[hist-analytic] Wittgenstein, Russell and 'Series'

steve bayne baynesrb at yahoo.com
Wed Feb 4 17:02:35 EST 2009

We need to consider why analyticity is important.
To do justice to Aune, I have to read the relevant
sections in Empirical Theory of Knowledge, which
can be accessed on the hist-analtyic website. For 
now I want to make a couple of historical points
that I think are related, although there is room
for skepticism.

I think the issue is related to translation in
such a way that it, too, becomes relevant to
Wittgenstein's "private language argument." 
(PLA) Kripke takes on certain questions related 
to series as fundamental to understanding both.
But a close look at wittgenstein may suggest
otherwise, at least when one considers the
philosophical significance attached to it by
the extremist Wittgensteinians who have tormented
Cartesians for a few decades.

Notice Wittgenstein's insistence (PI 143):

"Do not balk at the expression "series of 
numbers"; it is not being used wrongly here."

Well, maybe not "here" but what about elsehwere
in PI. Besides, Wittgenstein can no longer
silence his audience by the weight of his
well deserved respectability. So we ask: 
"The series of natural numbers in decimal
notation"? Ok, That seems to refer to a series.
But now jump forward towards the fun stuff. 
Wittgenstein says,

"Suppose the pupil now writes the series 0
to 0 to our satisfaction..." (PI 145)

Using Wittgenstein's technique (?) we ask:
Is 'series' here in its natural home? And what
is THAT? Later, he says

"...A writes series of numbers down...tries to 
find a law for the sequence..." (PI 151.

I think we need to ask the question he poses
about the grammar of 'know' to the grammar of
series. I don't think we are justified in
saying that the pupil writes down a *series*
of numbers unless it is indeed a series. But
what makes it a "series" if there is no
"law"? Well, that is an interesting use of
"law" when we might wish to look for a function.
There is every possibility that the "series"
of the pupil is simply a series in time; it is
not inconceivable that this is the only series
there is; and, if it is, then it may turn out
that we are talking about arriving at a "law"
by induction (which is, of course, not there).

Here is an interesting remark by Russell written
prior to the Investigations. Keep in mind that
when we speak of series, we can speak, alternatively,
of a function. Indeed it is a function we seek,
and if Kripkenstein is right there is none. But 
consider Russell:

"We have to find a set of integers and a corresponding
number of corresponding times...there will still
remain an infinite number of possible formulas, each
might claim to be a law.." 


"Every finite set of observations is compatible
with a number of mutually inconsistent laws, all
of which have exactly the same inductive evidence
in their favor. Therefore pure induction is invalid..."

But what of the validity of inferring a series from
what some kid put on the board. Why should we even
begin, lest we be beguiled by our love of arithemetic?
Notice the business of a number of inconssitent laws.
Now think 'translation' (analytical hypotheses) instead
of laws. Think of the same inductive evidence as
say stimulaus synonomy or some such. There is a connection
here. I'm not sure what, but there is equivocation in
W's use of 'series'. Moreover, we may in W's case be 
actually taking about a function as an inductive 
hypothesis. What consequences to this are there, and will
one consequence be enough to save the "phenomena."

Steve Bayne

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