[lit-ideas] Some like Witters but Frege's MY man
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- Date: Thu, 19 Jun 2014 13:46:57 -0400 (EDT)
Understanding the Grundgesetze
L. Horn coined the F-implicatures, for Frege-type implicatures. After all,
like H. Paul G., Frege was obsessed with 'but' -- he called it the 'colour'
(not the 'implicature') of the truth-functional operator "&". But he also
dwelt with quantifiers.
Witters regretted this. As Palma explains:
"While for Spinoza axioms are in a quasi-Cartesian way "evident" for
Witters the propositions are the framing of what he took to be the thinkable.
One can see the Tractatus Logico-Philosophicus as a proposal for an ontology
of facts and a metaphysics of propositions. The logic is faulty and he
failed miserably when he tried reductive explanatory strategies (e.g see the
botched understanding of what a quantifier does in Frege's Grundgesetze)."
Exactly. Because what a quantifier does is a thing to behold and admire!
Now, McEvoy wonders
In a message dated 6/19/2014 9:59:25 A.M. Eastern Daylight Time,
donalmcevoyuk@xxxxxxxxxxx writes:
This sounds to me like just the kind of cobblers that both the early and
later Wittgenstein were dead against. In case I am mistaken about this, and
this is in fact what is claimed as "the case" "For W.", please could
someone explain how _from Wittengenstein's writings_ we arrive at the claim
'"the
tree is growing" is a fact ontologically prior to the alleged "thing"
called growth or tree."
If this claim is in W's writings I appear to have missed it.
It may do to revise Witters's botched understanding of what a quantifier
does in Frege's Grundgesetze.
Only when we have quantifiers do we have individuals over which those
quantifiers range.
Consider:
i. The tree is growing.
ii. The tree has grown.
It is true that the tree is growing (as opposed to 'ungrowing').
(i) is more or less equivalent to
iii. Some tree is growing.
As opposed to
iv. All trees are growing.
But cfr.
v. Trees grow.
On the other hand,
vi. Money doesn't [or don't, as Geary prefers -- he sticks with "Proverbs
Explained"] on trees.
vii. Some money doesn't grow on trees.
viii. It is not the case that money grows on trees.
Is it the case that it is not the case that money grows on trees?
Frege would recourse to quantifiers -- "some money" -- "all money" -- "no
money".
Only once we have determined and stipulated what individuals we are going
to deal with ("some money", "all money", "no money"; "some trees", "all
trees", "trees") can we capture the truth (or falsity) of claims.
But Witters never understood what a quantifier does in Frege's Grundgesetze
Cheers,
Speranza
From:
Zalta, Edward N., "Frege's Theorem and Foundations for Arithmetic", The
Stanford Encyclopedia of Philosophy (Summer 2014 Edition), Edward N. Zalta
(ed.), forthcoming URL =
<http://plato.stanford.edu/archives/sum2014/entries/frege-theorem/>.
"In his two-volume work of 1893/1903, Grundgesetze der Arithmetik, Frege
added (as an axiom) what he thought was a logical proposition (Basic Law V)
and tried to derive the fundamental axioms and theorems of number theory
from the resulting system. Unfortunately, not only did Basic Law V fail to be
a logical proposition, but the resulting system proved to be inconsistent,
for it was subject to Russell's Paradox. Until recently, the inconsistency
in Frege's Grundgesetze has overshadowed a deep theoretical accomplishment
that can be extracted from his work."
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