--- by JLS
--- IN "PREJUDICES AND PREDILECTIONS", which is the title I prefer for "Reply to Richards", (online books), Grice speaks of "Bootstrap". I may have quoted verbatim what the principle amounts to in the Grice Club. From memory. It concerns Russell's neologisms:
object-language (here the hyphen is important and the idea of 'object' IS important)
meta-language.
Let's use L1 and L2 for those. Since this is really a System. We can deal with the first order System GHP, or first-order System CR, alternatively.
(But there is the caveat that 'second-order' does not really necessarily MEAN 'metalanguage').
So, let's grab the piece by Grice!
--- He writes:
It is p. 93 of P. G. R. I. C. E., ed. Grandy/Warner (Clarendon Press).
He is considering points which I have discussed in the club, as to levels of priority and levels of conceptual priority, and subscripting to levels of conceptual priority (reminiscing this PhD I was referring to recently at the Grice Club regarding the point of the "... means ..."). In any case, Grice is being VERY general here, and surely he doesn't have just '... means ...' as his focus. He is considering sense-data, and moral/legal notions, too. He is considering ontology and epistemology (ontological priority, epistemic ontology), etc. He writes:
"It is perhaps reasonable to regard such fine
distinction as indispensable if we are to succeed
in the business of pulling ourselves up by our
own bootstraps. In this connection it will be
relevant for me to say that I once invented
(though I did not establish its validity) a
principle which I labelled as Boostrap. The
principle laid down that when one is introducing
the primitive concepts of a theory formulated
in an object-language, one has freedom to use
any battery of concepts expressible in the
meta-language, subject to the condition that
counterparts of such concepts are
subsequently definable or otherwise derivable
in the object-language. So the more economically
one introduces the primitive object-language concepts,
the less of a task one leaves oneself for the morrow".
I propose the above vis a vis Jones's VERY intersting reflections, here and in the other two blogs, Grice Club and Carnap Corner, about the role of metalogic in the development of twentieth-century logic -- a topic that fascinates us both. And Jones's expertise allows him to utter some very bold and inspiring and truly exegetical claims in the direction where progress should lead to.
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Here's how I think and talk about the kinds of issue which I imagine Grice to be approaching in this material.
ReplyDeleteIn my opinion the central problem here is what I call "The Problem of Semantic Regress".
This is the problem that if you want to define the semantics of a language then you have to use some other language (or possibly the same one) to present the definition. To understand the definition, you have to know the meaning of the meta-language (even if its the same as the object-language). If its the same the definition is at risk of being pathologically circular (I call these "meta-circular" definitions) and there are other problems which lead Tarski to declare (perhaps prematurely) the illegitimacy of such meta-circular definitions.
If you do, as Tarski prescribes, use a distinct (and "stronger") meta-language, then the regress, through meta-meta- and onward ad infinitum seems inescapable.
So "the problem of semantic regress" is how to define the semantics of a language precisely, given the Scylla and Charybdis of semantic regress and meta-circularity.
When Grice talks of pulling himself up by his bootstraps, I presume he is assuming, that when it comes to ordinary language, the required semantic clarification must also be in ordinary language (and hence the implicit meta-language is the same as the object language, if there is any point in trying to make the distinction in this case).
For the Carnapians, whose primary interest in this problem is in respect of "artificial languages", the situation is different, the meta-object distinction less sensibly disposed of, the choice between circularity and regress is harder to make and the defects of these schemes must be faced.
RBJ