From the Around Toposes Blog: Ontologies and toposes
The slides of the double talk given by Laurent Lafforgue and myself at the recent Huawei workshop on semantics are now available:
Our talk is based on an expository article written by AI theorists on the general theme of “ontology” and “knowledge representation”. We explain that the theory of Grothendieck toposes, of their geometric presentations by sites and of their linguistic descriptions in terms of first-order theories provides the means to incarnate in mathematical objects amenable to computations what could have seemed at first sight loose philosophical views. We present a number of important basic ideas about Grothendieck toposes and motivations for beginning to study them, and give an idea of the possibilities of the theory of “toposes as bridges” and its significance for the problem of “knowledge representation”.
thank you very much for your work.
I suppose you know the work they do or did concerning "The Topos of Music" (a book that synthesizes the moment of work of that team, I think in Zurich).
Years ago it was a moving thing to read some of Récoltes et S., i.e. part of a translation they did in Spanish (I found it after finding Badiou's books and then his dissemination of the Topos thing... etc.).
We live in crucial times, very strange times, it seems.
Actually it seems that this wonderful "unifying movement" somehow symbolizes with the truth about our genesis as souls.
And the soul somehow is the invariant "universe" co-regulator of the process of presenting experiences (≈ relationships with an environment governed by laws; the laws have the purpose (unifying in itself) of expressing the principles of the infinite personality that created that soul (which is to be unique, as it seems our friend Aristotle already felt logically... and as his teachers felt, etc.)).
I am assuming, or "working" on the hypothesis that we are a soul; the soul is created by the creator of all the laws that express the principles of that creator. That would explain the appeal and power of simplicity... and the "unifying convergence"... and our feeling of direction, etc.
(btw, this also seems to explain why Grothendieck left professional mathematics.)
(Or: The precedence of the actual over the potencial, ...
i.e., that the chicken comes before the egg )
Hi Ivan, thanks for your message. Yes, I have had a look at the book "The Topos of Music", but was disappointed in not really finding any serious topos theory there. All the best, Olivia
This idea blew my mind.
I have been interested and working in Semantics, Logic, Foundations of Mathematics, and Computational Linguistics, and I had no idea there could be a topic straight in the intersection of all of those areas!
Will you be doing more about this idea of using toposes and ontologies?
Thanks for your comment. Yes, I will continue developing this idea; stay tuned! 😉