Re: Sign Relational Manifolds • Discussi on

Sign Relational Manifolds • Exposition

1. http://permalink.gmane.org/gmane.science.philosophy.peirce/8850
2. http://permalink.gmane.org/gmane.science.philosophy.peirce/8854
3. http://permalink.gmane.org/gmane.science.philosophy.peirce/8871
4. http://permalink.gmane.org/gmane.science.philosophy.peirce/8915
5. http://permalink.gmane.org/gmane.science.philosophy.peirce/8919

1. http://inquiryintoinquiry.com/2012/10/22/sign-relational-manifolds-1/
2. http://inquiryintoinquiry.com/2012/10/22/sign-relational-manifolds-2/
3. http://inquiryintoinquiry.com/2012/10/23/sign-relational-manifolds-3/
4. http://inquiryintoinquiry.com/2012/10/30/sign-relational-manifolds-4/
5. http://inquiryintoinquiry.com/2012/11/01/sign-relational-manifolds-5/

Sign Relational Manifolds • Discussion

01. JC: http://permalink.gmane.org/gmane.science.philosophy.peirce/8861
     JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8868

02. JC: http://permalink.gmane.org/gmane.science.philosophy.peirce/8862
     JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8872

03. IA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8866
     JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8875

04. JC: http://permalink.gmane.org/gmane.science.philosophy.peirce/8873
     JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8890

05. SE: http://permalink.gmane.org/gmane.science.philosophy.peirce/8874
     JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/8886

06. KM: http://permalink.gmane.org/gmane.science.philosophy.peirce/8878

KM: I must say I definitely side with Jon's views on the issue under debate:

KM, quoting IA:
     Jerry is quite right, that Riemann's concept of a manifold
     is a purely and exclusively a mathematical concept.

KM: I am not focusing on "purely", I focusing on "exclusively". -
     If that, or anything like that were true, then Peirce's
     philosophy would not be possible. To take just one example.

KM: If that claim is accepted, then all (and any) multidisplinary
     approaches would be impossible, just as well.

KM: It may be true that Riemann took his concept of a manifold as
     a mathematical concept only. - But from this it does not follow
     that all others should or only could take it is as such.

KM: Think about the duck/rabbit picture Wittgenstein used in his
     philosophy as an example. - In principle, someone could see
     only a duck, never a rabbit. - Would he be right in claiming
     that the picture in exclusively a picture of a duck? - Against
     other testimonies?

KM: Well, this picture, as well as other similar pictures,
     have been especially construed to instigate a spontaneous
     shift in perspectives, offering different meanings of the
     drawing. (Berkeley was quite right, we do see meanings.)

KM: But a perspective may be just as well be taken,
     as well as changed, deliberately & consciously.

KM: The perspective Jon has taken, involved in the following:

KM, quoting JA:
     The definitions of a manifold that I have in mind all exhibit
     variations on a particular genus of triadic relational structure

KM: is not a mathematical one. It is a philosophical and logical one. -
     It is about a certain kind of logical structure involved in
     definitions of a manifold.  - The definitions may well be
     mathematical ones. It does not matter a bit.

KM: I am quite convinced neither of you, Jerry and Irving,
     would be ready to claim that there is no logical structure
     in mathematics! - If you accept that there is, then you'll
     have to accept that it can be (rationally) discussed.

Kirsti,

I think you got the gist of it.  All through this long and winding
manifold of tangents to the topic of manifold theory, I keep being
reminded of William James' 1907 ''Pragmatism : A New Name For Some
Old Ways Of Thinking''.  His subtitle says a mouthful, as they say.

Manifold theory has its precursors in a panoply of ancient stories,
for example, “The Blind Men and the Elephant”, where the pachyderm
is the pragma, the object X of our seeking, and the perceptions of
the blind men are the individual charts of the atlas that form the
manifold structure over X.

Regards,

Jon

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