Scary philosophy: Truth

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.

  1. 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…)
  2. 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…

Antisophie

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7 thoughts on “Scary philosophy: Truth

  1. I am interested in how philosophers would categorise the ways that I perceive truth.
    For me there is the truth I can feel in my heart, resonating with the essence of my being as an eternal example of beauty, or there is the cold hard clinical truth that I see with my mind, through the use of logic. Forgive my ignorance but could you spare some time to help me name these two in terms of your expertise?

  2. Sinistre:

    Good question. What kind of candidates count as true? Or Truth-bearing?

    One answer I could give would be: “It doesn’t matter so much”, we are trying to capture as philosophers, some intuition that goes beyond theory, and in doing so, we are making a model about any statement that involves the form ‘x is true’. Whether that involves the claims of beauty, or an inner conviction, or some putatively natural property fact, is irrelevant

  3. Michael:

    Hold on there, Sinistre; you mention natural properties? Perhaps there is a distinction between propositions that possess natural properties, and those which do not. G.E. Moore spoke of the porpositions of morality like “This is wrong” as being not subject to naturalist analysis, that is, they are in some way qualitatively different from “water boils at 100C” propositions. The poingnant point about non-natural property propositions are that we can always ask “but was it good?” or “but was it beautiful?”. This is what is referred to as the Open Question Argument.

  4. Antisophie:

    If I may interject, boys, I also have a problematic with your commonsensical view, Sinistre: INTUITIONS are our source of philosophical analysis? This is a somewhat troubling view; you depict that we start off with pretheoretic intuitions, such as believing things are true or false, like “Brahms is better than Beethoven” (that is, late Beethoven…); and then we move to account for all our intuitions through constructing a formal theory.

    Sometimes theory trumps intuition, and shows our intuitions are wrong (consider folk physics). You need to be more careful about intuiions…

  5. Michael:

    I think Antisophie’s concerns about intuition are correct, if I may synthesise both of your concerns about accounting for intuitions, my concern for a different class of non-naturalist proposition, and antisophie’s concern about assertoricity, I think we can find a worthy resolve in the Kantian system.

    To say “This is beautiful” is true, is a different kind of proposition to “this is a cat”, due to the concept-intuition relation that forms cognition. Furthermore, “this is beautiful” is a genuine judgment of taste if and only if (or ‘iff’) it assents to certain conditions that form aesthetic judgment; disinterest (quality) universality (quantity) necessity (modality) and communicability…

    Although that said, I don’t think a Kantian system helps a model of truth-theoretic modelling; but, it does, PixieLiz, provide an intuitive (yet theoretic) distinction between subjective (but assertoric, and universally valid) claims to beauty, and normal cognitive propositions.

  6. Sinistre*:

    You fucking pissant philosophers arguing over each other…we are supposed to be a united front!

    I think Michael’s response is the actual answer you want, Ms. PixieLiz

  7. The second incompleteness theorem applies to any finite (or effectively describable) theory formalizable in first order logic which is capable of modelling Peano Arithmetic. This essentially means any theory of sufficient strength. Most interesting theories are of this type.

    Also the second incompleteness theorem pops up in other logics whenever the system of proof is sufficiently clear and unambiguous to support the original argument. Amongst set theorists and others in related disciplines there is an intuition that there is no sensible (at least effective) logic which is not subject to incompleteness of both types.

    Personally I think second order logic is a sort of mirage. It looks appealing until you really get to grips with it when it turns out to be full of empty promise.

    PixieLiz: I find it interesting that you percieve different domains of truth in that way. I don’t think that these are actually different domains. However, it seems likely that they are manifestations of different processes in your mind and are so perceived differently by you. I don’t share this feeling of a sharp distinction between emotional and analytic truth. In fact I find that my perception of analytic truth is often accompanied by a soaring feeling of beauty or a warm feeling of opening a deceptively wrapped present (and my perception of emotional truth is not always accompanied by powerful emotions). I would suggest that your perception of separate domains of truth may be a type of inner perceptual illusion and does not point towards a deeper understanding of the nature of truth.

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