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Author: John W EdserJohn W Edser Date: Apr 15, 2008 16:39
>> Not true. Mathematics is based
>> on pure logic, on things that
>> must be true regardless of
>> whether or not their are any
>> sentients to
>> discover or use them.
> Lots of mathematicians disagree.
> Alternative point of view is that
> math/logic merely reflect the way
> our brains work and have nothing
> to do with the "objective"
> reality.
JE:-
The short answer is that mathematics is *NOT* a science. This is only
because mathematics cannot be falsified so we can never know if prime
numbers evolved or not _until they become predicated by...
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Author: DKDK Date: Apr 16, 2008 10:19
In article darwin.ediacara.org>, "John W Edser" ozemail.com.au> wrote:>>> Not true. Mathematics is based
>>> on pure logic, on things that
>>> must be true regardless of
>>> whether or not their are any
>>> sentients to
>>> discover or use them.
>
>> Lots of mathematicians disagree.
>> Alternative point of view is that
>> math/logic merely reflect the way
>> our brains work and have nothing
>> to do with the "objective"
>> reality.
>
>JE:-
>The short answer is that mathematics is *NOT* a science. ...
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Author: Alan MeyerAlan Meyer Date: Apr 18, 2008 10:26
> ...
> Bottom line is, prime numbers "exist" no more than
> such things as negative or complex numbers or infinity
> do. All are inseparable from the way our mind functions.
I was with you, at least in part, until the last sentence.
I think I can easily separate numbers from the way our minds
function.
We don't have access to other minds and can't compare our
concepts to theirs. But we do know about electronic computers.
A calculator, for example, peforms arithmetic in a totally
different way from the way our minds function. We can understand
it. After all, we designed it. But how many people perform
subtraction by addition of two's complements, or perform floating
point operations with separate operations on fixed length
mantissa and exponent, or determine signs by "extending" the most
significant binary digit to the left for up to 16, 32 or 64
binary places, or perform any mathematical operation by first
converting numbers to binary representation?
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Author: Entertained by my own EIMCEntertained by my own EIMC Date: Apr 18, 2008 10:26
DK wrote:
> In article darwin.ediacara.org>, "John W Edser" ozemail.com.au> wrote:>>>> Not true. Mathematics is based
>>>> on pure logic, on things that
>>>> must be true regardless of
>>>> whether or not their are any
>>>> sentients to
>>>> discover or use them.
>>> Lots of mathematicians disagree.
>>> Alternative point of view is that
>>> math/logic merely reflect the way
>>> our brains work and have nothing
>>> to do with the "objective"
>>> reality.
>> JE:-
>> The short answer is that mathematics is *NOT* a science.
>
> Mathematics may very well not be considered a "science" ...
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Author: DKDK Date: Apr 19, 2008 23:03
In article darwin.ediacara.org>, Alan Meyer yahoo.com> wrote:>> ...
>> Bottom line is, prime numbers "exist" no more than
>> such things as negative or complex numbers or infinity
>> do. All are inseparable from the way our mind functions.
>
>I was with you, at least in part, until the last sentence.
>
>I think I can easily separate numbers from the way our minds
>function.
I don't think you can.
[snip calculator analogy for brevity]
>I argue that the electronic calculator produces the same answers
>that the human calculator does, not because it mimics the way our
>minds function, or because it "thinks" of or represents numbers
>the way we do, but because both we and the calculators execute
>functions derived from the fundamental properties of numbers.
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Author: Alan MeyerAlan Meyer Date: Apr 21, 2008 10:44
> ...
> You can argue that, sure, but you can't prove it (and the proof
> is likely impossible), and so I can, with the same strength, on
> a gut level feeling, argue that no, calculators are merely
> devices designed to deliver the same answers we do by means we
> are capable of.
I agree that "proof" is not the right word to apply to this
problem.
>>... II + II = IV no matter how the mind functions or
>>what tricks it uses to perform the addition.
>
> I am with you. I agree that this is entirely reasonable point
> of view. All I am pointing to is that it is nothing but a
> *belief*. There is nothing in what we know that affirmatively
> shows that numbers exist any more than color "green". (Which we
> know does not exist because we "know" it is just an
> electromagnetic wave of ~ 500 nm).
<... additional arguments elided ...>
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