[FOM] 511: A Supernatural Consistency Proof for Mathematics

Monroe Eskew meskew at math.uci.edu
Mon Jan 14 15:23:18 EST 2013

One informal conceptual environment could be one where Leibniz's principle of the identity of indiscernibles holds.  This is a philosophically plausible principle.  Although it is consistent with ZFC that every object has a definition, slight strengthenings of ZFC imply the existence of distinct objects that are not discernible with respect to any parameter-free first-order property.  Does this contradict the CONJECTURE?


On Jan 13, 2013, at 10:12 PM, Harvey Friedman <hmflogic at gmail.com> wrote:

> Con(ZFC) is not a natural principle when thinking about rainbows,
> horizons, and beauty.
> Harvey
> On Sat, Jan 12, 2013 at 3:44 PM, Vaughan Pratt <pratt at cs.stanford.edu> wrote:
>> On 1/10/2013 6:19 PM, Harvey Friedman wrote:
>>> CONJECTURE. In ANY informal conceptual environment, we can formulate
>>> principles that are natural and sensitive and plausible in that
>>> environment, which are mutually interpretable with ZFC, and weak and
>>> strong variants of ZFC.}
>> I'm not sure I understand your conjecture, Harvey.  Which of its conditions
>> are not met by the principle Con(ZFC)?
>> Vaughan Pratt
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