[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]
[peirce-l] Re: evolving universe
On 3/23/06, Benjamin Udell <[EMAIL PROTECTED]> wrote:
> Hi, Il-Young,
>
> Thank you for the clarification. Now I understand, too, what you mean about
> an effort for which science is ill equipped, an effort more philosophical,
> and an "infinite regress" in thirdness, i.e., the scientific enterprise as
> studying itself.
>
> This seems to happen in any field of research into reason & reason's
> crackups, and the fields themselves have sometimes been called disciplinally
> ill-equipped, dysfunctional, and, at any rate, "cracked up" into schools.
> Maybe it's the nature of the problems, something to do with the reflexivity,
> the researcher as part of the subject matter, inferential & ratiocinative
> processes. My guess is that the psychological & social studies have it worst,
> studies of rational beasts by rational beasts, with philosophy coming in a
> close second with its indeterminately or multiply answerable questions and
> problems inverse to those of deductive theory of logic. Deductive theories of
> logic, and of ordered structures & math-induction applicability, seem divided
> into schools at least in terms of infinities, the intuitionist minority,
> etc., though I haven't heard of these researches being characterized as
> "disciplinally dysfunctional" in the way that happens to the more obviously
> reflexive researches such as philosophy & the social & psychological studies.
>
> ***
>
> Peirce means what he says about mind and matter. He holds that matter is
> "congealed" mind, "effete" mind -- "effete" meaning spent, played out,
> exhausted, all birthed-out. According to Peirce, physical laws are habits
> into which mind has settled & rigidified. At the same time, people, and the
> scientific enterprise, embody a process of growing thirdness amid the decay.
> Peirce held that God is "real" and that it's a "fetich" to persist on the
> question of whether God is "actual." (See "A Neglected Argument for the
> Reality of God," where he discusses his three-way being-actuality-reality
> distinction.)
>
> Actual is that which reacts or resists, as in an experiment.
>
> Real is that which is independently of what you or I or any finite community
> of minds (scientific or otherwise) thinks of it, but is also that which would
> be reached by research sooner or later and which would necessarily be reached
> by research prolonged indefinitely. Laws & habits can be quite real without
> being concrete reactive objects.
>
> 1. The possible, -- being (in the broadest sense)
> |> 3. The (conditionally) necessary ("would have to" approx. = "should"), --
> the real
> 2. The actual, the reactive/resistant, -- the existent
>
> Best, Ben
>
Hello Ben,
Thank you for that bit of information and citation. I will search for
that article at the library tomorrow. But, let me respond to this
issue of "mind over matter". It is still not completely clear to me
what he means by mind and matter in this case although it is becoming
more clear with your help and my own research into the matter (no pun
intended). I am becoming more convinced that it is not quite correct
to interpret Peirce's statement quoted by Gene previously with
traditional (read: dualist) meaning of matter and mind. Let me quote
a rather long passage from Peirce's essay "What Pragmatism Is"
verbatim. It will serve to make my point a bit more clear.
"As to reality, one finds it defined in various ways; but if that
principle of terminological ethics that was proposed be accepted, the
equivocal language will soon disappear. For realis and realitas are
not ancient words. They were invented to be terms of philosophy in the
thirteenth century, and the meaning they were intended to express is
perfectly clear. That is real which has such and such characters,
whether anybody thinks it to have those characters or not. At any
rate, that is the sense in which the pragmaticist uses the word. Now,
just as conduct controlled by ethical reason tends toward fixing
certain habits of conduct, the nature of which, (as to illustrate the
meaning, peaceable habits and not quarrelsome habits), does not depend
upon any accidental circumstances, and in that sense, may be said to
be destined; so, thought, controlled by a rational experimental logic,
tends to the fixation of certain opinions, equally destined, the
nature of which will be the same in the end, however the perversity of
thought of whole generations may cause the postponement of the
ultimate fixation. If this be so, as every man of us virtually assumes
that it is, in regard to each matter the truth of which he seriously
discusses, then, according to the adopted definition of "real," the
state of things which will be believed in that ultimate opinion is
real. But, for the most part, such opinions will be general.
Consequently, some general objects are real. (Of course, nobody ever
thought that all generals were real; but the scholastics used to
assume that generals were real when they had h
[peirce-l] Re: evolving universe
On 3/22/06, gnusystems <[EMAIL PROTECTED]> wrote: > il-young son, > (I'm using that as your name because you didn't sign your message -- ) > > Welcome to the list, and don't worry about being "a novice when it comes to > Peircean literature" -- that's me too! > > [[ Smolin does state explicitly that Peirce anticipated a kind of > evolution of natural laws by "natural selection". The qualifier, > Darwinian is indeed missing however, the common usage of the phrase > seem to lend itself to the interpretation that there is indeed an > implication of associating Peirce with advocacy for Darwinian > evolution (tychism to use Peirce's term) in stabilization of laws of > nature. ]] > > I'm not sure i get your point here, but anyway, part of the problem is that > Darwin (as far as i know) never tried to extend the concept of natural > selection beyond biology into physics and cosmology. Peirce, at least in "A > Guess at the Riddle", only applied the term to the domain of "biological > development", but made it one stop on a continuous journey from logic to > physics. He decribed the course of his thinking as follows (EP1, 252-3): > I suppose all I meant was that the phrase "natural selection" implies a particular kind of evolutionary mechanism, namely neo-Darwinian. Given the following Peircean quote, perhaps it is not all that implausible if you interpret "to take habits" to mean a kind of selective pressure. I wonder what Peirce would have said about Dawkin's idea concerning cultural evolution. "If the universe is thus progressing from a state of all but pure chance to a state of all but complete determination by law, we must suppose that there is an original, elemental, tendency of things to acquire determinate properties, to take habits. This is the Third or mediating element between chance, which brings forth First and original events, and law which produces sequences or Seconds." > > Maybe. Or maybe the distinction between the two is too fine-grained to show > up in Peirce's vague idea of "evolution" by "habit-taking". > This is true. I'd like a clarification on this notion of "habits". --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: evolving universe
On 3/23/06, Benjamin Udell <[EMAIL PROTECTED]> wrote: > Il-Young Son, list, > > Il-Young Son wrote, > > I am not sure how many, if many, when pressed, would object to the notion > > that there are fundamental limits to models and that the mapping (or the > > mediator) between models and their corresponding natural phenomena cannot > > just dissolve into the model itself. As succinctly put by Korzybski, "map > > is not the territory". There are notable exceptions of course, such as > > Steven Weinberg, but I would hesitate to attribute such a view to the > > community in general. In any case, I am not sure if science itself is > > equipped to deal with the kind infinite regress this Thirdness implies. It > > seems to me to belong more in the domain of philosophising about scientific > > process itself. > > Would you clarify your words "...that the mapping (or the mediator) between > models and their corresponding natural phenomena cannot just dissolve into > the model itself."? I'm not saying that I see anything wrong with it. To the > contrary, it sounds good and it keeps nagging that I don't really understand > it! This I hope will clarify the sense of the implication that thirdness > involved an infinite regress with which science is ill-equipped to deal. > > Best, Ben Udell Hello Ben, By "...the mapping (or the mediator) between models and their corresponding natural phenomena cannot just dissolve into the model itself." I simply meant that the notion that somehow labour of science would yield a convergence to a set of laws that are True Laws in the sense that they are unmediated, singular, and completely stable (i.e., self-evident) seems to me implausible. Now, given Gene's response, I'm beginning to think I may have misread Peirce. Admittedly my reading of Peircean literature is limited as I was unaware of Peirce's statement quoted by Gene "that all matter is really mind". By Thirdness (as applied to laws of nature) what I thought he had in mind is something akin to (albeit in no way identical to) what Chomsky called ""a kind of chance convergence between aspects of the world and properties of the human mind/brain". But, this calls for a clairfication of what Peirce meant by "all matter is really mind" and if my memory serves me correctly I remember Peirce making a distinction between "reality" and "existence". I may be wrong here but this leads me to believe that what he had in mind is not a deference to mind as a source explanation (which is sort of what I gathered from Gene's response) nor an advocacy of nominalism. Given the limited knowledge of Peirce's writing, I still tend towards interpreting his Thirdness (as applied to evolution of laws of nature) as a description of scientific enterprise itself and not that mind sits at the top of "The Chain of Being". I should also clarify what I said in my previous post. I didn't mean to say it is of no value to consider evolution of laws of nature as a potential source of formal inquiry by the scientific community. I hope I didn't give that impression. --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: evolving universe
Hello, This is my first time posting to the list reason being that I am, at best, a novice when it comes to Peircean literature. So please freely point out any misrepresentation that I may promote during the course of this response. Response is in the body (sorry, for the sake of convenience, I've decided to comment both on both Gene's and Gary's response at once). On 3/21/06, gnusystems <[EMAIL PROTECTED]> wrote: > Gene, thanks for your response on that Lee Smolin piece -- > This was definitely an interesting essay, thanks for the link. > [[ Then, stepping away from it, it occurred to me that comparing Darwin and > Einstein, while taking from Peirce the idea that laws of nature are results > of natural selection, represents no "dangerous ideas" at all, only a nice > juxtaposition of accepted ideas. ]] > > Well, Edge is really a "sound bite" site, so one doesn't expect anything > truly profound there. Especially when it doesn't even spell Peirce's name > correctly. > > [[ Smolin assumes Peirce assumed natural laws evolved by Darwinian natural > selection alone, which seems to me a false assumption. ]] > > You may be right about what Smolin assumes; i don't think the piece is > sufficiently developed to be sure of that. Clearly the emphasis is on the > idea that the laws of nature themselves are evolving rather than fixed and > static, and i don't see Peirce having a quarrel with that. > Smolin does state explicitly that Peirce anticipated a kind of evolution of natural laws by "natural selection". The qualifier, Darwinian is indeed missing however, the common usage of the phrase seem to lend itself to the interpretation that there is indeed an implication of associating Peirce with advocacy for Darwinian evolution (tychism to use Peirce's term) in stabilization of laws of nature. > [[ He remains unaware of Peirce's truly dangerous idea, that there is "a > reasonableness, energizing in the universe." Mainstream science at the > "Edge" remains unwilling to confront the possibility that Thirdness is > irreducibly real. ]] > I can't see a real justification for claiming "mainstream science is unwilling to confront the possibility that the Thirdness is real" without convincing evidentiary support. I find, from experience, that this is a popular view about those practicing science and which I find little concrete support of. I can't speak for all scientists (including those featured on the Edge), however, among those involved in the task of doing "normal science" (in the Kuhnian sense, which I take it to be what you mean by mainstream science) I am not sure how many, if many, when pressed, would object to the notion that there are fundamental limits to models and that the mapping (or the mediator) between models and their corresponding natural phenomena cannot just dissolve into the model itself. As succinctly put by Korzybski, "map is not the territory". There are notable exceptions of course, such as Steven Weinberg, but I would hesitate to attribute such a view to the community in general. In any case, I am not sure if science itself is equipped to deal with the kind infinite regress this Thirdness implies. It seems to me to belong more in the domain of philosophising about scientific process itself. > My reading of Peirce's remarks on "natural selection" (for instance in > "Evolutionary Love") is that for him, Darwinian natural selection was one > instantiation of that Thirdness or "reasonableness", though certainly not I agree, Peirce seems to be more an advocate of Lamarckian evolution than Darwinian. > all of it; and you could read that perspective back into Smolin so that his > usage of it would be a sort of metonymy. But i think that piece is vague > enough to be open to your critical interpretation as well. Current Darwinian > or neo-Darwinian orthodoxy may hold that natural selection is all there is > to evolution -- i don't claim to know whether that's so or not; but clearly > that was not Peirce's view. > There's actually a body of evolutionary biologists who are bringing about a "renaissance of heresy", resurrecting the ghost of Lamarck. See epigenetics and adaptive mutation for example, if interested. Apologies in advance for the intrusion onto the list as I lack the authority to discuss Peirce intelligently. However, evolution does stimulate my curiosity a bit. --- Message from peirce-l forum to subscriber archive@mail-archive.com
