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Topic: [HM] Language of Discovery
Replies: 23   Last Post: Mar 15, 2001 1:04 PM

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Gordon Fisher

Posts: 367
Registered: 12/3/04
Re: [HM] Language of Discovery
Posted: Feb 23, 2001 10:21 AM
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"Samuel S. Kutler" wrote:

<< Heron might have taken the square root of a negative
number and thus DISCOVERED the imaginary numbers and soon
the field of complex numbers. Were they entities that
pre-existed so that they could be discovered by the one
with the sharpest vision? Were they instead entities to
be brought into being by someone who realized that they
could be postulated without leading to contradiction?
Or what? >>

It depends on what you believe the foundations of mathematics are
like. Cf. Platonists vs formalists vs intuitionists vs empiricists
vs ..... What if all of them are to some extent right, and to some
extent wrong?

And, it appears that Goedel, to take an example, was a declared
Platonist, but some logicians of note rejected Platonism of various
kinds? Does belief or disbelief in some sort of Platonism in which
one "discovers" what already somehow "existed" before discovery,
and perhaps "exists eternally," somehow time-independently -- do
differing beliefs in this matter affect what logicians, who take
a stand on discovery versus invention, in some dichotomous way, do
when they "do" logic? If so, how?

Gordon Fisher

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