FOM: Russell01 meeting abstract

[Harvey Friedman]

Here is my abstract for my talk at the Russell 01 meeting in Munich,
scheduled for 6/4/01. Please do not change any capitalizations (Conjecture
and conjecture).

Harvey Friedman

Research Program on Ways Out of Russell's Paradox

We Conjecture that all intellectually sensible consistent formal systems
are formally interpretable in current set theory (with large cardinals). It
should follow that all intellectually sensible consistent formal systems
are synonymous with a fragment of current set theory (with large
cardinals). In this sense, all ways out of Russell's Paradox - including
ways involving non set theoretic concepts - are Conjectured to be subsumed
under current set theory (with large cardinals).

We present a number of dramatic formal and informal conjectures that tend
to support this Conjecture. Recent results concerning these conjectures
suggest the viability of several new deep research directions in the
foundations of mathematics.