modern mathematicians water down concepts in order to keep them selves out of trouble
- From: "elsiemelsi" <cyprinsam@xxxxxxxxxxxxxxx>
- Date: Sun, 20 Apr 2008 21:11:26 -0500
The Australian philosopher colin leslie dean points out that modern
mathematicians water down concepts in order to keep them selves out of
trouble for the unwaterdown concepts would have stopped a lot of maths in
it tracks but mathematicians cant have this so they water it down
Tke the axiom of choice and skolems paradox
http://www.math.vanderbilt.edu/~schectex/ccc/choice.html
"The Axiom of Choice (AC) was formulated about a century ago, and it was
controversial for a few of decades after that; it might be considered the
last great controversy of mathematics
The controversy was over how to interpret the words "choose" and "exists"
in the axiom:
* If we follow the constructivists, and "exist" means "find," then the
axiom is false, since we cannot find a choice function for the nonempty
subsets of the reals.
* However, most mathematicians give "exists" a much weaker meaning,
and they consider the Axiom to be true: To define f(S), just arbitrarily
"pick any member" of S.
note in order to use AC modern mathematicians just water down the meaning
of words"
take the skolem paradox
when it was formulated by skolem mathematician of the time including
skolem saw it as a contradiction
note the definition of paradox is contradiction
http://www.thefreedictionary.com/paradox
1. A seemingly contradictory statement that may nonetheless be true: the
paradox that standing is more tiring than walking.
2. One exhibiting inexplicable or contradictory aspects: "The silence of
midnight, to speak truly, though apparently a paradox, rung in my ears"
Mary Shelley.
3. An assertion that is essentially self-contradictory, though based on a
valid deduction from acceptable premises.
Skolem said it was a contradiction in formulating his unaccepted
solution
http://en.wikipedia.org/wiki/Skolem%27s_paradox#Is_it_a_paradox.3F
"Hence there is no contradiction at all if a set M of the domain B is
nondenumerable in the sense of
the axiomatization;"
Fraenkal and most mathematician of the time saw it as a contradiction
"Neither have the books yet been closed on the antinomy, nor has agreement
on its significance and possible solution yet been reached." â?? ([[Abraham
Fraenkel] in "Einleitung in die Mengenlehre" 3rd ed p. 333, 1928, quoted in
"The Bulletin of symbolic logic"" Vol.6, no 2. June 2000, pp. 147
http://www.math.ucla.edu/~asl/bsl/0602/0602-001.p";
now mathematicians say it is a paradox but not a contradiction
thus they miss use the word paradox in its real meaning
and they have decided to not call it a contradiction even though most
mathematicians in history saw it as a contradiction
such that modern mathematicians can say it is a paradox but not a
contradiction
Skolem paradox appklies to set theory and it makes set theory
contradictory -as its name says- but ZFC is set theory so then under the
historical and dictionary view of paradox and what skolems paradox was - e
a contradiction- then ZFC is inconsistent
a situation modern mathematician cannot dare to accept but which is why
they say it is a paradox but not a contradiction - thus both abusing
language and deny the historical fact that it was seen as a
contradiction
Thus we see that modern mathematicians water down concepts in order to
keep them selves out of trouble so as to allow them to keep doing things
for if the concepts where used in done watered down manners their
endevours would stop
ie skolems paradox should have stop work in set theory - but mathematician
could not have that so they just abuse language and say a paradox is not a
contradiction and say in contarary to most mathematician historically that
skolems paradox is not a contradiction
The unwatered down AC would have stop a lot of maths in it tracks but
mathematicians cant have this so they water it down
--
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