015

What is Truth?

If I had to name the single most frustrating aspect of modern, popular debate, it would have to be the openly adversarial nature on which it all appears to operate.  Rather than work together on building a better understanding of our world, we instead seem to be more focused on scoring philosophical points against the "opposition."  Often times, this might even be by design, like in a courtroom setting where both advocates must dogmatically argue on behalf of their clients’ best interests.  The rest of the time, however, it seems to just happen spontaneously---as if no one really knows what the rules are when engaging in this process.  That's why so much philosophical debate in this world feels a lot like trying to play a game of chess against an opponent who thinks that this is supposed to be checkers.  Without some formal agreement over what truth is and how to recognize the truth when we see it, then there is simply no way to productively engage with opposing points of view.

To me, this presents a very strong incentive to just sit down and summarily examine the question of "What is truth?"  Fortunately, in the context of philosophical and mathematical logic, there are actually very well-established answers to this question.  It's just that you wouldn't really know it because no one ever seems capable of spelling them all out within a single, comprehensive reference.  That’s why I feel personally motivated to present my findings on this issue.  It’s a perfect opportunity to explicitly lay the foundations of basic epistemology for everyone to see, such that we can finally begin to hold each other accountable to a more rigorous set of philosophical rules.

To begin, it's important to understand that any time we talk about a thing like truth, we're not talking about some intrinsic metaphysical quality of reality itself.  Technically, what we're really talking about is a property of propositions.  That is to say, propositions can either be true or they can be false, but there is no such thing as raw "essence of truth" interwoven into the fabric of space and time.  Speaking more formally, a truth value is classically defined as a member of a binary set that contains the elements "True" and "False"  [1].  The purpose of this set is to serve as a kind of marker for linguistic propositions in order to help us measure their epistemic "correctness."  What exactly that means is open to some interpretation, but we can give it a rigorous definition through a mechanism known as a truth assignment.  Speaking formally again, a truth assignment (also called a truth valuation, or an interpretation) is defined as a mapping function between the set of simple linguistic propositions and the set of binary truth values.

If that sounds a bit technical at first, then just think of it like this:  Imagine me writing down a simple proposition on a post-it note and placing it in front of you.  In your left hand is a giant rubber stamp that says "true" while in your right hand is a another giant rubber stamp that says "false."  Your job is to decide which label deserves to be stamped on this note.  So ask yourself, how do you go about doing that?  Do you just arbitrarily stamp things randomly?  Or do you apply some set of rules that give your labels a more significant meaning?  Whatever answer you give to this question is effectively your truth assignment function.  It's an algorithm that takes simple linguistic propositions as an input and then determines a binary truth value as the output.

Now let's take it one step further.  Suppose you've stamped a dozen or so of these post-it notes with truth values, when suddenly you feel like connecting them together into more complex arrangements.  For example, maybe you think two true propositions connected left to right should also be stamped with a value of "true."  Or maybe you think two false propositions connected top to bottom should always be "false."  Maybe you think propositions stamped with "true" on the top should all be stamped with "false" on the bottom, and vice-versa.  These are all perfectly valid operations, and represent the role of logical connectives contained within the scope of propositional logic.  We like using logical connectives because they allow us to literally "connect" propositions together, thereby creating more interesting propositional formulas.

Notice also how there's nothing physically forcing us to stick with only a binary set of truth values.  For example, maybe you think truth would make more sense if we used a ternary set of values rather than binary.  It's a perfectly valid conception that's even used in practice today by scientists, engineers, and mathematicians [2].  Some systems of logic even treat truth as a continuum value rather than a discrete set [3], and again find use in modern scientific applications.  There is no objectively right or wrong answer except for the collective say-so of human philosophers in our ultimate quest for a meaningful conception of truth. 

This is all pretty standard material so far, and can readily be verified in most relevant textbooks on the subject [4,5].  However, something you generally won't find is an official stance over the precise nature of an ideal truth assignment.  It's as if we're all experts at manipulating truth values once we have them, but no one knows how to go about assigning those actual truth values in the first place.  That's a real shame, because this question represents the heart of what an idea like truth is supposed to philosophically encapsulate.  At best, we only seem to have this vague notion that truth should, in some way or another, represent a kind of "correspondence" between the set of linguistic propositions and the factual state of affairs in objective reality.  True propositions are those which effectively describe the real world as it really is, while false propositions do not.

This is a fairly common epistemic concept that philosophers like to call the correspondence theory of truth.  And at first glance, it does seem to be a pretty intuitive definition.  Unfortunately, there's also a glaring hole that needs to be addressed.  Namely, what exactly is this "correspondence" thing you speak of, and how do I recognize it when I see it?  For example, consider a simple proposition like "the Moon is round."  Is that true or false?  According to correspondence theory, the best we can say is that if the Moon is round, then it is "true" that the Moon is round.  Since that's obviously just a vapid tautology, correspondence theory of truth hasn't really told me anything about how to assign truth to propositions. 

But let's take it even further.  What if I stand outside one evening and simply look at the moon directly with my own eyes?  That way, if I see a generally roundish object, then I can legitimately say that the Moon is round, right?

Well, no.

For example, what if there was some kind of optical illusion brought on by the atmosphere that makes squareish things appear round?  Or what if I'm just looking at a giant photograph of the moon, or maybe some elaborate hologram?  Maybe it's all just an hallucination brought on by drugs, or perhaps a really vivid, lucid dream.  Maybe I'm being tricked by a magical demon, or maybe I'm really just a brain in a vat, plugged into some kind of matrix simulation.  I simply do not know, and what's more, I can't know.  No amount of reason or evidence can ever allow me to perfectly determine objective reality as it really is.  Correspondence theory of truth is therefore useless because it offers no way to differentiate between all of these competing  scenarios.  So if we're ever going to make any progress in building a viable epistemology, then we need to operate under the basic constraints that nature has given us.

This is a fundamental philosophical concept known as the egocentric position, or equivalently, the problem of external world skepticism.  All it says is that for whatever sensory perception you may be experiencing at any given moment, there are limitless ad hoc explanations for what might be causing it.  Remember that I'm just a sentient agent trapped within my immediate mental awareness.  It's not like I can just crawl out of that awareness and directly perceive reality as it really is.  And even if I could, how exactly would I correspond linguistic propositions to those objective states?  What are the rules I have to follow and how do I apply them?  We simply cannot ignore the fundamental barriers that exist between reality, our perceptions of reality, and our linguistic frameworks for describing reality.

This is the part where many philosophers really begin to butt heads with each other, but there are at least a few general principles that most people do tend to agree on.  For example, one theory of truth that has great utility is known as the principle of mental incorrigibility, or simply empiricism.  All this says is that any honest statement of immediate sensory perception is automatically a true proposition.  For example, consider a statement like "I feel a pain in my foot".  Even if it turns out to be a complete illusion (like an amputee with a bad case of phantom limb syndrome) I still cannot deny the fact that I am definitely experiencing a distinct sensory perception that is unique from many others.  It therefore seems perfectly reasonable to just acknowledge our perceptual data for what it is, designate those experiences with linguistic markers, and then assign a basic truth value to such propositions accordingly. 

Another popular method for assigning truth to propositions is the use of axiomatic formalism, or for the sake of this discussion, rationalism.  Basically, all this system says is that certain "obvious" propositions, called axioms, deserve a specific truth-value by rote fiat.  For example, take the reflexive law of equality: A = A.  No one derived this proposition from any prior logical framework, nor was it empirically discovered hiding under some rock.  It was just asserted outright as "true" because mathematicians needed a concept of equality from which to build a working system of algebra.  

Once we finally settle on an agreeable set of axioms, it then becomes possible to generate new true propositions out of the old ones by exercising rules of inference.  For example, one classic rule of inference is the transitive law of equality: if A=B and B=C, then A=C.  Again, no one derived this rule from any deeper foundations, nor was it empirically discovered.  It was just asserted outright as a thing we're allowed to do with the concept of numerical equality.  Any new propositions generated in such a fashion are then called theorems, and represent the core driver behind all propositional and mathematical logic.

This might feel like strangely circular reasoning at first glance, and in all fairness, it kind of is.  However, contrary to popular misconceptions, axiomatic systems like math and logic make no effort to describe any objective sense of mind-independent reality.  Rather, a far better way to think of such systems is as a kind of highly formalized language.  Good axiomatic assertions are therefore not really circular so much as they are definitional.  That's why all logical and mathematical theorems are said to analytic in nature, because such truths are ultimately derived entirely from the raw meaning we impose on the terms themselves, and not from any direct connection they have to the external world.  One could even argue that this makes analytic propositions a kind of formal extension on the incorrigible, since anyone is internally free to define their own personal vocabulary however they like.

But what about the so-called synthetic propositions that actually do attempt to describe objective reality---that is to say, the world "out there" beyond purely mental processes?  For example, consider a proposition like "all bachelors are bald" or maybe "all dogs live on Earth."  How do I assign truth to propositions in this category?  Again, it's not like I can just pop open a can of reality and directly observe the facts of the matter beyond my senses.  Nor can I logically derive their truth from any assigned meaning to the words themselves.  So what do we do?

This is another point where things tend to get very confusing, simply because there are so many oddball truth assignments to choose from and no real official answers to turn to.  For example, suppose we decide to assign truth to propositions that reinforce our sense of personal identity or social status. Let's call this egotistical validation.  Granted, it might not be a very good system, but it's still a perfectly valid function that operates under well-defined rules.  Maybe you've even encountered this system yourself, like in religious or political discussions where personal emotions tend to run very high.

Another interesting class of synthetic truth assignment is called Biblical inerrancy, and simply says that no true proposition can ever contradict the records contained within the Holy Bible.  It's actually a fairly common truth assignment, typically emerging from religious fundamentalist organizations.  Truth, in their view, is basically whatever the Bible says.  So while it is tempting to criticize the implicit goals contained within such a definition, it is hard to ignore the clear, meaningful distinction it represents.

But let's face facts.  Those truth assignments are obviously arbitrary and completely unsatisfying because they make no effort to philosophically connect our beliefs with any objective sense of mind-independent reality.  Unless we can find a way to overcome the egocentric position imposed on us by nature, then no system of truth assignment will ever have any meaningful sense of merit.  That’s why so much of the philosophical debate in our world appears to be so pointless.  Most truth assignment functions utilized in practice are either needlessly arbitrary, brazenly self-serving, or deliberately obtuse.

To address this problem, I find that it helps to step back and ask ourselves a fundamental question about truth that surprisingly few philosophers ever seem to ask.  Namely, why is it so god-damned important to believe in as many "true" propositions as possible while simultaneously rejecting as many of the "false?"  What difference does it make at the end of the day?  For instance, consider a possible world where everything I believe about the universe just so happens to be categorically false.  However, every single time I make a decision based off of those beliefs, the consequences are maximally predictable and desirable for me anyway.  Likewise, any time I commit a single "true" belief to action, the outcome is never predictable or desirable for me at all.  Now let’s ask ourselves - given such a world, is it even meaningful to call any of my beliefs "false?”  And if so, why would I ever want to believe anything that was true?  I could spend my entire life being completely wrong about absolutely everything and actually be better off for it. 

This simple thought experiment represents the core principle behind a system of truth assignment generally known as pragmatism.  All this system has to say is that the only meaningful reason why anyone would ever bother believing anything at all is so that we can eventually use that information as a guide for our actions.  Decisions based on “true” beliefs will therefore manifest themselves in the form of controlled, predictable experiences, while decisions based on “false” beliefs will eventually fail in that goal.  Any beliefs that refuse to drive any actions whatsoever, even in principle, are thus effectively reduced to useless rhetorical gibberish.

To illustrate how this system might work in practice, simply imagine yourself standing at a busy intersection when suddenly you decide that you'd like to walk across to the other side.  Sure, you can axiomatically declare premises and logically deduce conclusions all you want, but sooner or later you're going to have to translate that information into a real, committed action.  So while you may think you're being very clever with all your intellectual presumptions and sophisticated rhetoric, I have yet to encounter a single philosopher who could successfully argue with a speeding bus.  Everyone, everywhere, is therefore universally bound to the same pragmatic process in our daily epistemology.  We collect empirical data, we formulate it as a rationally descriptive model of objective reality, we exercise a decision accordingly, and then we empirically observe the outcome.  If our understanding of traffic behavior is indeed "true," then we can expect to safely cross the street without incident.  However, if our model contains flaws or inconsistencies, then it's only a matter of time before we eventually find ourselves getting plowed by oncoming traffic.

This is what makes pragmatism the only epistemology with any viable sense of “connection” to the external world beyond our senses.  Because even if my entire reality is little more than a glorified matrix simulation or demon-spawned hallucination, then even that reality is still objectively real, and apparently operating in accordance with causally predictive patterns.  So if on the off-chance that my actions have any influence on the outcome of future events, then I can use those outcomes to gain real information about the rules governing my reality.  Beliefs drive actions, actions have consequences, and consequences are objective.

We can give this process a nice, technical-sounding name like pragmatic empirical rationalism, but really, it's all just a glorified way of saying science.  Because really, that's all science fundamentally boils down to; a formalized system of gathering empirical data, expressing it within a rational, predictive framework, and then testing those predictions against quantifiable actions and consequences.  We like basing our beliefs on scientific methods because it ultimately allows us to make real decisions in the real world with real, empirical consequences.  Mental incorrigibility and axiomatic formalism are not mere ends unto themselves, but essential tools for the greater purpose of pragmatically navigating the world. 
Notice also how the pragmatic framework implicitly captures many other familiar principles of both science and scientific method.  For example, consider the principle of fallibilism, which simply states that no synthetic propositional model can ever be assigned a value of "true" with any kind of perfect, universal certainty.  At best, we only know what to expect from such models if and when we ever happen to find them.  Consequently, all knowledge claims about objective reality must always remain open to possible revision when faced with any newer and better information.  Likewise, the principle of falsifiability states that we can indeed be perfectly confident in assigning certain models a value of false.  That's because the very definition of a false propositional model is one whose empirical predictions fail to come to pass.  Likewise, we can even use pragmatism to quantify the principle of Occam's Razor (also known as the principle of parsimony): given two propositional models that happen to make perfectly equivalent predictions, then the model containing fewer assumptions is automatically preferable.  After all, if both models are empirically equivalent either way, then you might as well just go with the one that takes less work to think about.
But hey, maybe that's being too presumptuous.  Maybe you think pragmatism is a terrible principle of truth assignment, and that we should all replace it with some "higher" form of understanding.  But let's be clear about what that entails. Without some ultimately pragmatic purpose by which to measure our beliefs, then they are effectively disconnected from any empirically predictive decision we could ever hope to make.  I could therefore openly concede every last proposition you have to say about reality, and literally nothing in my life would ever have change as a result.  That's why no one cares how many angels can dance on the head of pin.  Any answer we give is necessarily going to be trivial and vacuous.  We do, however, care a great deal about what medicines work best for treating cancer and why.  That's because any decisions we might hope to make on the subject are necessarily dependent on the final answers we give.  So unless your truth assignment can somehow facilitate my desire to solve actual problems and reliably predict the outcomes of my actions, then by definition and admission, it is irrelevant and worthless.  Pragmatic scientific method therefore is the ultimate measure of all philosophical truth. 


  1. Usually denoted as {T, F}.
  2. See tri-state logic
  3. See fuzzy logic
  4. Hodel, R. E, "An Introduction to Mathematical Logic," Dover Books (2013)
  5. Priest, G. "An Introduction to Non-classical Logic," 2nd Ed, Cambridge University Press (2008)