Carnap and Grice pulling ourselves up by their own bootstraps

by JLS

THIS WAS MEANT as comment to the previous post, but system disallowed it.

Good. Yes, there must be something Tarskian behind this. Grice refers only briefly to Tarski in WoW:55 re: "Monkeys can talk", when he writes: "A theory of truth has (as Tarski notes) to provide not only for occurrences of true in sentennces in whch what is being spoken of as true is specified [in the object-language] but also for occurrences in which no specification is given (e.g. The policeman's statement was true)."

(Grice thought that Strawson's and indeed Ramsey's (whom he also quotes on that same page) failed to provide for that.

But I'm not sure about the NL-FL (natural-formal language) distinction at this point. Yes, there must have been something along that line in the Carnap-Grice difference of outlook. But I would think that syntax, even in NL, allows for a pretty easy way to mark the object-language/meta-language distinction: the simple quotes or scare quotes --. So, even in terms of syntactic admissability (which you say you are laxer when it comes to something like a System, and like to indulge in the semantics-ontology interface) I would think Grice is seeing a bigger problem there.

It would seem then that we do have an user of the L₁ -- this may be a given. A system like System G_HP, or System C_R, aims at reconstructing or constructing a segment of "NL" (or the language of scientists in Carnap's construal) as it is used (provisos there). But what about L₂? This is the system-analyst's job (There IS a discipline, 'systems analysis', no?, so I propose such a reference when we talk of approaching a System like System G_HP or System C_R --. A mere truth-functional equivalence, of the Tarski type, to allow for the specification of what the policeman said as true may be complexer than it sounds. For we will not be satisfied with 'Monkeys can talk is true' iff monkeys can talk. In 'elucidation' of various types, including philosophical, if we were asked to provide a truth-functional equivalence of "Monkeys can talk" we may rather be inspired to provide an excursus onto what we mean, in the object-language, by 'monkey', by 'talk', and by 'can'. Suppose we arrive at the conclusion that it means, 'Any specimen s of Pan troglodytes has a procedure in the repertoire which has a finite set of initial devices, together with semantic provisions for them, and a finite set of different syntactical operations or combinations, and an understanding of what the functions of those modes of combination are, so that s can generate an infinite set of utterances or complex devices, together with a correspodningly infinite set of things to be communicated by them" (apres WoW:296). Even here we would be using 'talk' in scare quotes, since apparently, Nim Chimsky may be said to 'talk' rather than talk -- i.e. the malleability of the phonetic apparatus seems to be missing.

But I don't think Grice was into specific claims in the object-language, "Monkeys can talk" that may need an elucidation in terms of the meta-language. Rather, as I believe Jones does, too with his interesting notion of semantic regress and meta-circular definitions, and the brilliant idea of the Scylla and Charidis -- bewteen meta-circularity and regressus ad infinitum -- the problem lies at the heart of the 'constructivist' enterprise.

In any case, it is a good reminder to keep a good eye on what logicians mean when they jump to metalogic (as some of them do) in a way that they think washes 'their hands' with respect to the object-language.

The 'order' index may be indicative too. System G_HP, or System C_R, may be thought of as a language, L₁. But what about L₂. As Grice describes System Q in his "Vacuous Names", he uses English, indeed, not System Q itself. But is this a mere 'abbreviatory' manoeuvre? We hope so. But are we sure? The point may be trickier. In an introduction or elimination rule for a connective, say, when a System like System G_HP uses the very idea of 'valid' inference, isn't it a bit of an 'act of faith' that such openly 'meta-linguistic' operation will yield an expression in the object-language? In some logic tracts the meta-language (meta-logic) is so much richer that one doubts! Or consider the semantics, where it interfaces with the ontology (or metaphysics as Grice would prefer -- recall that Part II of WoW is entitled, "Explorations in semantics and metaphysics" --. When the meta-language (in System G_HP) speaks of 'Corr (1)', correlation with truth, and 'Corr (0)' and correlation with falsity, as it provides the 'truth-tables' for each operator -- e.g. monadic or dyadic truth-functors -- what would THAT statement, i.e. the statement of each such correlation -- yield when expressed in the object-language. I AM hoping that Tarski was, as Jones said he was, 'premature' in rejecting meta-circularity. I am positive that Grice loved a circle! (WoW: Meaning Revisited -- last section, is all about Schiffer's allegations of circularity in Grice and he goes on to bring in the platonic "circle" as a case in point to prove Schiffer wrong!)