[lit-ideas] As far as I know, there are infinitely many stars
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sat, 8 Jun 2013 00:00:21 -0400 (EDT)
--- Grice, Way of Words, p. 163.
as an example which "would seem to involve nothing but an ordinary use of
language by any standard but that of freedom from absurdity." It is "not,
so far as I can see, technical, philosophical, figurative, or strained"; it
is an example "of the sorts of things which have been said and meant by
numbers of actual persons. Yet," it is "open, I think, at least to the
suspicion of self-contradictoriness, absurdity, r some other kind of
meaninglessness."
Cfr. Wittgenstein on finitism
and the footnote in Popper's book, to the effect that, in a finitist model
of mathematics, Euclid's theorem becomes, rightly, 'meaningless' (Popper's
term). ( -- cfr. Discussion by McEvoy, THIS LIST).
Indeed, Grice's favourite author (along with Kant -- vide J. Bennett, "In
the tradition of Kantotle"), Aristotle may be characterized as a strict
finitist.
Aristotle especially promoted the potential infinity as a middle option
between strict finitism and actual infinity.
Note that Aristotle's actual infinity means simply an actualization of
something never-ending in nature, when in contrast the Cantorist actual
infinity means the transfinite cardinal and ordinal numbers, that have nothing
to
do with the things in nature.
Aristotle writes in Book 3, chapter 6, of "Physics":
"But on the other hand to suppose that the infinite does not exist in any
way leads obviously to many impossible consequences.
There will be a beginning and end of time, a magnitude will not be
divisible into magnitudes, number will not be infinite.
If, then, in view of the above considerations, neither alternative seems
possible, an arbiter must be called in."
"Allow me to be him," said Grice.
Cheers,
Speranza
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