I was at a pretty fierce seminar with Michael last night; one of the things that Michael often says is ‘I don’t do “truth”‘. Theories of truth has become a very odd area of philosophy. It’s very scary, very scary. The seminar was concerned with a formal theory of truth. To try and put it in a little context, up until about 1903-4, every philosophy basically advocated a model of truth known as the correspondence theory. The correspondence theory of truth is highly intuitive, but almost hugely rejected. There are other theories of truth; identity theory, coherentist accounts, but the ones that I see people most fuming about are deflationary accounts and anti-deflationist accounts.
Truth is one of those areas of philosophy that integrate so many different areas; the philosophy of langauge, philosophical logic (arguably even mathematical logic), metaphysics and maybe some other stuff too like epistemology and philosophy of mathematics…
Some of you might be thinking, “Isn’t TRUTH the most important aspect of philosophy?”, isn’t TRUTH the most fundamental concept of reality that demands understanding? I answer to you, after scratching my head and thinking about it, yes, it is. But it’s damn hard. Kantian systematic philosophy is my upper limit of extremity in the comprehension of philosophy proper. Truth just blows my mind. But, being the daring idiot that I am, I try to understand the literature from time to time.
There were two interesting points of the seminar.
It seems that most of the formalisations of the theories of truth used first order logic, I found this curious, in that one of the counterexamples was a case that came from ‘Leibniz’ Law’. Or what should properly be refered to as the principle of the indiscernability of identicals (the leibniz connection isn’t really relevant in the modern literature). What one of my colleagues identified and correctly so, was that the formulations of the PII are putatively second-order. I wonder, what are the motivations for applying a model of truth to either first or second order logic; furthermore, what is significant about the two quantificational schemata that makes it significant when it comes to the truth predicate? (I think I just about understand what I said…)
Another point; how relevant is the Second Incompleteness theorem in regard to truth, or truth-theoretic models. I wonder, because I’m an idiot, if all theories are subject to the Godel theorems, or is it just Arithmetic as the candidate language? I hear often the suggestion that other theories are not subject to incompleteness. Perhaps this may lead to an answer to the first question. Are there any kinds of logic that are NOT subject to incompleteness; that is, is there a logical sentence that cannot be proven despite the axioms.
Truth really does my head in, I’m going back to Epistemology…