[FOM] New Umbrella?/big picture

Frode Bjørdal frode.bjordal at ifikk.uio.no
Thu Nov 6 17:58:05 EST 2014

On Wed, Nov 5, 2014 at 9:07 PM, Mitchell Spector <spector at alum.mit.edu>

> Harvey Friedman wrote:
>> ...
>> There is one quite friendly modification of the usual set theoretic
>> orthodoxy of ZFC and its principal fragments, and that is Flat
>> Foundations:
>> http://www.cs.nyu.edu/pipermail/fom/2014-October/018337.html
>> http://www.cs.nyu.edu/pipermail/fom/2014-October/018340.html
>> http://www.cs.nyu.edu/pipermail/fom/2014-October/018344.html
>> With regard to the last of these links, I think Leibniz is credited
>> for the general principle
>> x = y if and only if for all unary predicates P, P(x) iff P(y)
>> whereby giving a way of defining equality in practically any context
>> (supporting general predication).
>> ...
> Leibniz' principle, in this context, appears to be essentially a
> minimizing principle, making the mathematical universe as small as
> possible.  ("The universe is so small that there can be no two distinct
> objects that look alike.")
> This is in contrast to the maximizing principle which is a prime
> motivation of many large cardinal axioms -- saying that the mathematical
> universe is so very large that many objects in it are indistinguishable
> from one another (indistinguishable according to some specific criterion,
> of course, depending on the large cardinal axiom).

​It seems to me that this point may be made more appropriately against the
axiom of extensionality in classical set theory, which turns out false in
type free contexts such as in my librationist system £ and in earlier
literature referred to in my 2012 paper.


Professor Dr. Frode Bjørdal
Universitetet i Oslo Universidade Federal do Rio Grande do Norte
quicumque vult hinc potest accedere ad paginam virtualem meam
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