[lit-ideas] Re: Is 'All men are mortal' unscientific?
- From: Robert Paul <rpaul@xxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 16 Mar 2008 13:41:58 -0700
The other day I wrote
"I was really worried though about Quine's definition. Surely, 'All men are mortal' doesn't readily translate into a proposition about only one x. One would hope that the original version there was a universal
quantifier, 'For all x, if x is a man, and so on and so on…'"
to which Donal replied
As I understand it, when Quine starts with "(x)", that "x" refers to any 'x' not a specific
or particular or singular 'x'. To say that "(x)" is to say "that for any given 'x'", not merely to
say 'for some special or unique x'. Once 'x' is deployed in this way it is clear that when speaking of 'x dies at t',
Quine is speaking of any given x. (And so is Popper)
Donal is confused. True, Quine does use use '(x)' to mean 'for all (any)
x…' This does not mean that every instance of the variable 'x' in
Quine's (or anyone else's) writings is a to be read as 'for all x.'
Children in British secondary schools are ill-taught if that is what
they're told. The difference is clear from this near-formalization of a
universal generalization taken directly from Quine
(x)(if Gx then Fx
That is: 'For all x, if x is G, then x is F.' All ghosts are friendly,'
'If anything is a ghost it is friendly,' and the like. Strictly speaking
(strictly formally) the words 'if' and 'then' would be replaced by '—>':
(x) Gx —>Fx
although in Quine's day what is now expressed as '—>' would probably
have been expressed by something like a horseshoe turned on its side,
the closed end to the right.
'(x)' as a universal quantifier is now almost everywhere replaced by an
upside-down roman capital A. When this news reaches British secondary
schools textbook publishers will have cause for celebration.
This is doubly-clear when we consider that different 'x's will die at different
times. For "All men are mortal" may be put as saying that for any given man
['x'] there will be a time t when that man dies: this does not imply all the men or their
times of death are identical of course, merely that they all are subject to this
universal 'fact of dying at some point in time'.
This use of (x) to mean 'for any given x' is taught here in secondary
school maths: so it is hardly that recondite or esoteric.
So I am unsure that Robert Paul has really anything much to be worried about here, never mind "really worried". Have a chill-pill on this on me.
His worries are also not germane to the main point of Quine's and Popper's discussion.
They are only germane to it if they clear up a confusion in the way
Quine's views are represented. If not, not.
Let me be express my worry simply. 'All men are mortal' cannot be
sensibly rendered as 'there is a time t such that x dies at t.' For (1)
here, 'x' ranges over one individual and (2) propositions about men
should mention (all or some) men at least once. Here, for all we know,
x is a woodchuck.
Robert Paul
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