[FOM] Quotation from Frege

Jeffrey Ketland jeffrey.ketland at ed.ac.uk
Fri Nov 25 22:12:45 EST 2005

Dean Buckner,

> I have searched in all the obvious places but cannot find it.  It is
> something like "it is odd that the most exact of sciences [i.e.
> mathematics] should seek support from psychology, a science that is
> feeling its way none too surely .." .
> Grateful to anyone who can locate the source of this.  I had thought the
> Grundgesetze, but it seems to have disappeared from my copy.

It is from Grundlagen (1884), Section 27.

  For that reason, I cannot agree with Schloemilch either, when
  he calls number the idea of a position of an item in a series.
  If number were an idea, then arithmetic would be psychology. But
  arithmetic is no more psychology than, say, astronomy is.
  Astronomy is concerned, not with ideas of the planets, but with
  the planets themselves, and by the same token the objects of arithmetic
  are not ideas either. If the number two were an idea, then it would have
  straight away to be private to me only. Another man's idea is, ex vi
  termini, another idea. We should then have it might be many millions
  of twos on our hands. We should have to speak of my two and your
  two, of one two and all twos. If we accept latent or unconscious ideas,
  we should have unconscious twos among them, which would then
  return subsequently to consciousness. As new generations of children
  grew up, new generations of twos would continually be being born, and
  in the course of millennia these might evolve, for all we could tell, to
  such a pitch that two of them would make five. Yes, in spite of all this,
  it would still be doubtful whether there existed infinitely many numbers,
  as we ordinarily suppose. 10^10, perhaps, might only be an empty
  symbol, and there might exist no idea at all, in any being whatever, to
  answer to the name.
    Weird and wonderful, as we see, are the results of taking seriously
  the suggestion that number is an idea. And we are driven to the
  conclusion that number is neither spatial and physical, like Mill's piles
  of pebbles and gingersnaps, nor yet subjective like ideas, but non-
  sensible and objective. Now objectivity cannot, of course, be based
  on any sense-impression, which as an affection of our mind is entirely
  subjective, but only, so far as I can see, on reason.
    It would be strange if the most exact of all the sciences had to seek
  support from psychology, which is still feeling its way none too
  (Gottlob Frege, Die Grundlagen der Arithmetic, 1884, Section 27.
  Translated by J.L. Austin, fifth impression, 1980, pp. 37-38).

Regards --- Jeff

Jeffrey Ketland
Department of Philosophy
University of Edinburgh
George Square
Edinburgh EH8 9JX
United Kingdom
jeffrey.ketland at ed.ac.uk

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