FOM: Friedman's result on necessary use of large cardinals

Torkel Franzen torkel at
Mon Mar 16 11:45:23 EST 1998

  Joe Shipman's comments  suggest to me that my contributions to this
thread have been opaque in a way that I certainly didn't intend.

  First, my comments were made, not in response to Friedman's presentation
of his results, but to Simpson's touting of these results as an epochal

  Second, my objections to this strident claim were simple
enough. First, how much of a foundational advance this is depends
strongly on what applications can be found of the combinatorial
principles at issue. Second, it also depends strongly on the
epistemological status of the large cardinal principles involved. Bill
Tait points out that one might seek a justification in either
direction. This is no doubt so, but the controversial aspect remains.
(That the results are remarkable and of obvious mathematical interest
I thought I had adequately remarked upon.)

  A largely separate question, also relevant in view of earlier
disputes on the list, concerns the "general intellectual interest"
of Friedman's results. This question hasn't really been discussed
since the last outburst by Simpson to the effect that intellectual
interest is an absolute, independent of how many people are in fact

  Now, my presenting these simple objections to Simpson's claim in
terms of my own slack-jawed wonder at the complexity of the
combinatorial principles, and the prominence of Cardinal Grenvelle
over other subtle cardinals from a somewhat wider point of view than
that of f.o.m. was my own considered form of response to the style
and contents of Simpson's posting. While adding nothing to the
points I raised - and Friedman's worries that such remarks could
adversely influence innocent minds I find touching but bizarre -
such a form of expression is something that mathematicians and
other serious-minded professionals who would like to have an
intellectual influence on the world at large must get used to
and learn to deal with.

Torkel Franzen

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