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

[Roger Bishop Jones]

On Friday 12 Mar 2010 18:23, Jlsperanza at aol.com wrote:
> In a message dated 3/10/2010 8:49:34  rbj at rbjones.com
>  writes as per  below. Sorry for typo. Indeed I did mean
>  the Grice/Tarski interaction, not Tarski's interaction
>  with himself. R. B. Jones writes: "The most revealing
>  reference for Tarski is his paper, "On the concept of
>  logical consequence" ... conspicuously inconsistent".
>  since he muddles mathematical 'induction', algebra, 
>  non-logical with logical consequence ... shows Tarski to
>  be in a complete muddle  on this matter". Sad, my logic
>  tutor, G. Palau, wrote her PhD on "logical  consequence"
>  so I should ask her! --
> 
> But isn't 'consequene' really the
>  .
> .  .
> symbol used by logicians.

Certainly closely connected.

There are two other signs which are used metatheoretically:

" |-"  (turnstile) which is called "syntactic consequence"

	"P |- C"

means that sentence C can be proved from assumptions P in 
some deductive system.

"|=" is called "semantic consequence"

	"P |= C"

means that sentence C is entailed by premises P,

When "logical consequence" is used on its own in my 
experience that usually means semantic consequence or 
entailment.

The three dots are used to introduce a step in a proof.
It is short for "therefore", and so means that the following 
sentence "follows" from the preceding ones.  This requires 
that it obtainable by something that would be acceptable as 
a single step of inference in the relevant context (i.e. one 
does not need to supply more detail for this to constitute a 
proof).

Logical consequence does not have that characteristic, when 
we say "P |= C" we do not even state that there is a proof, 
let alone offer one.  Even if we say "P |- C", we only claim 
the existence of a proof, we are not necessarily offering 
one, and we are not saying that C is obtainable from P by a 
single proof step (which is implicit in the use of the three 
dots).

> As in Grice's example
> 
> "He is an Englishman;" Jill said of Jack, "He is,
>  therefore, brave"
> 
> Jack is an Englishman
> ----------------------------------
> Jack is brave.
> 
> Surely that is NOT a logical consequence, but it is a
>  consequence. I never understood the difference between a
>  conclusion and a consequence.

Conclusion is a bit vague isn't it.
One can have invalid or unsound conclusions, which is what 
you have if your conclusion is not actually a consequence of 
your premises.

Also "conclusion" is just a proposition, whereas a 
consequence is a relation between a conclusion and some 
premises.  i.e. one says "consequence of...(some premises)" 
but if one says "conclusion of ..." then one is talking 
about the thing which drew the conclusion not the premises 
from which he drew them.

>  But I suppose with a tweak
>  here and there, we can combine both notions.
> 
> If Tarski is considering algebra, which does rely on
>  'mathematical intuition', then, not all of the algebraic
>  consequences are logical ones,  right?

Well he doesn't say he is.
His paper begins with him expressing that any formalisation 
of the concept of logical consequence "will show arbitrary 
features to a greater or lesser extent", and he ends up 
locating that in the location of the boundary between 
logical and extra logical expressions.  So to that extent my 
slurs are out of order, he ended up with a position 
consistent with but more informative than his starting 
point.

However, the first thing he does is to strengthen his 
negative point by showing the inadequacy of certain attempts 
to formalise logical consequence, and it is the example he 
uses here which (if accepted) would entail that arithmetic 
is part of logic.

(He cites an w-incomplete system i.e. one in which every 
instance of some property of natural numbers is provable but 
the general claim is not.
He says it is intuitively quite clear that the universal 
sentence follows from the particular sentences.)


> ---- The problem with Grice at this stage is that he
>  found "implicit" premises leading to strict consequence
>  to be of more interest than actual 'proofs'. So that he
>  spends like 2 pages considering the different premises
>  that would make
> 
> Jack is an Englishman
> ---------------------------------
> Jack is brave
> 
> a sort of 'consequence' --. It could WELL be 'inductive'
>  -- almost in the mathematical sense. I.e. Jill believes
>  Englishmen TEND to be brave.  Etc.
> 
> At this point Carnap would allude (or refer explicitly)
>  to the 'meaning' "postulate"
> 
> (x)Ex --> Bx
> 
> If x is an Englishman, x is brave.
> 
> In which case we do need that as a premise to turn the
>  'consequence' into a logical one, no?

I think (would expect) that the meaning postulates count as 
axioms, and are not therefore needed as premises.

> "I think I probably will have to do that before
> long!" (read Quine in  Schilpp).
> 
> I wouldn't bother. I'd just read what Carnap understood
>  about it -- Now if a QUINEAN would be welcomed above
>  board by us, that IS a different issue!

Well I need to do it anyway for my Opus in progress (or 
about to progress, I'm hoping) in which an unravelling of 
Quine is called for (and will be addressed at the outset, of 
the writing if not of the book).

> :).  Oddly when I read Grice's contribution to the Quine
> : festchrift I almost
> 
> missed  Quine's reply -- so short -- have a page -- that
>  I almost found it insulting --  "Grice's doctrine", or
>  words to that effect, is "forbiddingly complex" -- he 
>  fails to mention the law that makes this illegal -- and
>  "in any case, otiose".  Ah well. He says that the way he
>  (Quine) uses symbols, he doesn't need any  scope
>  indication device for things. They are by default
>  understood as having  maximal scope in the order in
>  which they occur.

I can't say I'm surprised. However little I like the man or 
his philosophy, I can't deny that his competence as a 
logician outstrips not only Grice, but even, comfortably, 
Carnap.  Maybe even Russell, though its hard to compare 
across generations during a period of such rapid 
advancement.  Given his temperament and possible antagonism 
over Two Dogmas, Quine is unlikely to pull his "punches".

> On Quine's 'Two dogmas' as meant to undermine Carnap's
>  and Grice's campaigns:
> 
> "there is no case to answer
> (this is what Grice and  Strawson did)."

(after writing that I thought it perhaps not the best 
characterisation,  Its more that they took him to be 
attempting to impose an exceptional standard, and that by 
any normal standard for philosophical concepts "analytic" is 
unproblematic?)

> Right. Critics and defenders of the analytic-synthetic
>  distinction have only superficially read the
>  Grice/Strawson defence as concerned with NL rather than
>  FL, while it seems pretty easy to provide analogues of
>  Grice's and Strawson's examples of the type that would
>  relate to Carnap's enterprise.

The case is easier to make for formal languages, which are 
devised specifically to be more precise.  (notwithstanding 
Quine's arguments to the contrary).

RBJ