[lit-ideas] Re: Related issues/Understanding Why Newton Contributed To Human Knowledge With A False Theory
- From: Robert Paul <rpaul@xxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 04 Dec 2007 21:28:32 -0800
Donal writes
First, among the things I am intrigued about Wittgenstein (and, yes, he and
his work is intriguing, and certainly has a "beauty") is his [alleged]
'anti-realism'. _In extremis_, 'anti-realism' says that "2+2=4" is true only
by some adopted convention - in another time, and another world, it might be
different. I am unsure W ever defended this thesis _in extremis_.
He defended it (how well is debatable) in his lectures on the
foundations of mathematics at Cambridge in 1939, which Turing attended
for a while. None of this stuff is online as far as I know. I meant to
copy some of it and post it but that will have to wait unjtil I've
finished my research into Greek forensic anthropology. Shouldn't take long.
Palma talks of Popper's 'realism' (as opposed to 'anti-realism?') about maths
and logic. But a recurring point [and, of course, a questionable one] in
Popper's view of these things is this:-
a) the sequence of natural nos. did not exist before humans invented them;
b) once invented, that sequence contains consequences that exist whether or
not humans ever see them (e.g. 'odd and even nos.'; 'prime' nos.);
c) the exploration of "the seq. of nat. nos." [and its consequences] involves
a process that might be described as either one of 'discovery' or 'invention'
depending whether we emphasise the W3 'objective' aspects or the W2
'subjective' aspects.
I've never really known how to think about these things. I usually find
myself wanting to hold several contradictory views at once, e.g. that
things like mathematical proofs are inventions but their subject matter
isn't; that is, that numbers are real in Frege's small p platonic sense,
and we 'invent' what can be done with them. I'm attracted to Frege's
view that formalism—the notion that mathematics deals with marks on
paper (e.g.) and that these 'marks' have no reference to any other sorts
of entities—is absurd.
What Popper says at (b) is attractive but how different I wonder is it
from the view that although wheels were invented they may have many uses
and properties that humans never in fact discover?
I don't know. I'd like to understand the three worlds distinction
better. Is this right—tectonic plates exist in W1; the theory that their
movement plays an important role in geological change in W2; and Smith's
puzzlement over this theory in W3?
Robert Paul
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