[FOM] Presentation of Alternative Foundations?

[Harvey Friedman]

Dimitris Tsementzis wrote:

"To be more precise, I can give you an account of the new foundations
using seven basic notions: shape, point, symmetry, observation,
juxtaposition, amalgamation, path. These are the notions I used to
convince myself that I could justify the rules of HoTT without
resorting to to set-theoretic topology. (Resorting to set-theoretic
topology seems to me clearly the wrong way to go for an *intuitive*
justification of the rules of HoTT. Rather, it is the way to go for a
*formal* justification, i.e. for relative consistency results.) Anyway
I am prepared to do that — and in any case, as I have mentioned to
you, I believe such an account is possible, even if I have not found
the clearest way to do it."

Now this is the first time I have seen anybody even indicate that they
have any idea what I have in mind when I ask for a philosophically
coherent presentation of seriously alternative foundations for
mathematics.

I would be very interested to see an approach to general foundations
for mathematics based on your

shape, point, symmetry, observation, juxtaposition, amalgamation, path.

So go ahead and start presenting this.

Harvey Friedman