My postmodern defence of truth
Postmodernists are correct that truth depends on meaning yet meaning does not arise arbitrarily
Quine famously attacked the very concept of an analytic vs synthetic distinction. Analytic statements are tautologies - true by definition. For instance, “all bachelors are married”, “all triangles have three sides”, and “2+2=4” fall within this category. Meanwhile the truth values of synthetic statements depend on whether such values correspond to the actual state of the world. A prime example would be “all bachelors are unhappy”.
If a statement is true by definition, then it poses the question of what counts as a formal definition, and what makes such correct. This is not so clear cut. The convention is to use the standard rules of deduction given by propositional and first-order logic, whilst performing that arithmetic with the Boolean values to test whether the final statement is tautological. Remember your introductory logic class at college/university? However, the law of the excluded middle and double negation remain contested rules, and alternative logic systems such as intuitionist or Gödel logic have arisen as answers to such debates. Therefore the validity of a definition rests in part on our subjective assumptions on which set of deductions are valid.
Quine's solution is that knowledge and truth operate on an underlying web of connected beliefs over truth values and definitions. If our beliefs are revised, then the analytic statement no longer remains analytic. For instance, suppose that we suddenly change the law and redefine the very concept of a bachelor. Or we use an entirely different group (e.g. modular arithmetic) for our daily calculations. Then “all bachelors are unmarried” or “2+2=4” no longer become analytic. The former depends on our definitoon of bachelor. The latter becomes (2+2)mod1 = 4mod1 = 0, if we want our formal system to always return an empty value for any inputs, and use mod 1 arithmetic to achieve this. So in principle there are no a priori formal restrictions on what counts as truth. Truth is endogenous to our use of language.
A more grounded example is that if an object is uniformly red, this is incompatible with it being uniformly black. However black-and-white photography uproots this entire statement. Perception of colour depends on our mental states, which introduces some degree of subjectivity. The sorts of questions raised via discussions of qualia and our consciousness (for instance, is my red your black?) also undermine the notion that this is an analytic statement.
All of this sounds rather postmodernist. Yet neither is Quine nor I rejecting the very existence of objective truth. It does not follow that, because we lack a fixed and uncontested formal system and set of definitions to define truth ex-ante, objective truth per se does not exist. Our belief systems do not just arbitrarily arise out of thin air, yet are connected deeply to the reality under which the world operates and we live in. This must be the case for our beliefs and languages to yield any sort of utility. We define a concept of a bachelor as our legal and social institutions rely on such a distinction being made. We use base 10 as opposed to modular arithmetic, as we obviously need to count physical objects as they exist around us. Perception introduces a wedge between the mind and objective reality, yet survival relies on either a highly accurate approximation of reality or the ability to accurately perceive most of reality. If my green is your blue, then as long as us two independent observers agree that it is the same colour, then this is the best we can expect when definiting what counts as objective reality? If subjective perception does not generate meaningful variation in observations, then we have just introduced meaningless circularity that for practical purposes do not add to any understanding of our world, so can be erased.
In general, Tarski sought to overcome this very epistemic relativism. Truth is to be defined via correspondance with a formal system and a meta-system that holds the Boolean values consistent with empirical reality. The beauty in this correspondence is that the very concept of an analytic definition is preserved. We also eliminate any concerns over our use of the excluded middle and so on. If our tautologies and our truth values given by classic logic correspond with our meta-language as given by our beliefs and those truth values, then the distinction very much holds. In this sense, I subscribe to Hilary Putnam's solution to the dilemma.
Likewise, as Donald Davidson advocates, if truth is conditional on our semantic meanings, then we only need to know such semantic meanings to determine whether a statement is analytic. For instance, I only need know what the term “bachelor” means, in tandem with some fluency in English, to know that “all bachelors are unmarried”. In a sense, a semantic interpretation of meaning is sufficient for our meta-language.
What determines semantic meaning? The utility of our words as they correspond to the reality in which we operate in. Postmodernists are correct that meaning is ascribed by ourselves and our societal institutions, as opposed to just arising, yet such meaning yields a vital connection to reality. Even if truth is dependent on meaning, this should not be stretched to imply that objective truth does not exist.