[hist-analytic] "Ordine geometrico demonstrata"
Jlsperanza at aol.com
Jlsperanza at aol.com
Mon Feb 23 21:12:02 EST 2009
I'm enjoying the exchange Bishop/Bayne. I'd like to drop to the annals of
Spinoza's "more geometrico"
This seems to have been more influential on the Continent than on the Isles,
but then S. N. Hampshire did write a Penguin book on Spinoza.
I do not know as much as I'd need to know about Greek mathematics, but I
wonder sometimes if geometry is more basic than arithmetics. Or why would
Spinoza dub his thing 'more geometrico' rather than 'more arithmetico'?
>From online source:
"Baruch de Spinoza attempted to improve Descartes philosophy
by mathematically axiomatize philosophical thought into a coherent system
(starting definitions, axioms, postulates, theorems with their demonstrations)
= more geometrico (in the geometrical manner)."
I note that his fist book was on the principles of philosophy of Descartes
'MORE' geometrico demonstratae.
The 'Ethica ORDINE geometrico demonstrata' is later.
I always found that the way Grice 'caricatures' the 'formalists' (as he then
called them) in 'Logic and Conversation' (WOW, ii) -- first page -- is right
into the 'heritage of Spinoza' if you think about it (and even if you don't).
>From Bishop's notes:
I note that in his notes Bishop mentions the "Prolegomena" remarks by Grice
(re: Strawson (1952):
>"expressions which are candidates for being natural analogues to logical
By way of critique, as Bishop charmingly puts it:
>I was rather pleased to see Grice's list,
[which includes Strawson 1952 -- and hence the title "LOGIC and
Conversation" for the second lecture]
>for it contains many examples which I have come
>across and which I have previously myself felt to be unsound.
Exactly. But it would have been _anathema_ to contradict Strawson where I
>Pleased to see them, I suppose, because my familiarity
>with the literature has been insufficient for me to have seen
>these criticised before.
And Grice is being charming himself. For Strawson does acknowledge "Mr. H.
P. Grice" as his logic tutor "from whom I have never ceased to learn from logic
since he taught me in that area" (or words to that effect). A bit like
overqualifying the thing. ("just a logic tutor") but let that pass. (The memoirs
by J. D. Mabbott here are a delight. The man was Scots born, Mabbott, and in
his "Oxford memoirs" (published by a minor publisher of Oxford) wants to say
that Strawson was by far his most brilliant student (tutors have to be careful
there). He goes on to add, by way of support, "And so seems to have thought,
too, his other tutor at St. John's, the 'excellent' H. P. Grice" -- or words
to that effect. Or 'intelligent'. Mabbot retells in detail how Strawson came
out, poor thing, with a second, rather than a first. -- But we don't have to
spread _that_ news.
But this notes how parochial the whole thing was for we have:
1940s. Seminars Grice/Strawson (indeed Strawson was appointed Grice's tutee
-- _before_ the war, as I recall).
1952. Strawson, Introduction to logical theory. Methuen (crediting "H. P.
Grice" -- where? In connection with 'informativeness' -- one brief footnote).
1966. Chomsky cites "A. P. Grice" in Aspects of the theory of syntax" with
regard to the logical behaviour of 'and' (implicating: 'and then').
1967. Logic and Conversation, by Grice. Resuming the polemic.
------ But by 1967, Grice was able to provide a 'larger' picture. Strawson
comes out as an 'informalist' (later a 'neo-traditionalist'), opposing the
'doctrine' of the formalists (Quine, Russell/Whitehead) later called
'modernists' (heirs of PM).
Grice's point is that both camps _share_ the view that there _is_ a
divergence between, to use Bishop's wording -- citing Grice --:
(a) "expressions which are candidates for being natural analogues to logical
(b) "logical constants proper". Grice mentions the truth-functors but also,
let's recall the universal quantifier, the existential quantifier, and the
iota operator -- which are not truth-functors. Hence his label of them as
'(formal) [i.e. structural] devices'.
----- Personally, other than the Grice/Strawson polemic, I don't think I
recall anything as systematic in the American literature. Grice does suggest
that some philosophers (before him) have noted that there may be something
'unsound' about this -- i.e. that the divergence is _seeming_ rather than real.
(Also, Grice pedantically but so rightly puts it, "the thesis that there is,
or there _seems_ to be a divergence between..." -- for as things develop, he
would claim the divergence is a matter of implicature, i.e. _seeming_ and not
truth-conditional, in a way -- cfr. his "Valediction" or retrospective
epilogue which _notably_ focuses on the polemic with Strawson rather than any big
more fashionable issue of implicature per se -- I found that refreshing, that
he goes back to the source of inspiration of it all: Strawson and his
Now, I once tried -- and I think I did list in my PhD dissertation -- all
the postulates Grice _requires_ for the 'formalist' credo. They are quite a
bunch. They all sound, now having refreshed my Greek Mathematics (with Thomas,
and his two-volume Loeb) that it's the _axiomatic_ treatment, the Spinoza
'ordine geometrico' that he is talking about. Gentzen was just publishing those
things (right?) and Grice will have occasion to present a cruder version of the
'formalist' credo in his contribution to the festschrift for Quine ("Vacuous
Name", in Words and Objections, ed. Davidson/Hintikka, 1969).
In the Quine festschrift, Grice does stick with Gentzen's idea that for each
operator (or device) we do need a (+) rule and a (~) rule: introduction and
elimination, and proceeds to provide truth-table compatible introductions for
the functors and the quantifiers. This is clearer than most of what Grice
really does in "Logic and Conversation" which is merely jocular in the best
sense of 'jocular'.
I think it was Aloysius Martinich (the Russian-born philosopher at
UTexas/Austin) who noted this: they say 'Logic and Conversation' (WOW, ii) is a
_masterpiece_ of an essay, but on second thoughts, it's pretty inconclusive and
there seems to be a quick change of topic.
When Bishop summarises the chapter in his online notes, he goes straight to
Grice's definition of his term of 'art', "implicature" (I noted that Sidonius
uses 'implicatura' in his Loeb -- cited by Short/Lewis, though!). But it
should be noted that the discussion of 'implicature' (a special section)
_follows_ the account of the 'problem' (as Grice saw it) and the two tenets who share
a 'common mistake'.
I would think that Grice believed to his last day that the formal devices
can indeed be _saved_ by all means. I.e. an axiomatic treatment is possibly the
best thing to do cognitively.
But he was ready to admit or allow that in other areas, notably, the 'ordine
geometrico' (which seems to work best with 'extensional' rather than
'intensional' categories, including 'modal') seems more of a strain (if that's the
word) than anything 'liberatory'.
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