System GHP, System CR and Jones's Systems

By J. L. Speranza

JONES WROTE in his commentary to "System C_R and System G_HP"

"[Mine] is a first order set theory".

Obviously Grice was familiar with this, since often he would refer to set-theoretical concepts -- mainly in his attack of 'Extensionalism', which just ignores all that Carnap said about intensions or the mere possibility of defining intensions in terms of extensions. This is the only treatment of a bete noire in his "Reply to Richards". He tires with the details soon enough and proposes to deal with the twelve betes noires en bloc, as offsprings of Minimalism -- in THIS connection set-theory rears its head again, in that, for example, 'set' IS a sort of 'abstract entity' -- and thus Nominalism has to be refined to deal with the acceptance of sets. At some point Grice would say, 'rejection of all abstract entitities except sets' or something like that (as he tries to reconstruct rather than deconstruct the position). But in any case, Grice would prefer to talk of 'predicate calculus'.

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Notably in "Prejudices and predilections" he does mention the collocation, "first-order predicate calculus with identity" -- implicating that NO modal notions need be introduced -- which would have yielded a system like Kripke's System S.

When I look at the presentations of these calculus (the Praedikaet Calcul of the Germans -- based on the Propositional Calculus) I am sometimes intrigued by the ontological simplicity of it. It seems it is GOING to yield a pretty simple ontology -- i.e. the syntax (never mind semantics) is such, -- 'contrived' may be the word -- that it's no wonder that the ontology that it will be made to 'depend' on via the semantics will also be contrived.

Sometimes the way to distinguish a philosopher (such as Carnap, Grice, Jones, or Speranza) -- from a non-philosopher is to examine his reactions at the 'ontology', so I'm pleased that Jones likes to play with the ontologies and the semantics. The syntax, as Jones notes, has to reflect an ontology which will be as rich as we want it to make it -- to reflect what we see is the ontology of 'common sense' or 'ordinary language' or 'science' -- qua 'cathedral of learning'. This is QUITE a task!

In any case, Jones's use of 'first-order' merits a post, which I will entitle 'Bootstrap', soon.