[hist-analytic] A Priori/A Posteriori -- Revisited

Roger Bishop Jones rbj at rbjones.com
Wed Nov 18 16:46:14 EST 2009


On Tuesday 17 November 2009 01:00:05 Jlsperanza at aol.com wrote:

> --- I am also reminded of Dummett, and Jones may like to elaborate on that!

Don't understand this one, did I mention him somewhere?

>  For the intuitionists, a proof (or justification) is something that _TAKES
>  time_: it's a step by step process. So, I guess they would go on to say
> that all  proof (or justification) is _a posteriori_. Yes, we have had
> rounds of  discussion discussing the a posteriori of mathematical truths,
> but the Dummettians take it _pretty_ seriously.

This is rather a nitpick, but you do seem simply to take orderings as if they 
were necessarily temporal and this ain't so, and prior and posterior are 
applicable in the context of any ordering temporal or not.  Strictly speaking 
the propositions in a proof are partially ordered by the transitive closure of 
the relationship "A is a premise from which B is directly inferred (in the 
proof)".  This is not in itself a temporal order, though the ordering might be 
presented temporally.  It might be spatially presented on a page, or it might 
be just something in the memory of a computer, neither spatial nor temporal.

I'm not familiar with the Dummett connection, I am very ignorant about 
Dummett's philosophy.

> -- I wonder if by merely analysing the 'proposition' one should determine,
> by the mere lights of one's intellect -- cfr. Enlightenment -- where the
> proposition 'p' requires an a priori or a posteriori justification. I would
> think so, but examples do not come out easily.

Before Kripke (at least, in Carnap!) this story was fairly easy, because the 
analytic/synthetic distinction coincided with the other two, so to determine 
the epistemic status you have only to decide whether the sentence is analytic 
of synthetic.

Nowadays you have to reject Kripke's analysis of the relevant concepts before 
you can work in this way.

>      "Computers can't think"
>
> strikes me as 'analytic' (true or false) rather than in need of a
> posteriori justification. On the  other hand, Noel Coward was possibly 
> being jocular when he wrote in his re-write of Cole Porter's "Let's do it"
>
>      "Probably we'll live to see machines do it" (Let's  do it, let's fall
> in love).

Those are both hard cases.  But I'm pleased to see that you assume a 
connection between analyticity and a priority.

> --   If I understand Jones aright, he is saying that Kripke makes  a
> distinction (between a priori/a posteriori) that conflates with the
> 'necessary/contingent', if not the 'analytic/synthetic'. Wasn't Kripke's
> idea  that while the apriori/aposteriori distinction is epistemic (or
> doxastic), the necessary/contingent is 'metaphysical', or ontic, and the
> analytic/synthetic logical? God knows!

The "essential" difference, between Kripke and myself and Carnap is that Kripke 
held analytic, necessary and a priori all to be distinct, whereas we hold them 
to be at least coextensional.  I don't know how he described the 
analytic/synthetic, I would call it semantic, and I would observe that in this 
matter semantics and metaphysics are intricately intertwined.
Kripke cannot separate the two and be considered to be using the same concepts 
as Carnap.  However, our recent conversations have been on the epistemic 
connection, and in this Kripke's distinctive conceptions are completely 
broken.

> Back to propositions, I was amused (in a good way) by Jones's pragmatism.
> Surely he doesn't need to _specify_ what a 'proposition' is, and he is
> ready to  have the notion as 'language specific' and 'contextual' in
> nature.

Yes.
The context in question here. is any context necessary to disambiguate a 
sentence, so that "the proposition" which it expresses is definite, bearing in 
mind that the one constraint I offered for the notion of proposition was that 
the proposition should embody the determinate truth conditions somehow (though 
it might be more than that).
So the context is used to identify the proposition, and the proposition is 
itself insensitive to (this kind of) context.
I think elsewhere the word context might have been used with reference to the 
"possible world" relative to which a propositions truth value is determined.
It remains of the essence of the proposition that its truth value (unless it 
be necessary or contradictory) will vary in different possible worlds (or 
situations if you like, or state descriptions).

It might be worth pointing out the differences in attitude towards propositions 
which I take (depending on "context"!)

The talk of propositions here is in the context of a discussion of Carnap 
against Kripke, and the doctrines in question (Carnap's at least, not 
Kripke's) relate primarily to formal languages rather than to natural 
languages.   These are languages which have been designed
by some person (or committee!)  and which have been given a 
formal semantics.  Now with the methods I advocate the notion of proposition 
would feature in such a semantics and its details would be chosen to reflect 
the desired semantics.  However, one very general approach would be to have a 
proposition as a truth valuation (map from possible worlds to truth values) 
and the only bit of that likely to change from one language to the next would 
be the domain, i.e. the notion of possible world.  So the language specific bit 
of proposition is the metaphysics you want to embed into the language.
On this conception metaphysics is a part of a formal semantics and this 
explains how it is that a semantic concept like analyticity turns out to be 
the same as a "metaphysical" concept like necessity.
Carnap has a different explanation, which comes from taking necessity as "true 
in all possible worlds" and analyticity (aka logical truth) as (following the 
tractatus) "tautological" i.e. true for all state descriptions.  (of course 
you have to abandon Wittgenstein's insistence on the logical independence of 
atomic propositions for this to work).

If one wants to talk about propositions expressed by natural languages the 
situation is much more murky, for two reasons.
Firstly if you take a proposition to be the meaning of a sentence (in 
context), then its not so easy to figure out what meanings are.
Secondly, if you want proposition to mean what it means in natural language 
then that is something else again (in that case there are diverse uses to 
grapple with). Those are problems which don't interest me.

On other hand, though in the account above in relation to formal languages, 
propositions are just conveniences in presenting the semantics, there are 
interesting issues which arise if you start to worry about the identity 
conditions, and these I think set you off in the direction of something I might 
call metaphysics.  We can devise any number of different
formal languages in which the truths of elementary arithmetic
are expressible.  According to the above notion of proposition,
what we might informally think of as being the same 
arithmetic proposition is likely to be a different abstract entity in each of 
these languages.  At the same time, though for many purposes taking a 
proposition simply to be the truth conditions will suffice, this has the 
opposite disadvantage, all necessary propositions turn out to be identical.

So if you want a notion of proposition which is not just good enough to 
express the semantics of some chosen formal language, but is good enough to 
reflect the possibility that the same proposition can be expressed in many 
different languages, and to ensure that propositions are not identified just 
because they have the same empirical content (truth conditions), then it gets 
complicated.  That's a bit of "metaphysics", I don't know how 
important it is, but most of my talk about propositions belongs to semantics 
not metaphysics

> I was  reminded of a similar 'pragmatist' (but he'd call it
> transcendental) approach to  'propositions' by Grice in "Prejudices and
> Predilections" (aka "Reply to  Richards").
>
> Drawing on conversations with Geo. Myro (the Russian emigre from Ukrania
> that Grice befriended since he settled in Berkeley in 1967 -- Myro had
> studied  in Oxford, but I'm unaware if they had met back then), Grice
> mentions that
>
>     what a proposition is
>
> may well depend on the theoretical role it may play in different
> approaches.

Yes.

> A proposition, I hold, is what a theory of "propositional
> attitudes" needs.

Yes, though that's not the only reason we need them.
I would say however, that much of this is more to do with convenience than 
necessity.
Its not so much that one could absolutely not do without them, but that it 
would be much more complicated to deal with such topics while eschewing a 
convenient ontology.

This kind of pragmatism, which is in the spirit of Carnap whose "internal 
questions" are the results of pragmatic choices of ontology in the design of 
languages, I would urge upon Steve B., who constantly worries about supposed 
metaphysical problems arising from a usage which need not be construed as 
involving a metaphysical commitment (especially when its Carnap and we know 
that everything which sounds like the kind of metaphysics which he proscribed 
really isn't going to be that kind of metaphysics, and who invented the 
internal/external distinction just so that he could talk as if he had a 
metaphysics but not actually take that extra (content-less) step).

> We need propositions to have the propositional attitudes
> (so-called, Grice prefered, 'psychological attitude') hooked onto
> something.

"propositional attitude" is better.
Its what its about that makes it interesting here, not the kind of thing that 
is about it, and we are really talking about propositional attributes which 
are not psychological at all. so maybe "attitude" too strong.
Necessity and a priority, then, are propositional attributes?

Incidentally one of the main points historically about these things is that 
they are places where some kinds of "transparency" fail, e.g. referential,
and so you can't substitute synonyms willy-nilly in propositions of which 
someones attitude is asserted. These failures of substitution give us clues 
about propositional inequalities (the proscribed kinds of substitution give 
different propositions, that's why they can't be permitted).  So they give us 
information about some kinds of information which there must be in 
propositions over and above truth conditions (though possibly only about what 
must be in the propositions expressed in this particular natural language, not 
necessary yielding metaphysical truths about propositions.)

>
>                 ----  believes that ----
>
> (For a psychological attitude like 'belief' holds between the 'arguments'
> of the believer and what is believed -- and beliefs and psychological
> attitudes  are, contra Quine, compositional and relational, no?)

I don't know what that means.

> A metaphysician may need propositions for other reasons, i.e. to fulfil
> other theoretical metiers. Myro's point was that there is NOT just one
> answer as  to what a proposition is, but many (or none).

But perhaps some are better than others.

> --- Grice played for years -- as evidenced in Reply to Richards -- with the
>  idea of a COMPLEX (or propositional complex) as being more basic than
> proposition! A propositional complex (I think I've seen the same idiom in
> writings by Peacocke) is just the schematism of the _content_ of a belief,
> say, into its minimal components (the belief that SOME cat, Tibbles, is on
> some old  rug in SOME kitchen, say -- rather than talk, in abstracto and
> out of context,  of the proposition that the cat sat on the mat).

But propositions are closed under conjunction, so isn't a propositional 
complex only doing what might as well be done with a complex proposition?

RBJ




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