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October 15, 2021

Dynamics of Reason Revisited

Posted by David Corfield

A couple of years ago, I mentioned a talk reporting my latest thoughts on a very long-term project to bring Michael Friedman’s Dynamics of Reason (2001) into relation with developments in higher category theory and its applications.

While that Vienna talk entered into some technicalities on cohomology, last week I had the opportunity of speaking at our departmental seminar in Kent, and so thought I’d sketch what might be of broader philosophical interest about the project.

You can find the slides here.

Posted at October 15, 2021 10:19 AM UTC

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Re: Dynamics of Reason Revisited

I’m imagining that dialog in the Big Seminar in the Sky where Dan Kan and Archimedes talk about simplicial homotopy theory. Explaining the real numbers comes later.

Posted by: jackjohnson on October 15, 2021 5:06 PM | Permalink | Reply to this

Re: Dynamics of Reason Revisited

Unfortunately, it is a fact that «the philosophy of mathematics of past century did not want to know anything about its inner life». This led to the position that it became «hard to envisage internally-driven change».

Yet there is still a hope for «the dynamic interplay between mathematics and physics, each with their rich inner lives». Otherwise, «all mathematical activity is just some sort of proof machine».

Obviously, you shouldn’t be limited only to physics. But that is not the question.

Recognizing the dialectic between theoretical and applied sciences and mathematics, by adding philosophical aspects to it, we are interested in the issues that connect these disciplines. It will allow to «make the most informed decisions about our own methods and concepts».

Among these methods I will firstly point out cohomology and higher category. There are authoritative opinions regarding those. In particular, Eberhard Zeidler and Urs Schreiber, which indicate their ability to play a fundamental research role, for example, in physics.

But the problem is that there is still a disconnection between mathematics and scientific disciplines, especially when it comes to the application of algebraic methods. It is natural. And therefore, any steps aimed at bringing them closer are encouraging.

Posted by: Tevikyan Ashot on October 22, 2021 6:12 PM | Permalink | Reply to this

Re: Dynamics of Reason Revisited

Thanks, but I’m not sure where paraphrase ends and your own thoughts enter.

the philosophy of mathematics of past century did not want to know anything about its inner life

is (close to) something I wrote here years ago:

If you’ve read what I’ve written in philosophy of mathematics, you’ll know that a constant refrain of mine has been that philosophy, especially the English-language tradition of the past century, has wrongly not wanted to know anything about the inner life of mathematics.

And

Among these methods I will firstly point out cohomology and higher category.

That’s just what I’ve doing for years, taking centre stage in my Vienna talk.

Posted by: David Corfield on October 23, 2021 8:29 AM | Permalink | Reply to this

Re: Dynamics of Reason Revisited

I highlighted your thoughts with brackets, «». For my part, I would like to confirm your approach. I have not yet adhered to a different task.

Posted by: Tevikyan Ashot on October 23, 2021 8:58 AM | Permalink | Reply to this

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