[lit-ideas] Re: Ruth Barcan Marcus 1921-2012
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sat, 17 Mar 2012 14:37:42 -0400 (EDT)
In a message dated 3/16/2012 3, donalmcevoyuk@xxxxxxxxxxx quotes from the
bit in the NYT obit by S. Neale:
>>'Under her formula, “the second one entails the first one,” Professor
Neale explained. “That is, if all >>humans >are necessarily mortal, then
necessarily, all humans are mortal.”'
>I think this claim is wrong: if all actual humans must die it does not
necessarily follow that all possible >humans must die. Surely (unless we deem
all actual humans to exhaust the category of all possible >humans)?)
and later, in his reply to Palma:
>my post was an attempt to put >what I understood to be the logical point
at issue in ordinary language, and >to pass comment that it would seem that
"if all actual humans must die it does not necessarily follow that >all
possible humans must die...(unless we deem all actual humans to exhaust the
category of all possible >humans)".
>The point at (b) raises a number of questions - like whether this is an
accurate way to convey the logical >point at issue in ordinary language and
whether the logical point depends on what we "deem" as the >relation
between "actual humans" and "all possible humans". These questions are not
answered by >pointing out that 'Barcan's formula is a theorem' or asserting
that
'an objection cannot be detected'.
Perhaps symbolism may help.
Humans are mortal.
S is P.
All humans are mortal -- or every human is mortal, as I prefer, to stick
with the singular "is" in S is P.
Some humans are mortal; indeed all are.
cfr.
Socrates is mortal.
Socrates must be mortal.
Socrates must be human.
Cfr. Barcan Marcus's theory of the 'tag', as per wiki entry for her.
Universal quantification (substitutional or other) gets tricky when
formalised: an 'if' is involved. Is this 'if' truth-functional? It's not.
Quantified formulae are NEVER truth-functional, on top of that.
So, we may do with revising the formula in its symbolisms as we proceed. Or
not.
Cheers,
Speranza
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