In defense of his Language of Thought Hypothesis (SEP article), Jerry Fodor argues that Thought is recursively compositional in just the same way that Language is. When we understand a sentence, we invoke a representational token that corresponds to the proposition the sentence expresses, and this token is itself broken down into different cognitive representational parts according to the same logical form as that of the sentence. So it's all very Russellian in spirit.
In theories of Truth, it's not always taken for granted that our languages of interest are compositional in the way that Russell's Principia Mathematica language was. Stephen Yablo's Groundedness interpretation of Kripke's theory (e.g. Truth and Reflection ('85)) implies that sentences can't universally be simply broken down into parts in a properly stable semantic evaluation. In some such theories of truth, the Liar sentence L: (
L <-> ¬T([L])) emerges as semantically sensible, but given a non-standard truth value, yet, for example,
T(L) v ¬T(L) must also be standardly true.
There seems to be some intuitive pull to the idea of recursive compositionality in logical Truth, and I'm interested in this from a constructive mathematics perspective. I'm philosophically curious to cash out and critique that intuition by wondering about the reverse implication to Fodor's: whether if thought is recursively compositional, thus language. I have a particular concern in mind (does Fodor present any argument for what use he makes of strictly finite or computable methods in his view of the mind), but all the questions below seem interesting.
- Is Fodor's general project (or Functionalism in general) known to be challenged by derivations like the Liar sentence, Godel sentences or Turing halting problems as features of natural or grammatical language, and does he address this anywhere in his work?
- Does Fodor have a particular preference for strictly finitistic or classical theories of logical consequence or inference that would prohibit Liar-style sentences or non-compositional features? Does he explore or argue for this at any point in his work?
- If Fodor thinks that language and thought both follow a Tarski-style logical form, and given Tarski's own theorem about the undefinability of Truth for metalanguage in object language due to the Liar paradox, does this make meta-theory (e.g. mathematical computation or complexity theory) impossible for Fodorian minds? Why/not?
For non-Fodorians, I would also be interested in how other computational theories of mental representation might respond to the above questions!