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
On 1/17/2015 12:24 PM, Howard Pattee wrote:
At 12:44 AM 1/17/2015, Gary Richmond wrote:
Howard wrote: I agree with SEP
<http://plato.stanford.edu/entries/realism/> Realism
<http://plato.stanford.edu/entries/realism/>:
Those who have looked at this article may or may not, have noticed
that Peirce's understanding of realism isn't even mentioned in it.
HP: Which is why I keep asking for specific cases that Peirce did
/not/ consider real. If you say that a peer refereed and recently
updated review of /realism/ doesn't include Peirce's concept of
realism, then I think that is a reasonable question.
For example, it is not clear to me if Peirce considered as /real/ his
intuitive concept of infinity as a "supermultitudinous" collection of
sets of infinitesimals. In any case he concluded that this concept was
too unwieldy to be useful in scientific models. What about complex
numbers? What about n-dimensional spaces, etc. that /are/ necessary
for scientific models?
Howard
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
