System C, System G

By J. L. Speranza

R. B. Jones entitles his recent post, "meaningless 'systems'" or rather he refers to that phrase as provoked by Chapman on Grice.

The mention of 'system' is very relevant here.

Grice was fortunate to have a friend like Myro. In unpublished work -- but also in Myro's contribution to the Grice festschrift, Myro introduces the "System G".

This is of course apres Grice.

Grice had done the very same thing when inventing a System Q for Quine, which he had presented to the Quine festschrift. What amused me is that Quine responded, with a one-page long, "Reply to H. P. Grice" where he finds Grice's system to be 'forbiddingly complex' (Quine's word).

So we need a System C for comparison.

These Systems -- are indeed FL for short -- comprise

Syntactics: this is actually the _second_ component, since the 'vocabulary' is not even listed.

Semantics (optional): the truth-tables and the interpretations I, I', ... under a model M, M', ... etc.

Pragmatics (informal): where issues such as 'assertion', 'implicature' are considered.

So the idea of a 'meaningless' system relates to the "semantics" component. Many notions (if we may call them so) are perfectly manageable at the syntactics level only. This is the Hilbertian influence on Carnap. And it is what lies behind the very idea of a well-formed formula.

I often find 'well-formed' and 'formula' to trade on the redundant. After all a formula has to be well formed. An ill-formed formula is not a formula:

(x) Px --> Kx

Pirots karulise elatically.

is a wff.

The other possibilities

pirots elatically karulise

karulise pirots elatically
karulise elatically pirots.

elatically pirots karulise
elatically karulise pirots

seem okay but none of that freedom at the syntactic formal level.

Only

(x) Px --> Kx

is well formed. Also of course

(x) Kx --> Px
(x) Kx --> Kx
(x) Px --> Px

-- i.e. "Every karuliser is a pirot", "Karulisers karulise" and "pirots pirotise".

But you cannot have things like

Kx(x) Px-->

which is just an ill-formed formula, i.e. not a wff, i.e not a formula.

In some systems, any string from vocabulary items is deemed a formula and so the above "Kx(x)Px -->" would count as a formula. The syntactic rules (formation and transformation rules -- I'm using the latter apres Carnap) define a 'wff'. This gives 'wff' a value-oriented side to it. Like 'sentence', to use Grice's example, the idea of a formula is built upon our notion of a good formula, or well formed one. Etc.