[net.nlang] All men...

wws@siemens.UUCP (William W Smith) (07/25/84)

If all men must die, some men are female.

If all men (mankind) must die, some men (males) are female.

Without the parenthesized comments, this statement is true but very 
disconcerting in English.  With the comments, you the irony of the statement
is seen as a fallacy in reasoning.  In logic it is a perfectly acceptable
statement, "If all men (mankind) must die, some men (mankind) are female."

It is also an invalid deduction: "If all men (males) must die, some men
(males) are female."

Submitted for your approval by Bill Smith
			       ihnp4!mhuxi!princeton!siemens!wws

jacob@hpfclo.UUCP (jacob) (08/07/84)

It might be "a perfectly acceptable statement," but it is
an invalid deduction no matter which way to put it.  Let's
formalize the first statement ("A" = "for all", "E" = there exists):

(A x)(Man(x) -> Die(x)) --> (E y)(Man(y) ^ Female(y))

Do you still claim it is a tautology?  Same goes for the second, less
ambiguous statement:

(A x)(Human(x) -> Die(x)) --> (E y)(Man(y) ^ Female(y))

or, for that matter:

(A x)(Human(x) -> Die(x)) --> (E y)(Human(y) ^ Female(y))

None of the above, independently, are true, so they are not valid deductions.
The only reason the second formulation "feels better" is that we rely on
knowledge that there are female humans.  But that is the conclusion of
the statement, so if we accept it as a premise, we don't even need to know
if they die or not.

Jacob Gore
ihnp4!hpfcla!jacob