rhersh at math.math.unm.edu
Wed Sep 30 18:19:42 EDT 1998
I asked why you consistently persist in misinterpreting me.
You didn't answer, of course.
Instead, you send me another letter full of misinterpretations (I
could say distortions, but I want to be polite.)
Let's take them in order, starting at the top.
You say "you must dismiss Frege's work as a failure." Not at all.
I wrote, page 141 of W.I.M.R.: "Frege's introduction of quantifiers is
consdered the birth of modern logic." I have sent you bushelsfulls of
quotes saying that while his program for a logical foundation of
mathematics could not succeed, his contributions to logic are very
Still you accuse me of "dismissing Frege's work."
What motive can you have for persisting in this
accusation, that you must knw by now is false?
You wrote, "Don't you agree that this approach (fom) is more
fruitful than yours?
Of course a successful research program is more fruitful than
a critical comment about philosophy. But the two are not opposed to
or competing with each other. My remark doesn't hurt your research
program. You research program doesn't respond to my remark.
You say, "You present a a caricature of Hilbert's work, then attack the
caricature." No. I used the word "formalism in the common, colloquial
sense, not in Hilbert's sense. There is no caricature and no attack.
I've already explained this.
Why do you keep attributing to me wordsI never spoke,
after I've already explained to you what I actually said?
You wrote, "OK, now at last we know what you are talking about. When
you demonize foundationalism..."
There's no "at last." Foundationalism is defined and
discussed in my book, which for all I know you may
still have. I am not willing to go back through all these messages to
see how many times I explained foundationalism.
And what do you mean, "demonize"? When you attribute
such motives to me, it's I who am being demonized. To criticize or even
reject foundationalism isn't demonizing anything. It's what
people do in the course of finding their philosophical beliefs.
If I said that Descartes and Leibniz did not accomplish their
philosophical goals, would you say I was demonizing them? No, you
would not. Then may some philosophers be questioned, but not others?
You ask, "Isn't certainty the goal of all science?" Absolute
certainty, no. Increased certainty,or greater certainty, yes.
You write, "you regard the pursuit of certainty as evil
I am a mathematician. It's weird to tell me I regard the pursuit
of certainty as "evil incarnate." My proofs were checked by
referees. In the spirit of your challenges, I command you to read my
papers on pde's, random evolutions, and linear operator equations, and
find something uncertain. If you refuse this challenge, you must
retract your accusation that I regardd the pursuit of certainty as evil
incarnate. Where do you learn such expressions? Evil incarnate!!
What do I actually say about certainty? I'll explain again. I
believe that the motivating drive
for Brouwer, Frege, Russell and Hilbert was to restore certainty
to mathematics..I believe that the three "schools" wanted to restore
ceretainty by finding reliable foundations for mathematics. I
beleve that none of the three was able to carry out its program as
originally envisioned. But for all three, the
work on the program led to important progress in logic. Incarnate
evil? Not at all. Just an over-ambitious goal, now recognized as
You say, "If you are unwilling to study the role of infinity in
mathematics, then how can you expect anyone to take your comments on it
My comment, that the axiom of infinity is not inituitively plausible
as an axiom of logic, is not mine. It has been made by others
("various individuals at different times"!). I deserve no credit for it,
except in bringing it to your intention in the hope that you will see
one reason (among others) that people think the logicist program
was unsuccessful. You seem incapable of dealing with this well known
fact. I don't expect you to take my comments seriously. I expect
you to acknowledge and deal with the well knwon facts of the case.
You say, "You were arguing that it's OK to dismiss Hilbert's views
without a hearing." As I keep trying to explain, I never referred to
Hilbert's views at all. The word formalism has more than one meaning. I
can't believe you're unaware of that.
I will look at the 1988 JSL.
Please re-transmit your last collection
of misinterpretations (You titled it Hersh's something or other,
irrelevance?) My copy of it got lost.
By the way, Sol Feferman wrote "It is also clear that the search for
ultimate foundations via formal systems has failed to arrive at any
convincing conclusion." ("Logic of scientific discovery")
Now, to be fair, you'll have to accuse Sol of demonizing, attacking,
and being "so hostile" to fom!!
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