FOM: What is f.o.m., briefly?
Roger Bishop Jones
rbjones at rbjones.com
Wed Oct 3 00:59:56 EDT 2001
responding to Robert Black Tuesday, October 02, 2001 9:52 PM
| My problem with Peter Schuster's one-liner is not 'a priori' but
| rather 'synthetic'. I take it as uncontroversial that Kant's
| explication of 'synthetic' (or 'analytic') is no longer viable
| (because the subject/predicate theory of logic it presupposes was
| shot out of the water in 1879 by Frege).
I have to disagree with you here.
I don't dispute that Frege was able to make major advances
in logic by discarding the subject/predicate theory, but
nevertheless when we look at more recent work we find
in Church's STT an w-order logic in which all sentences
exept "true" have "subject/predicate" form.
This is now a very widely used logical system
(as these things go) among computer scientists at least.
Kants other formulation (self-contradictory negation) is also,
though of limited utility, not wholly without merit.
(the attribution to Kant, in both cases is doubtful since
both these definitions, if not the word analytic itself,
are found in Liebniz)
Its worth noting here that Quine, modern arch-enemy
of the analytic, attributed the "true in virtue of meaning"
version of its definition to Kant (which is not entirely
unreasonable if you get over the Fregean critique of
"subject contained in predicate" and ignore the previous
semantic accounts by Liebniz and Hume).
| The only modern notion of
| 'synthetic' that I know that gets off the ground is the Fregean
| notion that, roughly, synthetic knowledge is knowledge that goes
| beyond logical knowledge.
In my opinion, "synthetic" is best defined as "not analytic"
and prefer the plain "true in virtue of meaning" for its explicitly
semantic formulation of analyticity (nothwithstanding Quine).
I don't know of any statement in that form
prior to A.J.Ayer's "Language Truth and Logic", though I
wouldn't be surprised if there were an earlier one.
| But it's not at all obvious that
| mathematical knowledge goes beyond logical knowledge because:
| 1) Whether there is a philosophically significant distinction between
| mathematics and logic and if so where it falls is up for grabs (is
| 'second-order logic' logic etc)?
But surely if you are a logicist there isn't a significant distinction
and you needn't worry about which arbitrary place to draw it?
| 2) Even if you've decided which truths are logical truths, you've got
| to decide whether or not the the fact that a logical truth is a
| logical truth (rather than just true) is a further logical truth
| (e.g. you could plausibly claim that the logical truths of
| first-order logic are all the logical truths there are, and for each
| of them the fact that it is a logical truth is not itself a logical
| truth but a truth of set theory - because the semantics of
| first-order logic is phrased in set theory - and ditto [perhaps in
| some ways even more plausibly] for second-order logic).
Whether the claim that some sentence S in a language L
is analytic, is itself analytic or not, depends upon how S and L
If L is given by a definition which includes its semantics,
and S is given by an explicit definition, then the claim
will be analytic.
If L is given by a definition along the lines "the language
predominantly spoken in the British Isles" then analyticity
claims will be synthetic.
If L, like "English" (or S) is not given by a definition at all,
then I guess you have to figure out what they mean
by the usual sometimes inconclusive methods.
There may be difficulty in some cases in settling questions
about whether claims about analyticity are themselves
analytic, but we cope well enough with our fallibility
in determining truth in other areas.
For those who would prefer to identify "logical truth"
and "analytic truth", (among whom, I like to think,
Liebniz and Hume would have numbered had the
terminology then been in place) there is no problem about selecting
which logic is "the logic", for all the theorems of any sound
logic are analytic (assuming "sound" is defined as "analytic
axioms, inference rules preserve analyticity" and "analytic"
just means "truth follows from semantics").
And set theory is also analytic and a part of logic once you give
a sensible semantics to the language.
| 3) There are still a few logicists around who believe that all
| mathematical truths are logical truths.
Yes, I plead guilty.
Or at least, I believe they are analytic,
(under any reasonable account of the
semantics of mathematical sentences).
and would prefer that we count all analytic
truths as logical.
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