[lit-ideas] Re: Griceian Numbers
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: "lit-ideas@xxxxxxxxxxxxx" <lit-ideas@xxxxxxxxxxxxx>
- Date: Sun, 17 Jun 2012 23:58:26 +0100 (BST)
It was stated clearly in my original post that Ayer was offering the quoted
words not as criticism of W but as a statement of W's position. Then it was
repeated because JLS appeared not the grasp this. Now, as the cock crows, it is
repeated below.
________________________________
From: "Jlsperanza@xxxxxxx" <Jlsperanza@xxxxxxx>
>In "Ayer on Wittgenstein I", McEvoy quotes from Ayer:
“It would be wrong, however, to say that he was being shown numbers in the
way he was being shown specimens of building materials. The difference
lies not the different character of the ‘objects’, but in the different roles
that the two sorts of signs play in the language game."
And comments,
"This conclusion, I suggest, is Ayer’s own interpolation and not a
paraphrase of W’s text.">
That is, I suggest Ayer's quoted sentence is presented by Ayer not as criticism
of W but as a statement of W's position. And this is made even clearer in my
comments on this in the original post, which argued this presentation is
mistaken as 'exegesis' and it is a mistake that arises (at least in part)
because Ayer does not grasp the 'key tenet'.
As Ayer is not criticizing W in the quoted passage it must be a mistake to
think Ayer is criticizing W because W is against the view that mathematical
propositions hold in virtue of their correspondence with 'mathematical
objects'. [A view Ayer is also against afaik]. So the reference to Stanford is
beside the point.
Further, Pt II of the post (which was too long to posted as one whole)
discussed W's constructivism in the light of the 'key tenet', suggesting how
W's view was not that 'we-must-make-it-up-every-step-of-the-way' but was a
constructivism compatible with the view that
'unless-we-take-a-different-direction' in following a "rule" the direction (of
its development) may be set by the sense of "the rule" as it stands. And this
kind of constructivism is compatible with the 'key tenet' which would emphasise
that the sense of a "rule" as it stands is not said by the "rule" but may be
shown - shown even by how the "rule" continues to be applied.
>So, it may do to interpret Ayer's criticism in terms of Witters's broader
anti-objectual view of mathematics, as per the Stanford entry -- and all.
(Or not!) >
For a fourth time then: the quoted passage is not a criticism by Ayer and so
cannot properly be interpreted in terms of W's opposition to 'mathematical
objects' (especially as Ayer shares this opposition himself afaik).
To end on a less repetitious note: it may be suggested that, in the light of
the 'key tenet', commentary that tries to solve the supposed "paradox" as to
rule-following [by saying there are grounds for correct rule-following (for
example, in community sanctioned criteria) - and that these grounds can be
said] is on the wrong track. The solution to the apparent "paradox" lies in
recognising that we cannot say the sense of a "rule", and therefore we cannot
say what amounts to obeying or going against it, but we can show the sense in
particular cases and show in particular cases that some 'what-is-said' has a
sense (or is a nonsense) [although whether it has sense, or is nonsense, will
depend on much more than 'what-is-said']. If we try to do more than show the
sense we end up trying to say what can only be shown. And if W thought we could
do more than show the sense he would have said so: he quite conspicuously says
no such thing in PI and he doesn't say
he has ever said the sense of anything, including a "rule".
(Go figure.)
Donal
Salop
>----
>Yet cfr. this from Stanford:
http://plato.stanford.edu/entries/wittgenstein-mathematics/
"Wittgenstein stresses that he is trying to ‘warn’ us against this‘aspect
’—the idea that the foregoing proposition about fractions “introduces us
to the mysteries of the mathematical world,” which exists somewhere as a
completed totality, awaiting our prodding and our discoveries. The fact that
we regard mathematical propositions as being about mathematical objects and
mathematical investigation “as the exploration of these objects” is “
already mathematical alchemy,”claims Wittgenstein (RFM V, §16), since “it is
not possible to appeal to the meaning [‘Bedeutung’] of the signs in
mathematics,… because it is only mathematics that gives them their meaning [‘
Bedeutung’].”"
So, it may do to interpret Ayer's criticism in terms of Witters's broader
anti-objectual view of mathematics, as per the Stanford entry -- and all.
(Or not!)
I append for the record the reference sections.>
Other related posts:
