FOM: Goedel: truth and misinterpretations

Torkel Franzen torkel at
Fri Nov 3 02:37:22 EST 2000

Vladimir Sazonov says, with reference to

    (2) Even if every even number greater than 2 is the sum of two
        primes, this is not necessarily provable in ZFC.

  >Very good! Eventually, instead of "A is true" it is written simply A.
  >The ill-stared "truth" is banished!

  I'm aware that you're of the opinion that we should not "use the word
TRUTH (or GOD) without a very serious need or reason". However, I don't
believe we need to approach the foundational problems of mathematical truth
in any such spirit of awe and mystery. Why not just soberly consider
the concepts we use and the use we make of them? In the present context,
I have explained that "true" in "Goldbach's conjecture is true" is to
be understood in the mathematically defined sense, whereby "A is true"
is a statement mathematically equivalent to A itself.

  Your idea that (2) should be made mathematically precise is an odd
one, since (2) isn't even a mathematical statement. If you will allow
me to be a bit repetitive, the general tenor of your remarks isn't
difficult to understand. (2) is a statement of the same form as a
number of everyday observations, for example "Even if John is at home,
he will not necessarily answer the phone". Inspired, I believe, by
certain very natural metaphysical inclinations, you take the view that
a corresponding observation involving mathematical statements, like
(2), does not really make good sense. However, it is pointless merely
to *assert* that (2) does not make good sense, unless you have no
interest at all in putting your point of view across to other people
or in bringing them around to your way of thinking. You need to engage
in argument, which admittedly is always a prolonged and difficult
matter, and often frustrating. Nevertheless, as we are aware, it is
not impossible to influence both the thinking and the practice of
mathematicians and others by philosophical argument, as long as you
can make a connection with their actual intellectual concerns, in a
way that respects their actual mathematical or intellectual

  With this, I suspect that our particular exchange on this topic cannot
profitably be taken further. I'd like to mention here that I included
your essay "On Feasible Numbers" in the literature for a graduate course
in the philosophy of science at the cs department here, where it caused
many a furrowed brow as the students pondered the existence of 2^1000.


  Torkel Franzen

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