Willard Van Orman Quine

Quine and Logical Positivism 255
without appeal to analyticity. Holism lets mathematics share empirical content
where it is applied [emphasis added], and it accounts for mathematical
necessity by freedom of selection and the maxim of minimum mutilation.
(PTb 55–6)
And here is what he says in his 1996 “Philosophical Self-portrait”:
Mathematics, in so far as applied, is of a piece with natural science; for the
applied mathematical sentences are in the block of sentences that jointly
imply the [observation] categorical. Mathematics thus imbibes empirical
content in so far as applied. (APSP 465–6)
Quine was asked specifically to clarify his position on this issue.
Roger Gibson, in his essay “Quine’s Philosophy: A Brief Sketch”
(1998), writes that “in his latest book, From Stimulus to Science,
Quine seems to abandon the idea that even applied mathematics partakes
of empirical content” (p. 677), and Gibson quotes the passage
from that book extracted above. Gibson goes on to remark that “[t]his
apparent conflict with Quine’s Pursuit of Truth account might be
merely terminological (‘partake’ v. ‘confer’) or it might reveal something
more profound about Quine’s conception of cognitive meaning
and how his view differs from that of the logical positivists (or both)”
(p. 678). The word ‘partake’ as cited by Gibson comes from a passage
in “Two Dogmas in Restrospect” that I quoted earlier:
Sentences of pure arithmetic and differential calculus contribute indispensably
to the critical semantic mass of various clusters of scientific hypotheses,
and so partake of the empirical content imbibed from the implied observation
categoricals. (TDR 269)
It is joined by the words ‘share’ and ‘imbibes’ in the late passages of
Quine’s earlier view that I have just quoted.
Quine replied to Gibson’s query as follows:
Gibson has found, to my chagrin but gratitude, a disagreement between
my consecutive little books Pursuit of Truth and From Stimulus to Science
regarding empirical content of mathematics. I rest with the later position,
namely, that mathematics lacks empirical content. The point is that no
set of mathematical truths implies any synthetic observation categoricals.
(RGQ 685)
This reply is very odd. If what he said in From Stimulus to Science
expresses a new view, one that disagrees with his long-stated view of
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