FOM: NATURE of mathematics

[Julio Gonzalez Cabillon]

Dear Professor Silver,

Thanks for your reply. None the less, I still do not grasp what are
your *own* thoughts about the nature of mathematics. I am aware of
your posts, and your criticisms on Hersh's views -- you may remember
now that it was me who first asked Reuben Hersh to elaborate about
Martin Gardner's harsh review of "What is Mathematics, Really?".
You may remember also that I drew the attention on this forum to
the "Wigner's dilemma" (of unreasonable effectiveness of maths in
the natural sciences), and to the "Julio's dilemma" (of unreasonable
fitness of large portions of *certain pieces* of maths to large
portions of *other pieces* of mathematics, fully and independently
discovered/conceived in different times, places, and topics).

What I would like to ask you about here, and I would be most grateful
for your answers, is not what you are *against* in Hersh's philosophy,
but what you are *for* in your *own* philosophy.

For instance:

1) Should mathematics on other planets (of other galaxies) be entirely
   different from ours -- provided its existence? Should it be similar?
   Isomorphic? What do you think? ...


2) Do you endorse that "mathematical reality lies outside us, that our
   function is to discover or observe it, and that the theorems which
   we prove, and which we describe grandiloquently as our 'creations',
   are simply our notes of our observations"? If so, I would appreciate
   to know why?


3) In the following incomplete sentence,

          "Hamilton .......... the quaternions in 1843",

   let us suppose we have to fill in the blank with a word.
         
   [discovered / invented / constructed / found / conceived / ...]

   What would be your choice?


4) Do you think that the probability that there's another Mersenne prime
   is greater than that that there's a mistake in the proof that the one
   recently discovered is prime?


5) In what sense can we say that mathematics is timeless true?


6) In the year 2098 (say, in case our fragile planet still be there), do
   mathematicians will believe that there *really* are infinitely
   many natural numbers?... Yet, without doing futurology, do you
   believe here and now that there *really* are infinitely many natural
   numbers? If so, where are there?... Do you really believe that it is
   conceivable that these infinitely many natural numbers did exist on
   a Jurassic park despite the fact that there were no mathematicians
   around to imagine them?


I set forth these questions to make myself clear of what I intended in
my previous posting. According to your reply I can understand that I was
not sufficiently explicit. Please mind that I am aware that you already
acknowledged that you "do not have a fully developed philosophy of
mathematics".

Many thanks.

Sincerely yours,
                   Julio Gonzalez Cabillon