Dear list, This is the very first time I post here. I'm a student of Cognitive Semiotics at Aarhus University. When it comes to Category Theory, I have a favorite scientist (apart from Baez): Bob Coecke at Oxford. I thought I'd share some of his articles with you.
A category theory primer http://arxiv.org/abs/0808.1032 Quantum picturalism (diagrammatic reasoning!) http://arxiv.org/abs/0908.1787 "An alternative gospel of structure: order, composition process" (very Peircian-like) http://arxiv.org/abs/1307.4038 Best, Esteban Fredin On Wed, Apr 30, 2014 at 11:01 PM, Jon Awbrey <[email protected]> wrote: > Jeff, List, > > Yes, these sorts of discussion have always been a RIOT (Radical > Indeterminacy Of Translation), as Quine more or less put it, between what > seem to be practically incommensurable paradigms of thought. > > At any rate, it looked for a moment there like we might actually be > settling down to a serious mathematical discussion of potential > cross-pollinations between category theory and semiotics, all of which > inspired me to collect a sample of previously frayed threads for the > benefit of those who may have snoozed through them the first time around — > > Precursors of Category Theory > ============================= > http://intersci.ss.uci.edu/wiki/index.php/Precursors_of_Category_Theory > > Category Theory (Phenomenology and the Categories) > ================================================== > > JA:http://web.archive.org/web/20140311054002/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12131 > JA:http://web.archive.org/web/20140316160001/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12183 > > Category Theory, Relational Arrows, Sign Relations > ================================================== > > JA:http://web.archive.org/web/20140321150001/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12248 > RM:http://web.archive.org/web/20140321150020/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12249 > JA:http://web.archive.org/web/20140321152006/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12250 > RM:http://web.archive.org/web/20140322021358/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12256 > JA:http://web.archive.org/web/20140322021200/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12258 > JA:http://web.archive.org/web/20140322140001/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12262 > JA:http://web.archive.org/web/20140330033027/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12386 > > Category Theory In Math > ======================= > > JBD:http://web.archive.org/web/20140429200401/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12705 > JA:http://web.archive.org/web/20140429201000/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12713 > JBD:http://web.archive.org/web/20140430052801/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12715 > JLRC:http://web.archive.org/web/20140430052522/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12719 > JBD:http://web.archive.org/web/20140430054001/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12721 > JA:http://web.archive.org/web/20140430152001/http:// > permalink.gmane.org/gmane.science.philosophy.peirce/12722 > > The main obstacles to advancing this discussion are a couple of > recalcitrant category confusions, one between the semiotic roles of > syntactic means and objective ends and the other between different levels > of structure in the object domains, specifically. between the properties > proper to individual elements of sets and the properties proper to those > sets themselves. But perhaps we can be just as persistent in clearing up > those confusions over time. > > > Regards, > > Jon > > Jeffrey Brian Downard wrote: > >> Hi Jon, List, >> >> Thank you for sending the links -- especially to the discussion. It is >> helpful -- and quite funny. >> >> For those who are a new to category theory, the explanation provided in >> the Stanford Encyclopedia of philosophy is a pretty good place to start. >> The section on the history of category theory provides context that is >> helpful for seeing where the two works by Mac Lane, Lambeck and Scott that >> Jon refers us to fit into the larger story. The bibliography is fairly >> comprehensive. >> >> --Jeff >> >> >> >> Jeff Downard >> Associate Professor >> Department of Philosophy >> NAU >> (o) 523-8354 >> ________________________________________ >> From: Jon Awbrey [[email protected]] >> Sent: Tuesday, April 29, 2014 12:40 PM >> To: Jeffrey Brian Downard >> Cc: Peirce List >> Subject: Re: category theory in math >> >> Peircers, >> >> Category theory, along with its applications to logic and computation, >> has been a recurrent subject >> of discussion in many online groups over the last 15 years or so, just >> since I came online, anyway. >> Here are excerpts from basic texts that served as springboards and >> resources for these groups, along >> with a few bits of associated commentary and discussion, that I archived >> at the InterSciWiki site. >> Perhaps a few readers on the Peirce List will find these of use by way of >> informing their discussions. >> >> >> Excerpts from Saunders Mac Lane (1971/1997), ''Categories for the Working >> Mathematician'' >> ============================================================ >> ============================= >> ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_ >> Awbrey/Mathematical_Notes#CAT._Category_Theory >> ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_ >> Awbrey/Mathematical_Notes#CAT._Category_Theory_.E2.80.A2_Discussion >> >> Excerpts from J. Lambek and P.J. Scott (1986), ''Introduction To Higher >> Order Categorical Logic'' >> ============================================================ >> ===================================== >> ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_ >> Awbrey/Mathematical_Notes#HOC._Higher_Order_Categorical_Logic >> ☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_ >> Awbrey/Mathematical_Notes#HOC._Higher_Order_Categorical_ >> Logic_.E2.80.A2_Discussion >> >> Regards, >> >> Jon >> >> Jeffrey Brian Downard wrote: >> >>> Jerry, List, >>> >>> We might add that category theory, as it has been developed in >>> mathematics in the 20th century, is a generalization upon the conception of >>> a mathematical group. Peirce was quite familiar with Klein's use of group >>> structure as a basis for exploring the relations between different areas of >>> mathematics. As such, we should not assume that the general idea of what >>> is involved in the conception of mathematical category is entirely foreign >>> to Peirce. >>> >>> Jeff >>> >>> >>> Jeff Downard >>> Associate Professor >>> Department of Philosophy >>> NAU >>> (o) 523-8354 >>> >> >> > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm. > > > > > >
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
