Jim, List,
Yes, 0 and \infty are symbols for falsehood and truth, whose extensions
are the empty set and the universe, respectively. It is only for
infinite sums and products that we need a theory of limits.
In the language of lattices and partial orders, individuals and simples
would be called atoms and co-atoms, respectively, if I recall correctly.
Regards,
Jon
On 2/4/2015 3:33 PM, Jim Willgoose wrote:
Thanks Jon. I made a diagram to picture an (1) arbitrary x < A
returning o and (2) an arbitrary x >/ a /returning 00.
(fn. 16 refers to P's Boole article 1870 and calls this latter "1.") I
realize you have much more complex numbers and calculations in mind.
But the idea of an arbitrary next smaller or greater x allows one to
define a manageable boundary. Peirce calls these "ideals." But for
instance, given a time, space, or proof length constraint, thus a finite
condition, I must specify what an actual individual and a simple will be.
Jim W
1.) 0 <--x....( (A1) )
2.) ((A1) (A2) (A3) (A4) (A5))....../a/ --> 00
> Date: Tue, 3 Feb 2015 08:48:22 -0500
> From: [email protected]
> To: [email protected]
> Subject: [PEIRCE-L] Peirce�s 1880 �Algebra Of Logic� Chapter 3 �
Selection 2
>
> Peircers,
>
> Here is the next selection from Peirce's chapter on relatives
> in the 1880 Algebra of Logic, in which he defines the limiting
> concepts of "individuals" and "simples".
>
>
http://inquiryintoinquiry.com/2015/02/03/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-2/
>
> Regards,
>
> Jon
>
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