I've been wondering about this for the last few years.
- Is mathematics a feature of nature, or is it imposed on nature by
the sentient mind? Counting cows is easy, but what about pi and
sophisticated mathematics? See
http://en.wikipedia.org/wiki/Pure_mathematics
- The same for logic. Are the rules of logic also the laws of nature?
Or again, is this part of the human mind's way to understanding
nature? This becomes a problem with quantum mechanics: sub-atomic
particles don't obey the laws of the human-visible world.
Teleportation, persistence, and so on.
yrs,
andreas
www.andreas.com
On Fri, Oct 22, 2010 at 11:00 AM, Torgeir Fjeld <torgeir_fjeld@xxxxxxxx> wrote:
Donal writes:
We may say there was no number system on earth before humans invented one. This
would not mean such a number system could not apply to what is 'out there'.
Consider two number systems:- (a) '1, 2, 3, 5, more than 5'; and (b) '1, 2, 3,
4, 5, 6, 7, 8, 9, 10, more than 10'. The farmer with exactly 8 cows using
(a)can truthfully say he has 'more than 5' cows; and using (b) can truthfully
say he has exactly 8 cows. Without the man-made invention of a number system he
could say neither, but that does not mean the invention cannot be used to
describe what is 'out there'. A farmer with 8 cows but no counting-system would
still have 8 cows; this fact is true by virtue of what is 'out there'
irrespective of whether he has the means to express or know this fact. A
farmerless field with exactly 8 cows in it also has 8 cows in it - no more, no
less - irrespective of whether humans or any other creature have a number
system to say so.
There's a loophole in this reasoning. When Donal states that "A farmer with 8 cows
but no counting-system would still have 8 cows; this fact is true by virtue of what is
'out there'", is not the reason why the farmer has 8 (not 7 or 9) cows that Donal
states in the premise that he has that amount? The appropriate question is not whether
the farmer has 8 cows due to it being so /out there/, but whether the 8 cows appear so
/to the farmer/ (and not to some dislocated, ephemeral theorist outside the practice of
farming). And in order to answer this question the farmer's reportoire of articulation is
highly relevant.
Best,
Torgeir Fjeld
Norway
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