[lit-ideas] PI's 'key tenet' and W's philosophy of mathematics
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: "lit-ideas@xxxxxxxxxxxxx" <lit-ideas@xxxxxxxxxxxxx>
- Date: Sat, 9 Jun 2012 14:07:09 +0100 (BST)
In a critical spirit, I have specified what might refute the
interpretation of PI in terms of an
underlying ‘key tenet’ that the sense of ‘what
is said’ is never said in ‘what is said’ but may only be shown (a tenet I
have sought to show is implicit in what W there writes). (1) W explicitly (or
clearly by implication) disavowing any such tenet. (2) A counterexample to the
‘key
tenet’ such as a “rule” stated so that its
sense is said in its statement. (3) An alternative interpretation of
the text which ‘fits’ better: for example, one that gives a more persuasive
account of why W discusses possible ‘misunderstandings’ of a series of numbers
[e.g. ‘0, 1, 2, 3, 4….10’] or of a formula like ‘Continually add 2 to n’
– better than the suggestion these examples are used to show that the sense of
such a series or formula is not said in its statement, and that the sense may
only be shown.
So far, on the list, no joy in finding a refutation of the ‘key
tenet’ conjecture [pointing towards the voluminous work of Hacker and Baker
does not constitute an acceptable refutation in rational terms]. No one has
suggested anything that would support (1). Richard offered a counterexample as
per (2) but one easily rebutted using
what W says in PI. As to (3), no one
has seen fit to proffer their alternative reading with arguments as to why it
is a better ‘fit’. Interestingly A.J. Ayer does have an alternative
interpretation of PI that finds no
role for the ‘key tenet’; but not only is he not on the list, but the
shortcomings and ill-fitting character of Ayer’s interpretation may be left for
another post – suffice it to say, Ayer makes the basic error of taking what W
says in PI as constituting the point
of W saying it, whereas the point of
what W says lies in what it shows.
However, Ayer’s interpretation does provoke me to offer a
(4) in this list of possible lines of ‘refutation’: for Ayer touches on W’s
philosophy of mathematics and this may [or may not] provide a source for
rebutting the supposed ‘key tenet’. W’s philosophy of mathematics is the area
in which W himself thought his contribution was greatest [see:
http://plato.stanford.edu/entries/wittgenstein-mathematics/ ]. How might it
bear on the ‘key tenet’? Perhaps we could establish W’s ‘philosophy
of mathematics’, especially that of ‘the later W’, and on that basis show that
it is incompatible with the supposed ‘key tenet’. Whether this may be done may
be left open here. But it is at least a lacuna, if not a significant omission,
that my posts have not explained the relation between the ‘key tenet’ and W’s
philosophy of mathematics. And that this post carries on that ignoble tradition.
Donal
Looking forward to the soccer
Plymouth
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