FOM: Response to adverse comment on the Arche project

[Roger Bishop Jones]

In response to Neil Tennant Wednesday, March 14, 2001 8:35 PM

> On Sat, 10 Mar 2001, Roger Bishop Jones wrote:
>
> > I have two critical remarks to make in relation to the Archie project
> > recently mentioned on fom.
> >
> > Firstly, in its statement of "the research problem"
> > http://www.st-and.ac.uk/~arche/ahrbresearch.shtml
> > the Archie website grossly distorts the history of its subject by
suggesting
> > that logicism received absolutely no further support from philosophers
after
> > its abandonment by Frege.
> >
> > In fact, the word logicism does not seem to have been applied to the
> > philosophy of mathematics until decades later (1931)
>
> Would it not be irrelevant whether the term "logicism" was in use only at
> a later date?

Unless the non-use of the term were to play a role in a defence
of the claim made on the web site.
(which is unlikely since no defence is likely to be mounted)

> The question is rather whether any doctrine recognizably
> logicist in nature was held by any philosophers in the immediate aftermath
> of the discovery that Frege's class theory was inconsistent.

No.
The question is whether it is correct to claim that following
Frege's abandonment of Logicism three generations of philosophers
were unanimous in rejecting logicism.

I am please to see that this claim has now been removed from the page in
question.

> > Secondly I observe that it seems to me a sad comment on contemporary
> > Philosophy of Mathematics that philosophers should consider that the
status
> > of the axiom of infinity is materially changed when it is disguised as
> > "Hume's Principle".
> > I doubt very much that Frege would have taken refuge in such
equivocation.
>
> For a disguise to be effective, it must be possible to attribute to the
> one devising the disguise the intention to mislead his audience as to the
> true nature of what is (supposedly) being disguised.

No, it is not hard to find examples disguise which involve no intention..
Furthermore, I have not claimed that the disguise is effective.
Furthermore my use of the word "disguise" at all is pretty much
peripheral to the point I was seeking to make.

> But there can be no
> doubt that Wright and other thinkers interested in neo-logicism have no
> such intention. For them, it is obvious---and obvious that it will be
> obvious to any other competent and interested party---that Hume's
> Principle packs even more ontological punch than a standard axiom of
> infinity. (An axiom of infinity usually states only that a countable
> infinity exists, and it is left to the powerset axiom to "blow it up" to
> get even higher infinities, via Cantor's Theorem.)

And consequently if logicism is insupportable because of doubts
about the necessity of the axiom of infinity it will be even less credible
when based on "Hume's principle".
(and if the asiom of infinity is not in doubt, why do we need Hume's
principle?)

Roger Jones