Jerry, list,
Your messages aren't being distributed by the peirce-l server (I've
checked the IUPUI peirce-l archive). I've read them only in responses by
others to you. You're sending from another email address (an icloud.com
address) than the one that I find in your most recently distributed
posts to peirce-l (which were from a me.com address). The peirce-l
server identifies peirce-listers by email address. Have you tried to
subscribe to peirce-l using your icloud.com email address?
You wrote,
[Quote]
More to the point, does the meaning of mathematical symbols reside
in mathematics itself or do the meanings refer to the reference
systems for the symbol system, that is the application to a
particular material reality, such as the atomic numbers? Or the
sequence numbers for a genetic sequence? Or protein sequence?
[End quote]
In Peirce's view, the signs in pure mathematics do not refer to
particular or singled-out material things but, at most, refer to them
only potentially.
[CP 5.567, from part written by Peirce of the article "Truth and
Falsity and Error," Dictionary of Philosophy and Psychology, ed.
J.M. Baldwin, pp. 718-20, vol. 2 (1901). Quote]. These characters
equally apply to pure mathematics. Projective geometry is not pure
mathematics, unless it be recognized that whatever is said of rays
holds good of every family of curves of which there is one and one
only through any two points, and any two of which have a point in
common. But even then it is not pure mathematics until for points we
put any complete determinations of any two-dimensional continuum.
Nor will that be enough. A proposition is not a statement of
perfectly pure mathematics until it is devoid of all definite
meaning, and comes to this — that a property of a certain icon is
pointed out and is declared to belong to anything like it, of which
instances are given. The perfect truth cannot be stated, except in
the sense that it confesses its imperfection. The pure mathematician
deals exclusively with hypotheses. Whether or not there is any
corresponding real thing, he does not care. His hypotheses are
creatures of his own imagination; but he discovers in them relations
which surprise him sometimes. A metaphysician may hold that this
very forcing upon the mathematician's acceptance of propositions for
which he was not prepared, proves, or even constitutes, a mode of
being independent of the mathematician's thought, and so a
_/reality/_. But whether there is any reality or not, the truth of
the pure mathematical proposition is constituted by the
impossibility of ever finding a case in which it fails. This,
however, is only possible if we confess the impossibility of
precisely defining it.
[End quote]
Now, when Peirce says that a pure mathematical proposition is "devoid of
all definite meaning," he does not mean 'devoid of all definiteness'.
And by 'meaning' he means meaning as to the real. In a passage that I
can't find right now, he says that a good way to look at it is that a
mathematical proposition is definite in just those respects in which it
needs to be definite, and quite indefinite in all other respects. He
also allows that pure mathematical objects can 'mean' or refer to one
another or themselves. In "Syllabus" circa 1902 CP 2.311, he says
[Quote]
An Index can very well represent itself. Thus, every number has a
double; and thus the entire collection of even numbers is an Index
of the entire collection of numbers, and so this collection of even
numbers contains an Index of itself.
[End quote]
Now, when Peirce discusses the vague or indefinite, this is often in the
sense of that which we call the variable _/x/_, that is, as consisting
an alternative among _/a, b, c,/_ ..., often such that we don't have and
maybe can't have a full list of them individually designated or
indicated, since we're concerned with a denotation projectable endlessly
to encompass all the things - be it atoms, kinetics, or whatever, that
conform to the mathematical assumptions of the given mathematical
proposition. Now, the endless transformabilities whereby mathematical
objects are connected as by bridges means that if any math is applicable
to the real, then all of it will be, albeit sometimes trivially; some
people naturally will be interested in the nontrivial applications.
Best, Ben
________________________________________
From: Jerry LR Chandler
[[email protected]<mailto:[email protected]><mailto:[email protected]>]
Sent: Tuesday, August 19, 2014 9:28 PM
To: Jeffrey Brian Downard
Cc: Peirce List
Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category
theory
Jeffrey:
Your posts become increasingly mystical.
This is not a judgement, merely an observation from a philosophy of mathematics
perspective.
At issue is how to you assign meaning to mathematical symbols.
In particular, in light of K.S. and his comments on the meaning of number in
the context of his description of gold?
More to the point, does the meaning of mathematical symbols reside in
mathematics itself or do the meanings refer to the reference systems for the
symbol system, that is the application to a particular material reality, such
as the atomic numbers? Or the sequence numbers for a genetic sequence? Or
protein sequence?
In yet other terms, does the concept of order infer a universal meaning or a
meaning dependent on the nouns of the copulative proposition?
Perhaps you can address these vexing issue?
Cheers
Jerry
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
