Thank you Ben for a clear answer. I would say,
then, that in thinking about formal mathematics
Peirce was to some extent nominalistic, which of
course leaves him free to be realistic about
diagrams and physics. The basis for considering
logic to be realistic is still mysterious to me.
Of course there is still a great epistemic
variety among today's mathematicians and
physicists, largely because of great mysteries.
Natural selection has made sure we begin life as
naive realists which is necessary for immediate
survival. However, as physics has had to rely
more and more on creative imagination for models
of events, which are way beyond natural senses
and common sense, it is only reasonable that the
models become more nominalistic.
Howard
At 12:59 PM 1/17/2015, Benjamin Udell wrote:
Howard, lists,
My sense of it is that Peirce does not push the
idea that mathematicals are real. His
discussions of math and reality tend to involve
a variation of sense of word 'real' into the
concretely real, the actual, the existent, etc.
He says that mathematicians (of whom he of
course was one) don't care about the real and
that their ideal forms are the truly real to
them a la Plato. I do recall Peirce somewhere
saying that the question of whether
mathematicals are real is a question for the
metaphysician, not the mathematician, and I
recall him not answering the question at that
point. Peirce always says that mathematical objects are purely hypothetical.
Here's an example, from _Writings_ 6:255:
The reasonings and conclusions of the
mathematician do not in the least depend upon
there being in the real world any such objects
as those which he supposes. The devoted
mathematician cares little for the real world.
He lives in a world of ideas; and his heart
vibrates to the saying of his brother Plato that
actuality is the roof of a dark and sordid cave
which shuts out from our direct view the
splendors and beauties of the vast and more
truly real world,—the world of forms beyond. A
great mathematician of our day said with gustful
emphasis: "A great satisfaction in the study of
the theory of numbers is that it never has been,
and never can be, prostituted to any practical application whatever."
[End quote]
Peirce positively rejects the reality of
generals proposed by false propositions. Such
generals are figments, e.g., bat that evolved from bird.
Best, Ben
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