[lit-ideas] Re: Philosophy Of Maths
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 17 Jun 2008 20:04:57 +0000 (GMT)
>> The
> > view that there could be such objective knowledge is
> odd;
> > insofar as
> > I understand Popper, objective knowledge _comes from_
> the
> > 'thought
> > content' of W2 subjective experience (after which
> W2
> > thought processes
> > may consider that content by way of deciding its
> truth,
> > refining it,
> > expanding on it, etc).
As the extended quotation from _Schilpp_ indicates, though the position is
basically as Robert Paul states, it is part of Popper's position that what
_comes from_ a certain realm may _transcend_ that realm.
Indeed this is a key aspect of Popper's metaphysics - the idea of the
'emergence' of entities that are not reducible to (or fully explicable in terms
of) the states from which they emerged. So for example, from a world of physics
there emerges a world of chemistry; from a physical-chemical realm emerges a
world of biological creatures; from the biological realm emerges creatures
(e.g. humans) with a psychological and sociological dimension to their
existence that cannot be reduced to (or explained in terms of) mere physics,
mere chemistry, mere biology etc.
The sequence of natural numbers may _come from_ W2, for example, but the
sequence has properties that transcend what has been consciously developed in
W2 e.g. odd numbers, primes, and the property of being infinite a sequence.
Odd numbers and primes cannot exist without the existence of the sequence of
natural numbers - in this way they are logically dependent on that sequence.
But they are not reducible to that sequence as we may see by asking whether
there is a greatest prime [knowledge of the sequence of natural numbers is not
sufficient to answer this question; to answer, we need a _theorem_ about the
character of that sequence - a theorem that cannot simply be "read off" the
sequence itself]. In Popper's terms, once the sequence of natural numbers
exists in W3.1 or W3.2, primes exist in W3.3 (as do related problems such as
whether there is a greatest prime).
In this way it is not "odd" that what _comes from_ or emerges via W2 may
nevertheless transcend what W2 has consciously produced; indeed W2 operates by
interaction with the (W2-transcending) products of W2.
This interaction is central to Popper's theory of how human knowledge is
"objective knowledge" that works on a feedback system and the mutual
interaction between conscious W2 processes and W3 objects.
Donal
Fifty pee richer soon methinks
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