Integrand wrote:
Let X be a chick in the world of all chicks.
Hotness is subjective, coolness is not; hence we have the axiom:
Axiom 1: "Every cool chick is hot."
The contrary is not always true,
for suppsoe the contrary, then;
every hot chick is cool,
Consider the counter example (pick one, mine is Paris Hilton)
and so we have a contradiction, i.e. our assumption is false.
In summary, ''hot'' is a necessary condition for ''cool'', but ''hot'' is not a sufficient condition for ''cool''.
LOTS OF MISTAKES:
1) Why is cool objective ? Because 'cool' is similar to 'cold', and that's why it's unemotional? But you can still be subjective, while being unemotional, for instance when you comit logical mistakes, as you did in the following.
2) Why: 'hence' we have the axiom ... ?
If something is true without doubt, from an unemotional point of view, it can be VERY doubtful from an emotional point of view, see politics, and, see, of course all our errors in love and sex ...
3) The (logical) contrary of 'every cool chick is hot' is,
'not every cool chick is hot', or, equivalently,
'there exists a cool chick which is not hot'.
Hence, the sentence
'every hot chick is cool'
is NOT the (logical) contrary of
'every cool chick is hot'.
4) Why is Paris Hilton hot, but not cool? Most men would indeed say she is hot, but many also think, that she is cool (because of her up-to-date fashion, her smile, her scandals, or EVEN JUST BECAUSE SHE IS HOT).
5) Hot is NOT a necessary condition for cool.
Example: Whoopy Goldberg; most men believe, she is not hot, but definitely most say she is very funny, witty, intelligent, and THEREFORE cool.
6) The two alternatives 'cool imples hot', or 'hot implies cool', can be also analysed from statistical point of view, that is, if a huge majority of men votes for 'hot implies cool' (I believe that this is true!) then linguists, sociologists, and shortly, most people , accept the sentence 'hot implies cool' as a truth.
If you analyse the alternatives from the purely logical point of view, then both are wrong, as the following two examples show:
a) Paris Hilton is hot, but (most probably) stupid, and therefore some men (presumably a few only) but definitely many women, don't consider her as cool.
b) Whoopy Goldberg is cool, but not hot, presumably most men and women agree on that.
Thus, from a logical point of view, I agree with your last sentence 'hot is not a sufficient condition for cool'.
COOL DOWN, PALS!
YOU PLAYED CHESS EVEN BETTER, THAN AT YOUR OTHER ACTIVITIES!..