Wednesday, September 17, 2014

Truth

Adapted from my post in comp.ai.philosophy 2010-07-19
Thread: Truth (Was: Re: PROOF INFINITY DOES NOT EXIST!)


     I don't think "exist" is a good word to use about truth. I prefer "subsist" as the technical term. But that's a side issue. This sub-thread on truth is marred by an absence of definition. Exactly what is meant by truth? What do the other contributors to this thread mean?
     All the examples used are statements, which should be a clue. That is, an implicit stance in all the arguments so far is that truth is a property of statements. I don't think that is a good enough concept, as part two of this screed will I hope demonstrate.

A) Formal (logical) and contingent truth
     I taught formal logic in high school (I sneaked it in under the aim of "teach critical thinking"). As you might expect, some students twigged to the fact that "truth" is a vague, ambiguous, polysemous, slippery term. Our discussions covered the following points.
     "Logical truth" is clearly defined: A statement is "logically true" when it has the form X = Y, where X and Y are well-formed statements in some language, and the rules of inference allow the transformation of X into Y, and vice versa. Note that this is a characterisation of a statement.
     However, it is not clear that X or Y are themselves true. A logical argument can demonstrate that some conclusion follows from some premises. If the premises are true, then so is the conclusion. But logic cannot demonstrate that the premises are true. You can show that the premises follow from some other premises, and so on, until you get to the axioms. But the truth of the axioms must be assumed. Therefore we need some means for agreeing on the truth of the premises.
     At this point in the discussion, students started invoking experience, common sense, obviousness, etc. And realised that "what is true for one person is not true for another." It was difficult to get them past that, but in the end most accepted that some replicable procedure could guarantee a limited truth: If we have the same experience, and say the same or similar things about it, then the odds are that what we say is true, more or less. If we differ, then what we have said is more or less wrong. Since someone can always disagree about what we have said, all statements about common experience are more or less wrong (and conversely more or less true). This too is a characterisation of statements. Here we have contingent truth.

B) Truth as a relationship
     So, what do we mean when conceive "truth" as a property of statements? A statement is an image of a concept. It has the same relationship to a concept as a photograph has to its subject. Of both we say that they are "true" if we apperceive some similarity between the statement and the concept, the photograph and its subject. Ditto for a theory (model) and the slice of universe it refers to.
    IOW, "truth" is a relationship between image and object, where "image" can be a sentence, a picture, a piece of music, an equation, etc, and "object" is whatever those images "are about".
     That relationship between image and object is an unanalysed given: we either get it or we don't. It rests on some formal equivalences, on patterns. We are a pattern-perceiving species, so much so that we often perceive patterns "that aren't really there", in the sense that a slightly different point of view may destroy the pattern, while a "real" pattern can be perceived from several (sometimes drastically different) points of view. Science has been characterised as the search for patterns that remain the same no matter how you look at them: these patterns are called symmetries.
     In a sense, we are democratic about truth, as other posters seem to be claiming. That is, if a lot of people can see the same pattern from many different points of view, and/or if many people can replicate the pattern by some agreed-upon process, it is "really there." But we are also elitist: some patterns can be perceived only after more or less arduous training. But amongst those who have undergone this training, there is a pretty strong consensus on what the "real" patterns are, hence on what can be truthfully said about them.
     It should be obvious that consensus truths are contingent. They are also empirical: Some unanticipated future experience may change our notion of what they refer to, of their limits as true statements. This is so even in the realm of formal truths, where we often do not know a priori whether any two statements are logically equivalent, or whether some set of premises implies some set of conclusions. Only the experiment of devising proofs can decide the question. And those proofs may show that the equivalence or conclusion is limited to a range of values (i.e., objects that it refers to). In this respect, mathematics resembles empirical science.
     For more on how we arrive at some consensus about what's true, see Bas van Fraassen's The Empirical Stance (Yale University Press, 2002).
     Disclosure: Bas and I were classmates many years ago, and discussed much of what I've distilled above. He discusses these themes much more expertly than I can. Hence my recommendation of his book. We do not entirely agree: Ask two philosophers a question, and you'll get four answers. At least. ;-)

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