Thomas, list,
> Peirce's version of the proof for Cantor's theorem can be mapped in a quite
> straightforward way to the structure of the New List of 1867. At the same
> time the proof of Cantor's theorem can be extended by continued
> diagonalization (which latter, by the way, Peirce discovere
Thomas,If you don't mind my asking, what's wrong with the "nonstandard analysis" approach to illustrating continuum, so long as that approach is VERY nonstandard? I was quite convinced by Hilary Putnam's introduction to "Reasoning and the Logic of Things." Putnam suggests that rather than understan
On Mon, 13 Mar 2006 19:37:14 +0100, Marc Lombardo <[EMAIL PROTECTED]>
wrote:
Thomas,
If you don't mind my asking, what's wrong with the "nonstandard analysis"
approach to illustrating continuum, so long as that approach is VERY
nonstandard? I was quite convinced by Hilary Putnam's introductio
Thomas
TR: Thomas Riese
AS: Arnold Shepperson
TR: Peirce is exactly interested in the relation between isomorphous forms.His primary relation is the general form of transitivity.
TR: The difference has far reaching, profound implications.
AS: I agree with you on this. Contemporary work that
Dear Arnold,
I believe L 224, the letter Peirce wrote to William James on 1909 Feb 26 is
exceedingly important here. In print you find it in volume III/2, p.836
ff. of
"The New Elements of Mathematics", ed.: Carolyn Eisele.
What is important is the fact that general transitivity has a propert
Arnold says:
I would venture to suggest (subject to the better sense of those on
the list who have greater experince with the MSS than I have) that the notion of
a Sign contains the concept of a transitive function, making a very strong case
for what Thomas has said on this subject. Other
Thomas:Your thoughts on the potential relation between Peirce's continuity and mathematical history were fascinating. I must confess that I am a bit of a skeptic when it comes to the possibility of a sensible relation between logic, any logic, and a philosophy of mathematics.Nonetheless, I remain
Joseph Ransdell a écrit :
Arnold says:
I would venture to suggest (subject to the better sense of
those on the list who have greater experince with the MSS than I have)
that the notion of a Sign contains the concept of a transitive
function, making a very strong case for what
Dear Thomas, dear List,
¨ ¨ I am sure you are right that many of his general ideas about logical
form where already actively structuring Peirce's work on logic and the
categories around 1867. Even earlier he had identified the transitivity
property of inferential relation as the crucial requi
Bernard, list,
> I returned to the sources and fell short with the
following:--CP
3.175175. The forms A -< B, or A implies B,
and A ~-< B, or A does not imply B 3, embrace both hypothetical and
categorical propositions. Thus, to say
Thanks Ben, I think that you have got it better than me.
What is meant is certainly as you put it: "to say that all men are
mortal is the same as to say that for every man, for every character, if
said man possesses said character, then there is a mortal who possesses
said character". This expr
es and whether and how to translate between discourses.
I cannot yet see how to handle 3.175, but thought I would contribute this much.
Jim W
-Original Message-From: Benjamin Udell <[EMAIL PROTECTED]>To: Peirce Discussion Forum Sent: Thu, 16 Mar 2006 10:52:03 -0500Subject: [peirc
Thanks for your response and interest, Jerry.
You do of course touch the most subtle and perhaps difficult to understand
point
in Peirce's conception of logic.
What concerns the "grounding" or perhaps "foundation", I would say it has
no
foundation in the sense you probably mean. I has none
Dear Helmut Pape, list,
thank you very much for you thoughtful response.
It is still something different that I am after.
I would like to propose to try, whether or not it is possible, to put the
Cantor
proof and the New List side by side "synoptically" and see whether or not
it is
possible
Dear list,
Some request from me again...fact is that I am getting some great insights
at the moment, but need to have some better understanding from the term
"diagrammatic" as stated by CS Peirce.
What I want to truly understand is what he meant by this term. For that I
need to know where to find
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