FOM: Simpson't pointless persistent misinterpretation of Hersh
rhersh at math.math.unm.edu
Tue Sep 29 18:56:44 EDT 1998
I will try to correct a few of your misinterpretations. I can
still hope that you will read my actual words with their obviously
intended actual meaning.
You accuse me of "attacking " Frege and Hilbert. I attackaead
no one. To say of a philsophical trend that it was unable to
accomplish its goal is not an attack. Maybe the goal was
unattainable. Maybe (as I've said to you repeatedly) the
benefits of their efffort more than justified it, even if
the goal was unattainable.
I see that you can restate the goals of formalism and logicism
in terms that wipe out their original goals, and make them
appropriate in the light of today's situation. That's fine,
but why not say that your are updating the goals?
You persist in not knowing what I mean by foundatIonalilsm.
As I've told you before, this is a term coined by Imre Lakatos,
to express his insight that formalism. logicism, and intuitionism
shared a common goal of restsoring certainty to mathematics, and
differed in the means to that end. That insight was expressed byh
giving a comomon name to all three. Foundationalism is a grab baG
word that means logicism, formalilsm, or ilntuitionism, based on
the insight that they shared a comomon goal. (The inclusion of
intuitionism is based on the view that the reason for rejecting
LEM was that reaxoning based on LEM was less reliable, less certian
than non-LEM reasoning.)
You can deny; that these three "schools" have something in common,
you can object to the word which Lakatos invented to include all
3, but how can you keep on saying that you don't understand hat
I cited the axiom of infinity as evidence that logicism's
goal of reducing mathematics to logic had not succeeded. I
even gave a reference (which another member of FOM dismssed as
"what various folks said about it at different times."
I had earlier in that message mentioned that both Russell and
Frege gave up on logicism, I even gave a quote from Russell which ;you
can find in my book if you still have it. I don't know if Russell
and Frege were includead lin the "various folks at different times."
You challenge me to study how the axiom of infinithy is
used. You are indignant that I don't immediately volunteer for
this assignment. Let me tell you something important: I am
not, never was, never claimed to be an FOIM'er. Saying that
is not an attack on FOM. There are many other subjects where
I could equallhy declare my nonmembership.
You seem to think that no one but an fom'er is allowed to
be interested in the nature of mathematical existence and
knowledge. This attitude on your part is understandable,
perhaps not u;nique. But the fact is you do not have ownership
rights on the philosophy of mathematics.
Your presenting me with an impressive list of achievements
in foundations does not compel me to say I disagree with any of
them. Obviously, I'm not going to do anything of the kind.
Saying logicism formalism and intuitionism made major contribution
to logic but
failed to make mathematics indubitable is not attacking any;;one!
Oh, but indubitability is a" straw man."
Yes, it is, now, but it wasn't a straw man for Frege or
Russell or Hilbert. I write that indubitabililty is no longer regarded as
a viable goal. You say it's a straw man. It seems your'e agreeing
with me while thinking you're attacking me.
You misquoted me seriously when you said I said Hilbert isn't
around. You can check and see that I said Hilbert's formalism isn't
araound. That is, to my knowledge, nobody is pushing Hilbert's
separation of mathematics into two parts, one free of doubt, and
the other to be reduced to the first. I'm impressed by your 85% result,
and will actually try to read that paper. If you or others
are pushing Hilbert's approach, good luck. In that case I retract my
that it's not around any more. However, when formalism is
mentioned nowadays, as one of the members of FOM said jestinglhy "in
gossip im math common rooms" what is meant is reduction of math to
formal symbols, formal calculations, formal derivations. You can
look at the quotes from Cohen and Dkeudonne in my book, if you still have
it. I could also quote Henle (article in Math Intelligencer) and
Curry and Tiles and Resnik, but I doubt that it's worth the trouble.
You will find a way to misinterpret, no matter what.
In conclusion, I suggest you read the review of What is Math Really? in
August issue of Physics Today. Oh, you can say, a physicist, what does
he know about fom?
I am on this list by invitation.
Joining the list did not mean becoming an fom'er or an uncritical booster
of fom. The idea was that people with different viewpoints may try to
understand each, and possibly learn from each other.
I certainly don't mean to suggest you have anything to learn from me.
I am still trying to learn from you, but mostly I'm learning
obstinate debaters points and wilful misunderstanding.
As far as incoherent, you certainly haven't shown that my ideas
are incoherent, since you never even considered them.
ProbabLY YOU MEAN THAT WHAT I SAY DOESN'T COHERE WITH YOUR FOM
IDEOLOGY. THERE YOU'RE RIGHT.
BEST WISHES, HAPPPY JEWISH NEW YEAR.
More information about the FOM