It seems that the sense of the expression is 'For if reason is not grounded in
universals, it is applied in vain to particulars.' The remark therefore
impinges directly upon the later mediaeval discussion of universalism and
nominalism.
John P. Burgess and Gideon Rosen, in their "A Subject with No Object:
Strategies for Nominalist Interpretation of Mathematics" (OUP, 1997) remark
(p.18) that contemporary nominalism in its various forms bears little or no
historical connection with the late-mediaeval nominalism associated in
philosophy especially with Ockham. Instead, they date it to Nelson Goodman's
work, begun in the 1940s and taken up by Quine et al.
My question concerns the older tradition, and I ask it in more or less
complete ignorance of work in historical mathematics relating to that period,
so I ask for your indulgence.
This is my question:
Were the fourteenth-century nominalists engaged in any attempt to make a
mathematics that accommodated their nominalism and their rejection of
universals as extra-mental entities? (It is a mistake, as I am sure is well
known, to say that they denied universals altogether, for Ockham quite
specifically identifies them as mental entities in the Quodlibetal Questions
5.13 et al.)
If anyone is interested, I ask the question because I am investigating a
philosophical background for the mathematics of emergence in complexity
theory, that is, a 'bottom-up' mathematics that reflects the way parallel
processor computers generate patterns from particulars rather than from
top-down design.
I would be most interested to hear from anyone else on the historia-matematica
list who shares this interest, which I acknowledge is not part of the list's
primary focus.
John Puddefoot