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September 1, 2010

The Philosophy of the Logic of Sheaves

Posted by John Baez

An unusual conference in an unusual venue:

Colin McLarty will be speaking about the work of Grothendieck!

Here’s the announcement:

Classical Logic and Set Theory influenced deeply the emergence of Analytical Philosophy at the beginning of XXth Century. After a hundred years, it may be time that the Logic of Sheaves and Category Theory help to create alternative forms of practicing Philosophy. Closer to the concepts of movement, flow, passage, boundary and contamination, Sheaf Logic and Category Theory must reinvigorate some regions of Philosophy abandoned by the Analytical dogmae. “Naturalized” Phenomenology, “Mathematical” Metaphysics, “Semiotical” Hermeneutics, between others, may thus emerge with new instruments at hand. The Symposium Philosophy of the Logic of Sheaves hopes to establish the state of the question, profiting from a creator of the Logic of Sheaves (Caicedo) and some major specialists in the Philosophy and History of Category Theory (Krömer, Marquis, McLarty). Forty years after Grothendieck’s departure from the IHES, the Symposium will be devoted in part to his legacy.

Speakers:

- Colin McLarty (Case Western Reserve University)

- Xavier Caicedo (U. de los Andes, Colombia)

- Jean Pierre Marquis (Université de Montréal)

- Andres Villaveces (U. Nacional, Colombia)

- Ralf Krömer (Nancy Université / University of Siegen)

-Fernando Zalamea (U. Nacional, Colombia)

PROGRAMME:

Colin McLarty: Grothendieck’s ‘Incorrigible Naivety’ in Building Worlds for Mathematics

Xavier Caicedo: The Model Theory of Sheaves or the Logic of Variable Structures

Jean-Pierre Marquis: Sheaves, Spaces and Logic

Andrés Villaveces: Bridging a Gap between Physics and Logic: the Role of Sheaves

Ralf Krömer: From Cantor to Sheaves: the development of the concepts of direct and inverse limits — a case study on shifts in mathematical methodology in the prehistory of category theory

Fernando Zalamea: Sheaf Logic: a mathematical conspectus and a philosophical prospectus

Posted at September 1, 2010 7:33 AM UTC

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11 Comments & 1 Trackback

Re: The Philosophy of the Logic of Sheaves

Closer to the concepts of movement, flow, passage, boundary and contamination

Contamination?

Posted by: Urs Schreiber on September 1, 2010 8:58 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

Dunno. I guess we have to go to Cali.

Posted by: John Baez on September 1, 2010 10:50 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

“dogmae”?

Shouldn’t that be “dogmata”? Or maybe it would be better to stick with “dogmas”.

Posted by: Tim Silverman on September 1, 2010 9:08 PM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

> Contamination?

Fernando Zalamea uses the word “contaminación” in a non-pejorative
way, to designate interactions across subjects. It is opposed to the
“pure”, the naive viewpoint that for example number theory is
independent of analysis, or logic independent of geometry. (The first
example, analytic number theory, goes back to Lautman [1] (but I guess
the word “contamination” does not), the second example, sheaf theory,
is key to Zalamea’s case studies of the works of Serre, Grothendieck
and Lawvere.)

“Contamination” is one of many keywords in Zalamea’s attempt [2] at
description of contemporary mathematics as it is really practiced, and
as it ought to be studied by philosophers of mathematics, and one of
many aspects overlooked by the classical (analytical) philosophers of
mathematics accused of thinking that the workings of mathematics can
be uncovered by studying workings of propositional logic or some
paradoxes in set theory.

Refs:

[1] F. Zalamea, “Albert Lautman et la dialectique créatrice des
mathématiques modernes”, préface à: A. Lautman, “Les mathématiques,
les idées et le réel physique”.

[2] F. Zalamea, “Filosofía sintética de las matemáticas
contemporáneas”, UNC, Bogotá, 2009.

Posted by: Joachim Kock on September 12, 2010 2:04 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

Re: contaminación - how about ‘cross fertilization’? (or cross-fertilization?) This has similar connotations in English, but without the negative implication. Cross fertilization can be a contamination, in a laboratory or even agricultural setting, but also positive thing, as in hybridisation or in cultural setting.

Posted by: David Roberts on September 12, 2010 11:30 PM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

Joachim wrote:

Fernando Zalamea uses the word “contaminación” in a non-pejorative way, to designate interactions across subjects.

I guess everyone is thinking it, but I’ll say it out loud: in English, it’s impossible to use “contamination” in a non-perjorative way.

I’m imagining sentences like “Are you in the Department of Pure Mathematics, or the Department of Contaminated Mathematics?”

Posted by: John Baez on September 13, 2010 1:39 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

John, in linguistics people use word contamination for the instance of a language change in which a individual form’s shape is affected by the behaviour of the shape of another word which appears in the same context. There is nothing negative about it: the language may become even more regular by such contaminations; and the changed form will be often synchronically correct while its non-contaminated form will be synchronically incorrect. People also talk about contamination of different languages in contact but this is different; the contamination above is about a single word/shape within single vernicular.

Posted by: Zoran Skoda on September 16, 2010 3:39 PM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

Fernando Zalamea uses the word “contaminación” in a non-pejorative way, to designate interactions across subjects.

I see, thanks.

Is it too late to find a well suited word? I might suggest interrelation.

By the way, also the word boundary in the list

Closer to the concepts of movement, flow, passage, boundary and contamination,

does seem to contradict the other words. This reminds me of my little nephew’s preschool exercises: cross out the word that does not fit with the others.

Maybe not important, but my impression was that there is a promotional intention here. I expect that would be achieved better with a list like, say: movement, flow, passage, and interrelation .

Posted by: Urs Schreiber on September 12, 2010 9:24 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

Re interrelation and cross-fertilization:

Presumably, philosophers choose their words carefully.
It seems that such words are not formally defined terms
that can easily be summarised in five lines (as I
attempted to), and I suspect that it might not make much
sense to rename a concept: possibly, the denoted concept
itself depends on the connotations of the word. Control
over the connotations could be one of the reasons for
Zalamea to write his treatise in Spanish, although he is
quite fluent in both English and French. To suggest better
‘terminology’ one should probably be a native Spanish-speaker
and first read the whole treatise. But of course, each of
us makes his own interpretations and approximations, as part
of the reading process.

PS: I also find the word strange in the context, and even
more to see it appearing in a list of five keywords of a
conference, which as Urs points out, serves as advertising.
Perhaps it is a deliberate eye-catching trick, like oDD cASING:
after all, at least four people, on this café alone, have
paused to reflect on the meaning of the word…

Posted by: Joachim Kock on September 13, 2010 1:36 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

after all, at least four people, on this café alone, have paused to reflect on the meaning of the word…

At least after I asked about it. Myself, I asked because this appeared on our blog. Had I seen the abstract elsewhere, I believe I would have ignored it. Comparably to when I walk through the city – not to mention the internet – and see something that does not make sense to me, I might simply ignore it, but if it occurs in my living room, then I inquire what’s going on.

Posted by: Urs Schreiber on September 13, 2010 7:48 AM | Permalink | Reply to this

Re: The Philosophy of the Logic of Sheaves

Interesting! One of my very first posts on this blog raised the question of what kind of transformation category theory might bring about to philosophy. Some approaches to the question were sketched in Giandomenico Sica’s collection What is Category theory?.

Posted by: David Corfield on September 1, 2010 9:13 AM | Permalink | Reply to this
Read the post Zalamea on Sheaf Logic
Weblog: The n-Category Café
Excerpt: Zalamea seminar announcement
Tracked: October 3, 2011 2:49 PM

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