Re: Problem with addition
- From: herbzet <herbzet@xxxxxxxxx>
- Date: Sun, 17 Aug 2008 21:52:15 -0400
John Jones wrote:
A problem of addition can be summarised thus
1) To be countable, elements must be alike.
2) Elements that are indistinguishable cannot be counted.
herbzet's axiom (ta daa!):
Things are different only insofar as they are different, and no farther.
Corrollary:
At a sufficient level of abstraction, any two things are the same thing.
The axiom and its corrollary are more useful in polemics than in
mathematics. Sophists constantly draw irrelevant distinctions
in a given context, and conversely, overlook relevent distinctions
in a given context.
On the face, both statements seem true. Counting is an impossibility.
Yet we can count, nevertheless. Indeed, the problem is not confined to
counting but to any mathematical manouvure.
It may or may not be wise to search for a resolution to this problem by
exploiting the difference between 'alike' and 'indistinguishable'. A
difference between 'alike' and 'indistinguishable' has been suggested by
Kant who thought that all mathematical entities were temporally placed.
Indistinguishable objects that are placed temporally become
distinguishable and alike, thus allowing for the existence of
mathematics. Temporality of course can be abstractly configured through
sequence and order which, we must suppose, are the lynch-pins of any
mathematical structure.
--
hz
.
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