[lit-ideas] Re: Need some help...
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 21 Sep 2004 15:19:49 +0100 (BST)
> You're a good man. My brain is currently functioning at the level of a
> three year old. Don't even ask.
Not wanting Julie to be misled, is '2 + 2 = 4'? really a tautology, never
mind a "perfect" one? (And who might be demanding one of Julie and why, btw?
Though fair dos - best to be prepared).
My three year functioning brain (still under guarantee) suggests that the
view that mathematical statements are tautolgous (as per Wittgstn's TLP) is
controversial to say the least, and perhaps to be rejected (as it is by many
philosophical mathematicians) - rejected essentially because the meaning of
'12' is not contained in the meaning of '5' and '7', and equally the meaning
of '4' is not contained in the meaning of '2'. That is, mathematics is
synthetic, albeit not empirical as in testable/falsifiable by observation.
This 'synthetic' quality is shown by the fact certain mathematical theorems
have been disproved, whereas one cannot disprove a definition.
In fact, maths works by searching for counter-examples, as does science -
except the counter-examples as not observable properties but, for example,
the 'fact' the theorem gives rise to a contradiction of some kind. That is,
the correct philosophical account of the status of mathematical truths is
Popperian ie. that maths works by way of attempted proofs and attempted
refutations.
With these simple remarks I leave this difficult topic as my head hurts a
lot.
Donal
Freonic Mason
Knights of the Popper Circle
London Branch
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