Bootstrap: System CR, System GHP

by J. L. Speranza

THIS MEANT as commentary to Jones's commentary -- but system disallowed it. It's all about 'pulling oneself up by one's bootstraps' in special connection with something like Carnap's System C_R and Grice's System Q which becomes Myro's System G_HP.

Very good points. Indeed, System G_HP is intended as a 'model' of, say, say English. I call it "H. P." to refer to 'highly plausible' or 'hopefully powerful' -- while sticking to the initials of Grice being H. P, Herbert Paul.

And you are right that it's not meant as a 'meta-language' in principle. Indeed, in defining System Q (which is the one that Grice himself created) he uses natural English, ordinary English, as the metalanguage for his Sysem Q (and Myro does the same when defining his System G -- on which System G_HP is based. Consider:

"If phi is a formula, phi /\ psi is a formula".

That simple enough 'formation rule' for System G_HP -- actually subscripts for the three elemnts of "phi /\ psi" would be needed -- may cover some complexity should we want to define it in the object-language of System G_HP itself. For it involves a sort of predicate-calculus, and we are dealing with the propositional-calculus segment of System G_HP. For " ... is a formula" is really quite a piece of work, if you ask me! In any case I would think that Grice intends his System Q to cover BOTH the object-language (L1) and the meta-language -- but I would need to revise this. Similarly, in WoW:first two pages of 'Logic and Conversation' when he paints the picture of the Formalist (alla Hilbert) as dealing with a 'set of formulae' which may be taken as axiomata, etc., he seems to be talking of 'system', as he indeed is, as the 'proper' set of formulae -- 'proper' in the sense of 'itself', not qua technical term in set-theory! -- rather than as the set of formulae cum editorial work that the meta-language L2 may provide. But this may be tricky. In any case, there seems to be some sort of regress in that if, as Grice thinks, the formalist's point in constructing L1 is to free the language of 'metaphysical excrescences', what would the point be if any such excrescence, metaphysical or other, is brought onto the system via the meta-language?

Tarksi is a good case in point, maybe -- for I thought his "Semantic definition of truth" FULL of metaphysics at the meta-level. And it may be something like an examination of work being done by Davidson at Berkeley that had Grice formulating Bootstrap in the first place! (I am referring to Davidson on his "Truth" essay in Synthese that apparently had a big influence on Strawson's student, Strawson). But will re-read stuff and elaborate (mean: think). Thanks for input.