[FOM] Fwd: Alternative Foundations/philosophical

Sam Sanders sasander at cage.ugent.be
Sun Mar 2 19:36:46 EST 2014

Dear Nick,

In principle, I agree with the open approach you and Chow advocate.  

However, things are rarely as simple in the real world.  For instance, 
would you qualify the following work by Cabbolet (based on matrices with sets as entries) as a “foundation for physics”?


There was a huge stink about Marcoen Cabbolet’s PhD thesis in the Netherlands.  

Would you say the Dutchmen were narrow-minded and closed as a community to act
in the way they did?

(I do realize Carnap was talking about FOM)



On 27 Feb 2014, at 11:15, Nick Nielsen <john.n.nielsen at gmail.com> wrote:

> The "Mathematicians' Liberation Movement" characterized by Chow might
> be formulated in terms of the Principle of Tolerance, or, to be more
> specific, the Principle of Tolerance in Foundations. Precisely
> parallel to Carnap, one can say that it is not our business to set up
> prohibitions, but to arrive at conventions in FOM.
> Chow's advice to, "open-mindedly explore if the new system helps
> foster new ideas," is an instance of what Carnap called, "simultaneous
> investigation... of language-forms of different kinds."
> Carnap famously said, "In logic, there are no morals. Everyone is at
> liberty to build up his own logic, i.e., his own form of language, as
> he wishes. All that is required of him is that, if he wishes to
> discuss it, he must state his methods clearly, and give syntactical
> rules instead of philosophical arguments."
> Here Carnap lays down a condition of syntactical rules, but in a
> Principle of Tolerance in Foundations we could just as well lay down
> the conditions that Harvey Friedman has formulated, and say that,
> "Everyone is free to elaborate his own foundations. All that is
> required of FOM is that its discussion embody absolute rigor,
> transparency, philosophical coherence, and addresses fundamental
> methodological issues."
> Of course, cashing out these conditions will be a lot more difficult
> than laying them down.
> Best wishes,
> Nick Nielsen

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