[peirce-l] Re: Peirce and Prigogine
Jerry, List JC: Jerry Chandler AS: Arnold Shepperson On 4/22/06, Jerry Chandler wrote: JC: Ipresuppose that most readers of this list will find these statements to clash with their philosophy of physics, the philosophy of genera. I can merely add that the symbol system of physics is not the sole symbol system and that the philosophy of physics is not the sole philosophy of science. The philosophy of the chemical sciences is vastly more complex than the philosophy of physics because it must posit quantitative relations among individuals, species and genera. It must provide a source of generative grammars, not merely genera. Such is Life Itself. AS: My reading of Peirce suggests that he was aware of the distinctions between such `grammars' and how much confusion arose among the philosophers of his time because they tended to take one of them (whether physical, chemical, biological, or whatever) as `defining' all the others. In Vol IV of the Collected Papers (and, I would guess, throughout the New Elements of Mathematics, a copy of Eisele's edition of which I would dearly love to get!) he goes to considerable lengths in exploring the role that the mathematics of transitive phenomena plays in grounding higher-order mathematical systems. Indeed, the importance of transitive phenomena in Peirce has recently been discussed briefly on the list. In short, we may well find that the very notion of a Symbol System involves transitivities, and that Peirce very thoroughly investigated this relation (as, of course, a species of the Logic of Relations!!). Cheers Arnold --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Fw: What is Category Theory?
Does anybody know anything about category theory in math, which is what the book in the forwarded message below is about. What is it? Does it actually have any philosophical interest? Is it relevant to Peirce? Joe Ransdell - Original Message - From: G. Sica [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, April 28, 2006 10:50 AM Subject: What is Category Theory? Please allow me to bring to the attention of list members a recent publication about the foundations of Category Theory: WHAT IS CATEGORY THEORY? Editor: Giandomenico Sica http://www.polimetrica.com/polimetrica/389/ Price: 30 Euro. Forwarding and delivery charges are not included in the price. Publisher: Polimetrica International Scientific Publisher. Contributions and authors: Abstract and Variable Sets in Category Theory (John L. Bell) Categories for Knotted Curves, Surfaces and Quandles (Scott Carter) Introducing Categories to the Practicing Physicist (Bob Coecke) Some Implications of the Adoption of Category Theory for Philosophy (David Corfield) Sets, Categories and Structuralism (Costas A. Drossos) A Theory of Adjoint Functors ��� with some Thoughts about their Philosophical Significance (David Ellerman) Enriched Stratified Systems for the Foundations of Category Theory (Solomon Feferman) Category Theory, Pragmatism and Operations Universal in Mathematics (Ralf Kr��mer) What is Category Theory? (Jean-Pierre Marquis) Category Theory: an abstract setting for analogy and comparison (Ronald Brown ��� Tim Porter) On Doing Category Theory within Set Theoretic Foundations (Vidhy��n��th K. Rao) The best way to purchase this book is to buy it directly from the publisher's web-site: http://www.polimetrica.com . I hope you can be interested in this information. If not, please accept my sincere apologies for the trouble: this is not a spam message. Many thanks. All the best, Giandomenico Sica -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.385 / Virus Database: 268.5.0/325 - Release Date: 4/26/2006 -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.385 / Virus Database: 268.5.0/325 - Release Date: 4/26/2006 --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: Fw: What is Category Theory?
Joe, list, The popular discussions of category theory on the Internet haven't helped me very much. Apparently the basic explanational problem is that it's based on higher math, so it's just hard to explain. I once asked a singularity theorist, okay, it's about categories, so what are the results? The results? Yes, what _are_ the most basic categories? Well, it's not that kind of theory. I'm unsure whether he was correct about that. One piece of info which I eventually sought and could not find until I asked John Sowa, was this: Is an antiderivative (a.k.a. indefinite integral) a morphism? In general, is a relation which maps one value of x to more than one value of y, a morphism? The answer is, _no_. The answer is also _no_ for a many-to-many relation such as x^2 + y^2 = 1. A morphism is one-to-one, e.g., f(x) = x+2, or many-to-one, e.g., f(x) = x^4. Best, Ben Udell - Original Message - From: Joseph Ransdell [EMAIL PROTECTED] To: Peirce Discussion Forum peirce-l@lyris.ttu.edu Sent: Friday, April 28, 2006 12:49 PM Subject: [peirce-l] Fw: What is Category Theory? Does anybody know anything about category theory in math, which is what the book in the forwarded message below is about. What is it? Does it actually have any philosophical interest? Is it relevant to Peirce? Joe Ransdell --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: Fw: What is Category Theory?
See: http://plato.stanford.edu/entries/category-theory/ Though this may be more useful: http://mathworld.wolfram.com/Category.html I asked at a conference recently why category theory was considered so important and the claim was made that it is important because it is our most advanced form of mathematics. It is certainly interesting - but I have not made that assessment yet myself. As to Peirce, I am not sure of a direct connection - there is no obvious one - but in so far as he was deeply concerned with the nature of relations it would be interesting to note any coincidences, perhaps with his relational graphs. With respect, Steven Joseph Ransdell wrote: Does anybody know anything about category theory in math, which is what the book in the forwarded message below is about. What is it? Does it actually have any philosophical interest? Is it relevant to Peirce? Joe Ransdell - Original Message - From: G. Sica [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, April 28, 2006 10:50 AM Subject: What is Category Theory? Please allow me to bring to the attention of list members a recent publication about the foundations of Category Theory: WHAT IS CATEGORY THEORY? Editor: Giandomenico Sica http://www.polimetrica.com/polimetrica/389/ Price: 30 Euro. Forwarding and delivery charges are not included in the price. Publisher: Polimetrica International Scientific Publisher. Contributions and authors: Abstract and Variable Sets in Category Theory (John L. Bell) Categories for Knotted Curves, Surfaces and Quandles (Scott Carter) Introducing Categories to the Practicing Physicist (Bob Coecke) Some Implications of the Adoption of Category Theory for Philosophy (David Corfield) Sets, Categories and Structuralism (Costas A. Drossos) A Theory of Adjoint Functors � with some Thoughts about their Philosophical Significance (David Ellerman) Enriched Stratified Systems for the Foundations of Category Theory (Solomon Feferman) Category Theory, Pragmatism and Operations Universal in Mathematics (Ralf Kr��mer) What is Category Theory? (Jean-Pierre Marquis) Category Theory: an abstract setting for analogy and comparison (Ronald Brown � Tim Porter) On Doing Category Theory within Set Theoretic Foundations (Vidhy��n��th K. Rao) The best way to purchase this book is to buy it directly from the publisher's web-site: http://www.polimetrica.com . I hope you can be interested in this information. If not, please accept my sincere apologies for the trouble: this is not a spam message. Many thanks. All the best, Giandomenico Sica --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: Fw: What is Category Theory?
As far as i know, informally speaking category theory studies mappings (i.e. morphisms) between two sets of objects belonging to the same category. for example between two groups, rings, vector spaces, topological spaces, etc. in some sense, it can be thought of as an abstraction of already abstract field of algebra. as far as i know it was an extension of algebraic topology. as i haven't formally studied category theory i can't say anything beyond this. i did find this introductory notes on category theory online. maybe this will help illuminate things. http://www.andrew.cmu.edu/course/80-413-713/notes/cats.pdf On 4/28/06, Joseph Ransdell [EMAIL PROTECTED] wrote: Does anybody know anything about category theory in math, which is what the book in the forwarded message below is about. What is it? Does it actually have any philosophical interest? Is it relevant to Peirce? Joe Ransdell - Original Message - From: G. Sica [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, April 28, 2006 10:50 AM Subject: What is Category Theory? Please allow me to bring to the attention of list members a recent publication about the foundations of Category Theory: WHAT IS CATEGORY THEORY? Editor: Giandomenico Sica http://www.polimetrica.com/polimetrica/389/ Price: 30 Euro. Forwarding and delivery charges are not included in the price. Publisher: Polimetrica International Scientific Publisher. Contributions and authors: Abstract and Variable Sets in Category Theory (John L. Bell) Categories for Knotted Curves, Surfaces and Quandles (Scott Carter) Introducing Categories to the Practicing Physicist (Bob Coecke) Some Implications of the Adoption of Category Theory for Philosophy (David Corfield) Sets, Categories and Structuralism (Costas A. Drossos) A Theory of Adjoint Functors ��� with some Thoughts about their Philosophical Significance (David Ellerman) Enriched Stratified Systems for the Foundations of Category Theory (Solomon Feferman) Category Theory, Pragmatism and Operations Universal in Mathematics (Ralf Kr��mer) What is Category Theory? (Jean-Pierre Marquis) Category Theory: an abstract setting for analogy and comparison (Ronald Brown ��� Tim Porter) On Doing Category Theory within Set Theoretic Foundations (Vidhy��n��th K. Rao) The best way to purchase this book is to buy it directly from the publisher's web-site: http://www.polimetrica.com . I hope you can be interested in this information. If not, please accept my sincere apologies for the trouble: this is not a spam message. Many thanks. All the best, Giandomenico Sica -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.385 / Virus Database: 268.5.0/325 - Release Date: 4/26/2006 -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.385 / Virus Database: 268.5.0/325 - Release Date: 4/26/2006 --- Message from peirce-l forum to subscriber [EMAIL PROTECTED]
