Peirce's 1870 “Logic Of Relatives ” • Selection 10

Post   : Peirce's 1870 “Logic Of Relatives” • Selection 10
http://inquiryintoinquiry.com/2014/03/09/peirces-1870-logic-of-relatives-%e2%80%a2-selection-10/
Posted : March 9, 2014 at 1:30 pm

Peircers,

Here is Selection 10 (CP 3.75) from Peirce's 1870 “Logic Of Relatives”.
I will go ahead and post a plaintext transcript to the List, but please
see the blog post linked above for the fully fledged copy, as Peirce uses
a wide variety of different typefaces for closely related formal entities.

We continue with §3. Application of the Algebraic Signs to Logic.

<quote>

The Signs for Multiplication [cont.]
------------------------------------

The sum x + x generally denotes no logical term.  But x,_∞ + x,_∞ may be considered as denoting some 
two x’s.

It is natural to write:

x + x  =  2.x ,

and

x,_∞ + x,∞  =  2.x,∞ ,

where the dot shows that this multiplication is invertible.

We may also use the antique figures so that:

2.x,_∞  =  2x ,

just as

1_∞  =  1 .

Then 2 alone will denote some two things.

But this multiplication is not in general commutative, and only becomes so when it affects a 
relative which imparts a relation such that a thing only bears it to ''one'' thing, and one thing 
''alone'' bears it to a thing.

For instance, the lovers of two women are not the same as two lovers of women, that is:

ℓ2.w  and  2.ℓw

are unequal;  but the husbands of two women are the same as two husbands of women, that is:

h2.w  =  2.hw ,

and in general;

x,2.y  =  2.x,y .

</quote> (Peirce, CP 3.75)


Jon Awbrey wrote:
 > Post   : Peirce's 1870 “Logic Of Relatives” • Preliminaries
 > http://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-%e2%80%a2-preliminaries/
 > Posted : January 27, 2014 at 12:34 pm
 > Author : Jon Awbrey
 >
 > Peircers,
 >
 > I've been trying to get back to my study of Peirce's 1870 Logic Of Relatives for several years 
now and 2014 looks to be as good a year as any.  I thought it might be more pleasant to carry out 
the work on my blog than to hermit away on the wiki where I last left off, so I'm going to try doing 
that and see how it goes.
 >
 > Peirce's 1870 “Logic Of Relatives” (excerpts and commentary as far as I got)
 > http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives
 >
 > The formatting required for Peirce's text exceeds what I can convey by email.  Plus I'm hoping to 
turn my ASCII figures into genuine graphics, since one of the things that attracts me to this text 
is the way that Peirce's proto-graphical formulas anticipate aspects of his later logical graphs. 
Consequently, I'll largely be limited to posting links to my blog as I proceed.
 >
 > Regards,
 >
 > Jon
 >

-- 

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