[lit-ideas] Maths, music and World 3
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 6 Jul 2011 14:16:21 +0100 (BST)
http://www.independent.co.uk/arts-entertainment/classical/features/the-enduring-myth-of-music-and-maths-2307387.html
One of the assumptions that underlies Popper's idea of World 3 [which he
thought long and hard about before deciding he had something worth publishing]
is the role of the _abstract_ in affecting what might be called 'non-abstract'
reality. This role goes much further than maths and music, and the relation of
maths and music (even from a cognitive POV) might be placed in the wider
context of the affect of the _abstract_ on the non-abstract.
Popper's version of W3 is linked to his assertion of the primary role of
_problems_ in the development of knowledge, as knowledge develops by proposing
solutions to a problem: for example, in some form of the schema
"P1->TT->EE->P2" . For Popper, 'problems' are real and their existence has a
causal affect on both human and animal and even plant behaviour [in the title
of one his books: "All Life is Problem-solving"]. These effects are perhaps
most obvious on life and its evolution when failure to solve a problem ends the
existence of an organism; conversely, the evolution of life on earth may be
understood as the result of ever-changing problems arising from an
ever-changing ecological niches and the relative success of different organisms
various attempts to solve these problems.
When we refer to the ecological niche or 'problem-situation' of an organism, we
are referring to something that may be physically embodied but where what
constitutes the niche or problem-situation is nevertheless to not reducible to
what is physically embodied: what is physically embodied by the situation of a
bear sleeping in a dark cave may, without any physical change, constitute a
very different problem-situation depending on whether the organism facing this
situation is a spider or a human or even a baby bear. This sense, in which
problem-situations are not reducible to their physical or chemical embodiment
in World 1, is one sense in which their existence may be understood as both
dependent on and yet also independent of the physical and chemical world.
When as a child we begin to grasp a problem [how to understand the speech of
others being a prime example] we are grasping a set of abstract relations such
as those, as in 'naming', between spoken-sounds and their 'objects'. Only by
means of grasping these abstract relations can we hope to acquire language.
That these 'abstract relations' are not reducible to any physical or merely
causal process, can be shown by reflecting that even in the simplest use of
language ['naming'] there is no merely physical or causal principle by which we
can cut into a sequence of sounds so as to correlate particular sounds with
particular objects: human 'intention' is necessary to interpret a sequence of
sounds so as to correlate particular sounds with particular objects, and that
'intention' is not explicable in purely physical or causal terms.
Though gravity is something more 'abstract' than matter, as it is disembodied,
it is nevertheless 'real' and shows its reality in its affect on physical
bodies. Similarly, our intellectual grasp of the world depends on grasping
abstract relations, including the content of a proposition _which is always
'abstract' qua content_, but the reality of these is shown by their affect on
physical bodies as mediated through human thought and behaviour.
Donal
London
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