Thanks Irving,
I found your "Peirce Rustled, Russell Pierced" article online that references that manuscript. I cannot find the manuscript online however. If it's only on JSTOR that would explain why.
Steven,
Peirce's anti-solipsism/anti-Cartesianism that anchored his triadic semiotic was rooted in his view of infinity. Via Euler, he refined synechism to account for the effects of infinity on thought. In "How to make our ideas clear" he writes:
But the answer to this is that, on the one hand,
reality is independent, not necessarily of thought in general, but only of what
you or I or any finite number of men may think about it;It is this implication that infinite amount of thoughts can shape reality that suggests the interpreter must play a role to determine the nature of the sign's infinity. The type of infinity represented by a sign determines the type of thought that the interpreter can have about the object.
Peirce continues to explain the role of infinity in "A Neglected Argument for the Reality of God" writing:
The
hypothesis of God is a peculiar one, in that it supposes an infinitely
incomprehensible object, although every hypothesis, as such, supposes its
object to be truly conceived in the hypothesis. This leaves the hypothesis but
one way of understanding itself; namely, as vague yet as true so far as it is
definite, and as continually tending to define itself more and more, and
without limit. An interpreter is necessary to establish that the object is "infinitely incomprehensible". The comprehensibility of the sign is determined by the interpreter.
As for Whitehead, he was dealing with theology too, but had a different view of God. He was much more centered on "process" than definitions, though there is a lot of overlap. Whitehead's focus made infinity something that was indefinite. He acknowledges that the infinite object can be finite in another sense, but doesn't see a need to describe the reasons. He assumes that an object's finite and infinite natures are independent of the observer. Whitehead's type theory requires that a set be viewed as something other than an element to avoid paradoxes concerning infinity, the pragmatic requirement. However, you need an "observer" factor to keep his type theory consistent when you apply it; the interpreter decides if something is to be considered a set or an element.
> Date: Thu, 13 May 2010 19:52:16 -0400
> From: ianellis <at> iupui.edu
> To: peirce-l <at> lyris.ttu.edu
> Subject: RE: [peirce-l] Between Peirce and Whitehead...?
>
>
> If you want to consider Peirce on Cantor's paradox, and in general
> Peirce on Cantorian set theory, in comparison with Whitehead & Russell,
> from a technical (mathematical) perspective, you should definitely
> start with Peirce's
>
> "Some unmanageable problems. Notes on Cantor's "Beiträge zur Begrundung
> der transfiniten Mengenlehre", ms., 7pp., n.d. ca. 1900-1901; Robin
> Catalogue #821.
>
> I have never really found the time to do much with this, and haven't
> looked at this particular manuscript in nearly 20 years, and although I
> have wanted to get back to it since then, at my age, I am increasingly
> unlikely to do so. It has, as I said, been a very long time since I
> last looked at this (and related) manuscripts, but as I seem to vaguely
> recall, Peirce came up with (a version of) the Russell paradox on his
> own in this manuscript, which I seem also to recall, was in effect a
> combination of the Cantor and Russell paradoxes rolled into one.
>
> For a historian of mathematics or a historian of logic and set theory
> such as I, this should be a very interesting and worthwhile, even
> compelling, undertaking. As a matter of fact, the more I think about
> it, the more I want to pick this up again.
>
>
>
> ----- Message from klkevelson <at> hotmail.com ---------
> Date: Thu, 13 May 2010 17:56:01 -0400
> From: Keith Kevelson <klkevelson <at> hotmail.com>
> Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
> Subject: RE: [peirce-l] Between Peirce and Whitehead...?
> To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>
>
> >
> > Adrian,
> >
> > You might want to consider a comparison/contrasting between "Peirce
> > on Cantor's Paradox" and page 316-318 of Principia
> > Mathematica(co-written by Whitehead and Bertrand Russell). It seems
> > to me that dipolarity and triadism deal with experience by
> > mathematically viewing infinity differently.
> >
> > From: aivakhiv <at> uvm.edu
> > To: peirce-l <at> lyris.ttu.edu
> > Subject: Re: [peirce-l] Between Peirce and Whitehead...?
> > Date: Thu, 13 May 2010 09:44:57 -0400
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > Thanks very much for those references, Jaime and Gary. I'll follow up on
> > them. And, apparently, Scott Sinclair's dissertation is a comparison
> > of the two
> > thinkers' concepts of God.)
> >
> > Best regards,
> > Adrian
> >
> >
> >
> > ----- Original Message -----
> > From:
> > Gary Richmond
> > To: Peirce Discussion Forum
> > Sent: Wednesday, May 12, 2010 5:57
> > PM
> > Subject: Re: [peirce-l] Between Peirce
> > and Whitehead...?
> >
> > Adrian,
> >
> > You might take a look at some of John Sowa's
> > work, especially: http://www.jfsowa.com/pubs/signproc.htm
> > While I don't necessarily agree with all his conclusions, you might find
> > something of value in this paper, one of his best known (at least in KR
> > circles).
> >
> > Best,
> >
> > Gary
> >
> >>>> "Adrian Ivakhiv" <aivakhiv <at> uvm.edu> 5/12/2010 11:55 AM
> > >>>
> > I have a question to list members about the relationship
> > between Peirce and Whitehead.
> >
> > Two questions, really. The more general
> > question concerns comparative assessments of the two thinkers' metaphysical
> > systems. I've only found a few brief comparisons here and there.
> > (See the blog
> > post linked to below for a couple of them.) Are there others anyone knows
> > about, especially recent ones?
> >
> > The more specific question is this. I'm
> > wondering whether it makes more sense to try to bridge the two thinkers
> > (assuming that's a useful task) by:
> >
> > (a) comparing Peirce's triadic
> > account of the sign with Whitehead's account of actual occasions,
> > e.g. seeing
> > Peirce's triadism (representamen-object-interpretant) as an expansion of
> > Whitehead's dipolarity (subject-object), where what's missing from, or at
> > least inexplicit in, Whitehead is the 'standing for something' that
> > is central
> > to the sign relation,
> >
> > or
> >
> > (b) comparing Peirce's categories with
> > something broader in Whitehead's philosophy (e.g. firstness = 'eternal
> > objects', secondness = 'prehension', thirdness = 'symbolic reference' or
> > 'mentality', as Jaime Nubiola has suggested)? If so, what exactly?
> >
> > A
> > longer version of this question has been posted at
> > http://immanence.blog.uvm.edu/2010/05/between_peirce_whitehead.html.
> > Comments here or there will be warmly
> > appreciated.
> >
> > Thanks,
> >
> > Adrian
> > Ivakhiv
> >
> >
> >
> >
> >
> >
> > ___________________________________________________________________
> > Adrian
> > J. Ivakhiv, Associate Professor
> > Coordinator, Environmental Thought and
> > Culture Graduate Concentration
> > Environmental Program / Rubenstein School of
> > Environment & Natural Resources
> > University of Vermont, 153 S. Prospect
> > St, Burlington VT 05401
> > Tel 802.656.0180 Fax 802.656.8015
> >
> > Adrian.Ivakhiv <at> uvm.edu
> > www.uvm.edu/~aivakhiv
> > http://immanence.blog.uvm.edu
> >
> > -----
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> ----- End message from klkevelson <at> hotmail.com -----
>
>
>
> Irving H. Anellis
> Visiting Research Associate
> Peirce Edition, Institute for American Thought
> 902 W. New York St.
> Indiana University-Purdue University at Indianapolis
> Indianapolis, IN 46202-5159
> USA
> URL: http://www.irvinganellis.info
>
>
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