1880 Algebra Of Logic : Logic Of Relatives
•••:http://comments.gmane.org/gmane.science.philosophy.peirce/15566
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1870 Logic Of Relatives : Doctrine Of Individuals
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15673
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Jim, List,
At this point we need to go back to the 1870 Logic of Relatives
and review what Peirce wrote about the "Doctrine of Individuals".
This passage represents one of the most radical insights in all
of Peirce's thought and it is crucial to understanding the way
he managed to finesse the whole debacle of nominal thinking.
But I know I've reviewed and we've discussed this many times before,
so I'm thinking I might save a few quanta of mental effort by going
back and looking up some of the previous visitations.
May take a while to collect the links ...
Jon
On 2/17/2015 11:05 PM, Jim Willgoose wrote:
jon, list I changed my mind. "The simple is the negative of the individual." This is the last line of
section 1. I took the sign "~a" as 0 on the grounds that the product of negated individuals would be 0 if
"a" is the logical sum of individuals. I then assumed you could introduce something else, say "b,"
and if not, then a single algebra is defined. That may be ok. But that is not the problem. Rather, both limits
collapse forcing a redescription of what is individual and what is simple. Thus, what is in an individual up to N comes
unglued in R. Correspondingly, what is a simple in R requires more flexibility in the definition of an individual.
Jim W> Date: Mon, 16 Feb 2015 11:00:06 -0500
From: jawb...@att.net
To: peirce-l@list.iupui.edu
Subject: [PEIRCE-L] Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 6
Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 6
http://inquiryintoinquiry.com/2015/02/16/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-selection-6/
Posted : February 16, 2015 at 10:30 am
Peircers,
As long as I've got the WordPress warmed up,
I might as well post the last paragraph of
the present section, CP 3.222. And then
I think it's probably time to balance,
or ballast, these flighty abstractions
with a few bags of concrete examples.
Regards,
Jon
<blockquote>
Chapter 3. The Logic of Relatives (cont.)
§2. Relatives (concl.)
222. Instead of considering the system of a relative as consisting
of non-relative individuals, we may conceive of it as consisting of
relative individuals. Thus, since
A = A:A + A:B + A:C + A:D + etc.,
we have
A:B = (A:A):B + (A:B):B + (A:C):B + (A:D):B + etc.
But
B = B:A + B:B + B:C + B:D + etc.;
so that
A:B = A:(B:A) + A:(B:B) + A:(B:C) + A:(B:D) + etc.
</blockquote>
References
• Peirce, C.S. (1880), “On the Algebra of Logic”,
American Journal of Mathematics 3, 15–57.
Collected Papers (CP 3.154–251),
Chronological Edition (CE 4, 163–209).
• Peirce, C.S., Collected Papers of Charles Sanders Peirce,
vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),
vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,
Cambridge, MA, 1931–1935, 1958. Volume 3 : Exact Logic, 1933.
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition,
Peirce Edition Project (eds.), Indiana University Press, Bloomington
and Indianapolis, IN, 1981–. Volume 4 (1879–1884), 1986.
Resources
• Peirce’s 1870 Logic Of Relatives
http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives
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