Willard Van Orman Quine

218 daniel isaacson
the logical” 5 (p. 281). Empiricism, the doctrine that all knowledge
depends ultimately on (sensory) experience, 6 is the taproot of this
development and reaches back to Aristotle.
Mathematics is the biggest stumbling block for empiricism, since
mathematical knowledge is, on the face of it, obtainable by pure
thought alone. 7 Following Michael Ayers, I want to distinguish between
“concept-empiricism, according to which all our ideas ultimately
derive from experience” and “the stronger, or at least
different, view, knowledge-empiricism, according to which all propositional
knowledge is empirical, ultimately based on sensory knowledge”
(Ayers 1991, 14–5). Aristotle’s empiricism is a form of conceptempiricism,
and so is Locke’s.
David Hume (1711–76) espoused knowledge-empiricism, with the
restriction that it does not apply to the propositions of mathematics.
He drew a distinction between “matters of fact” and “relations of
ideas.” Truths of mathematics are relations of ideas, and relations of
ideas are known by pure thought:
All the objects of human reason or enquiry may naturally be divided into
two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind
are the sciences of Geometry, Algebra, and Arithmetic; and in short, every
affirmation which is either intuitively or demonstratively certain. That the
square of the hypotenuse is equal to the square of the two sides, is a proposition
which expresses a relation between these figures. That three times five
is equal to the half of thirty, expresses a relation between these numbers.
Propositions of this kind are discoverable by the mere operation of thought,
without dependence on what is anywhere existent in the universe. (Hume
[1777] 1975, 25)
As to matters of fact, some are known immediately from “the present
testimony of our senses, or the records of our memory” (p. 26), but
clearly many matters of fact are not immediately determined by observation
(present or remembered). Hume raises the question what
kind of evidence we have for matters of fact not established immediately
by observation:
It may, therefore, be a subject worthy of curiosity, to enquire what is the
nature of that evidence which assures us of any real existence and matter
of fact, beyond the present testimony of our senses, or the records of our
memory. (p. 26)
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