Grice's eight 'inclinations' on the construction of a predicate calculus (Grice, in Davidson/Hintikka, p. 118-9)

by J. L. Speranza
for the Grice Club.

Grice notes that there seem to be at least eight 'natural inclinations' as they bear on the construction of what will transpire as his natural deduction system (that Myro dubbed System G, and I have elsewhere referred to as System G_HP). Let's revise them one by one.

First inclination:

"admit [the] individual constant".

What is an individual constant? It is not so much a constant which is individual. It's more, rather, a constant FOR an individual. I.e. a, b, c, ... in the logical vocabulary, and alpha in the metalogical vocabulary. In grammatical parlance, this amounts to admit [a] "name" (rather than a mere definite description). It clashes with the non-standard view held by Quine on, to use Grice's wording, 'the eliminability of singular terms, including names' (p. 118).

Second inclination:

"allow 'vacuous'[sic in scare quotes] names" -- Grice's example: "Pegasus". Grice's labelling here is informal. We say that 'Pegasus' is a 'vacuous' name in that "'Pegasus' "is not the name of any existent OBJECT".

---

Third inclination:

allow an individual constant -- e.g. "p" for 'Pegasus' -- "to lack [a designatum]" and thus allow that formulae about Pegasus 'may be represented in the system'.

---

Fourth inclination:

formulate ~ as contradictory negation. No truth-value gaps or non-bivalent logics allowed. Grice expresses this in terms of the 'categorial' subject-predicate "Fa":

If Fa is true, ~Fa is false, and vice versa, "in any conceivable state of the world."

----

Fifth inclination:

-- allow for a reading which yields 'true' (or 1) to "It is not the case that Pegasus flies" -- since Pegasus does not exist.

This is done via entailment, aided by implicature and disimplicature: "the king of France is bald" entails there is a King of France; "the king of France is not bald" merely implicates it.

----

Sixth inclination:

allow Universal instantiation and Existential Genersalisation "to hold generally".

----

Seventh inclination:

admit as theorem (x)x=x

---

Eight inclination:

suppose that if phi /- psi, 'any statement represented by phi ENTAILS a corresponding statement represented by psi'.