Willard Van Orman Quine

254 daniel isaacson
Stuart Mill supposed, but it imbibes it in the hypothetico-deductive
manner of theoretical science” 34 (CPT 333).
Is Quine’s attempt to apportion empirical content to mathematics
more successful than Mill’s? This is large issue, not simply settled,
but in brief I think that ultimately it is not. The confirmation of,
say, Newtonian mechanics by celestial observation did not make
the calculus more probable than it had been. Conversely, if a bit
of incorrect mathematics enters into a theory later found lacking
by the tribunal of experience (e.g., a mistake in arithmetic while
putting up some shelves), the response will be to find the error in
the mathematics. The failure of the shelves to fit in the intended
space alerted us to the fact that we should check the mathematics –
and by the criteria for correctness particular to mathematics. The
mathematics itself is sui generis with respect to the theories of the
world into which it so essentially enters.
But is it actually Quine’s position that mathematics shares the
empirical content of confirmed theories in which it is applied? A late
formulation by Quine seems to show that this is not his position,
or if it was, that he ultimately abandoned it. In his final book, From
Stimulus to Science, Quine wrote as follows:
The accepted wisdom is that mathematics lacks empirical content. This
is not contradicted by the participation of mathematics in implying the
categoricals, for we saw (Chapter IV [p. 48]) that such participation does
not confer empirical content. The content belongs to the implying set, and
is unshared by its members. I do, then, accept the accepted wisdom. No
mathematical sentence has empirical content, nor does any set of them.
(FSS 53)
Also in keeping with the accepted wisdom, of mathematics as independent
of sensory experience, is this passage: “I have stressed
the kinship of mathematics to natural science, but there is no denying
the difference. Pure mathematics has the advantage of being deducible
from first principles without sensory disruption” (RM 416).
But in other late publications Quine continued to promulgate
what appears to have been his earlier view of mathematics.
Consider, for example, the following revision to his Pursuit of Truth:
[A]nalyticity served Carnap in his philosophy of mathematics, explaining
how mathematics could be meaningful despite lacking empirical content,
and why it is necessarily true. However, holism settles both questions
Cambridge Companions Online © Cambridge University Press, 2006