"The point of this seminar is not only to acquaint us with the vibrant landscape of contemporary mathematics – and the field of sheaf logic and category theory, in particular – but to show us how this landscape’s powerful new concepts can be deployed in the fields of philosophy and cultural production. Its aim is nothing less than to ignite a new way of thinking about universality and synthesis in the absence of any absolute foundation or stable, pre-given totality – a problem that mathematics has spent the better part of the last fifty years thinking its way through, and which it has traversed by means remarkable series of conceptual inventions – a problem which has also animated philosophical modernity and its contemporary horizon.
"Our guide in this endeavour will be Fernando ZALAMEA, a Columbian mathematician, philosopher and novelist whose work seeks to explore the life of contemporary mathematics while redeploying its concepts and forces beyond their native domain. In an incessant, pendular motion, he weaves the warp of post-Grothendieckian mathematics through a heterogeneous weft of materials drawn from architecture and fiction, sculpture and myth, poetry and music.
"Just as analytic philosophy emerged from the shockwaves of the explosion of classical logic and set theory onto the scene in the early 20th century, the conceptual force of mathematics after Grothendieck holds the potential to spawn a new, 'synthetic' vision of mathematically-conditioned philosophy for the present age, one which Zalamea foreshadows under the rubrics of transitory ontology, epistemological sheaves, and universal pragmaticism."
It turns out Zalamea is a big fan of Peirce. Here's* one of his articles on Peirce. The first thing of interest is that in exploring Peirce's Logic Notebook Zalamea appreciates that it is a chronological diary of the development of Peirce's thought. I.e., it shows the process of how Peirce came to his conclusions, the brainstorming, the multifarious and scattered ideas that only later became refined into his formulations. I've oft said that is IPS, how the threads and dialogs explore various topics, and how we then come to more solid positions. It's a media in res, continually.
ReplyDeleteWhich is another of Zalamea's appreciations in the above. How Peirce mixes and matches various fields and paradigms, finding those interstices of intersection between domains and categories. And which Zalamea himself uses in his own interlacing Vennish mixes of sheath logic and category theory.
* http://www.pucsp.br/pragmatismo/dowloads/lectures_papers/zalamea-paper.pdf
Also see Zalamea's essay on transmodernism.* From the Intro:
ReplyDelete"Transmodernity' –both diachronic and methodological- hopes to reintegrate many awkward postmodern differentials, to balance some supposed breaks with more in-depth sutures, to counter relativism with a topological logic where some 'universal relatives' provide invariants beyond the flux of transformations [....] [with a] merging [of] reason and sensibility which must explore the borders (TRANS) of thought [....] to reinterpret universals as partial invariants of a logic of change, where the borders of reason and sensibility appear as objects of reason in their own right. The important crisis revealed by Postmodernism (impossibility of unique perspectives, impossibility of cutting out antinomies, impossibility of stable hierarchies, etc.) can nevertheless be well understood using a continuous geometrical logic of reason and sensibility, open both to changes and invariances. This short article is intended as a programmatic one, pointing out the possible relevance that some non-standard pragmatic thinking (Peirce’s 'pragmaticism', Latin America’s 'razonabilidad') may have for our Transmodern epoch."
* http://lnx.journalofpragmatism.eu/wp-content/uploads/2009/11/09-zalamea.pdf
This is interesting, from pp. 3-4 of the last citation:
ReplyDelete"Broadening these precepts to the general context of semiotics, for knowing a given arbitrary sign (the context of the actual) we must run through the multiple contexts of interpretation that can interpret the sign (the context of the possible), and within each context, we must study the practical (imperative) consequents associated with each of those interpretations (the context of the necessary). In this process the relations between the possible contexts (situated in a global space) and the relations between the fragments of necessary contrastation (placed in a local space) take a fundamental relevance; this underscores the conceptual importance of the logic of relations, which was systematized by Peirce himself. Thus the pragmaticist maxim shows that knowledge, seen as a logico-semiotic process, is preeminently contextual (as opposed to absolute), relational (as opposed to substantial), modal (as opposed to determinate), and synthetic (as opposed to analytic). The maxim filters the world through three complex webs that enable us to differentiate the one in the many, and, inversely, to integrate the many in the one: the modal web already mentioned, a representational web and a relational web.
"One of the virtues of Peircean pragmati(ci)sm, and, in particular of the fully modalized pragmaticist maxim, consists, however, in making possible it to reintegrate anew the multiple in the one, thanks to the third-relational-web. Indeed, after decomposing a sign into subfragments within the several possible contexts of interpretation, the correlations between the fragments give rise to new forms of knowledge, which were hidden in the first perception of the sign. The pragmatic dimension stresses the connection of some possible correlations, discovering analogies and transferences between structural strata that were not discovered until the process of differentiation had been performed. Thus, although the maxim detects the fundamental importance of local interpretations, it also encourages the reconstruction of the global approaches by way of adequate gluing of the local. The pragmaticist maxim should accordingly be seen as a kind of abstract differential and integral calculus, which can be applied to the general theory of representations, i.e. to logic and semiotics as understood, in a more generic way, by Peirce."
And this is nice, resonant with my boundary reveries here* and following:
ReplyDelete"Peirce’s modal, multipolar and topological system investigates then the study of transferences of information around regions and borders on such a continuum. The TRANS motto is a crucial one for Peirce. His many classifications of the sciences show how one can 'tincture'the regions of knowledge using his cenopythagorical categories (1-3), and Peirce’s most creative ideas [...] lie precisely on the borders of regions where information is being transferred" (4).
* http://integralpostmetaphysics.ning.com/forum/topics/states-stages-the-wc-lattice-and-the-fold?commentId=5301756%3AComment%3A50570
I'm also reminded of our prior discussion of Peirce in this post* and following. Above that I was discussing Marks-Tarlow on boundaries, and below relating it to my later concept of rhetaphor.**
ReplyDelete* http://integralpostmetaphysics.ning.com/forum/topics/object-oriented-ontology?commentId=5301756%3AComment%3A41724
** http://integralpostmetaphysics.ning.com/forum/topics/object-oriented-ontology?commentId=5301756%3AComment%3A41815