# [hist-analytic] Carnap and Grice on "logical"

Roger Bishop Jones rbj at rbjones.com
Fri Mar 5 08:42:29 EST 2010

```On Friday 05 Mar 2010 07:08, Jlsperanza at aol.com wrote:
> In a message dated 3/4/2010 7:25:30 A.M. Eastern Standard
>  Time, rbj at rbjones.com writes:
>
> in first  order logic, none of the logical operators
> are  constants.
>
> -----
>
> Excuse me, again, my naivete. You mean they are not
>  non-logical constants? I can see that 'constant' has
>  these two uses:
>
> non-logical constant (of individual): a, b, c, ... n
> non-logical constant (of predicate): F, G, H, ...
>
> but there would be
> logical constant for 1-ary truth-functor: -
> logical constants for 2-ary truth-functors: &, v, ->
> logical constant for quantifier: (x), (Ex), (ix).
>
> --- And what Toulmin seems to be saying as per you above,
>  that the choice of the logical constants in a language
>  is a matter of choice. Modal logic alla  Kripke, for
>  example, has the Nec. operator as a logical constant.
>  Hintikka's  doxastic logic may have "Bel" as a logical
>  constant -- although it looks  like a common-or-garden
>  dyadic predicate to me. Etc.

Well we are talking about usage here, usage of the term
"constant" which is not uniform across different disciplines
and contexts.
Let me be more explicit about the contexts in which the
claims I made are normally accepted.

First there is Wittgenstein's denial in the Tractatus that
there are logical constants.  What do we suppose he meant by
that?  My guess is that he was denying that the operators
such as \/ and /\ are names of existent entities.  So his
denial is a little bit of dogmatic nominalism.

The logical system in the Tractatus is quite precisely
identifiable as what logicians call first order logic (in its
simplest variety, without functions, without equality).
Its precise delineation can be seen because Wittgenstein's
defective apercu which he is keen to press, is that logic is
truth functional and that logical truths are tautologous.
He has Hume's fork in mind here, he wants there to be just
the logical truths and the empirical ones, and so he wants
the non-tautologies to have real empirical content (which he
later discovers to be not the case because of things like
colour exclusion principles, "~(red x /\ green x)"..).
He also excludes equations as propositions because they
don't fit this picture, which gives him a pretty naff account
of the status of mathematics.

Anyway if we come to first order logic, which belongs to
mathematical logic rather than philosophy, and consider the
language they use, it is pretty similar to Wittgenstein's.
They don't make the metaphysical pronouncement, but what
they mean by constant is very specific.  It is a name
denoting a fixed value in each interpretation of a first order
language, and which may only occur in certain places in the
syntactic structure of the language.  The places you can put
such a constant are distinct from the places in which you
can place a logical operator.  Mathematical logicians in the
context of talking about first order logic, simply do not
count "and" "or" etc. as constants.

However, sticking to the "constant is a name" paradigm, when
logicians talk about higher order logic (at least in
Church's formulation) then the situation is entirely
different.  In Church's STT (on which HOL is based) the
logical operators are bona-fide constants.  They name certain
functions in the domain of discourse.

However, going back to the philosophers, thinking again of
Tarski and Quine debating the relationship between logical
truth and analyticity, here it is not constants which are at
issue, even though they may talk about "logical constants".
The issue at stake is how much of the semantics of the
language can be taken into account in determining whether a
sentence is a logical truth.  If we insist that only the
"logical" features of the language can be taken into account
then we get a narrower conception of logical truth than of
analyticity, but we also get one which must surely be
language relative, and therefore does not really warrant (in
my opinion) the very nice label "logical truth", which
should go to something really important, like Hume's "Truths
of Reason" or Aristotle's "Demonstrative (or intuitively
certain)" (which is one of the ways Hume explicates "truth
of reason").

RBJ

> Grice was possibly upset that Quine did not take the
>  "Defense of a dogma" seriously enough, as coming from
>  two 'ordinary-language philosophers'. This must  have
>  hurt Grice quite a bit -- especially since he would
>  remember his own  polemics with Strawson on this -- and
>  the next thing he was mixing with all the  possible
>  logicians in the area -- both East (Boolos, Parsons) and
>  West (Myro,  Mate) to get to see if he could provide a
>  better definition of 'logical', inter  alia.

What Grice failed to understand was what Quine had learned
by observing the attitude of the Viennese rednecks
(excepting Carnap) toward Wittgenstein.  Viz. that the
ultimate token of respect for a philosopher, and what a
philosopher must aspire to inspire in others if he is to be
of the first rank, is

```