Inquiry Blog
http://inquiryintoinquiry.com/2015/01/30/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-preliminaries/
http://inquiryintoinquiry.com/2015/02/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-1/
http://inquiryintoinquiry.com/2015/02/03/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-2/
http://inquiryintoinquiry.com/2015/02/11/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-3/
http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-4/
Peirce List
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15566
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15607
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15608
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15616
JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15624
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15634
JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15636
JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15639
JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15641
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15646
JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15657
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15659
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15660
JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15664
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15665
Jerry, List,
When in doubt, please refer to my blog versions where
I can use the appropriate math formatting and typefaces.
Peirce uses roman (non-italic) typeface for constants or
individuals, that is, proper names of individual entities.
So I use LaTeX \mathrm{A}, \mathrm{B}, \mathrm{C}, etc.
for these. Think "Ann", "Bob", "Cal", etc. for these.
Math style sheets dictate italics for variables,
so this is the default in LaTeX math settings.
The only variable used in CP 3.220 is ''x''.
A general term is one that denotes any and all the elements of a set.
Peirce uses terms like "aggregate" or "logical sum" to refer to sets.
General terms and variables are not exactly the same thing,
although there is a relation between them in some contexts
since a variable ranges over the members of a set.
So if Bob and Cal and Don each love only Ann,
but Ann loves only Don, then the dual relative
ℓ = lover of = B:A + C:A + D:A + A:D.
I think the problem is that "member" has two meanings.
It can mean "member of a set" or "member of a tuple".
Regards,
Jon
On 2/12/2015 11:55 PM, Jerry LR Chandler wrote:
List, Jon:
If read from a technical perspective, this passage (CP 3.220) can be
interpreted as nearly self-contradictory or utterly ambiguous. It appears that
CSP is unable to distinguish between nouns as Proper Nouns and nouns as
generals. But this can be a perplex gloss.
Contrast:
Every relative, ..., is general;
(seemingly inferring that a relative is a general, that is, a mathematical
variable.)
An individual relative refers
to a system all the members of which are individual.
(seemingly inferring that and INDIVIDUAL relative is not a general (!)
and further, requiring that the concept of "an individual relative" also makes
necessary a system of relations such that only individuals (that is, perhaps
non-generals? ) are the only members allowed.)
The expressions
(A : B)
(A : B : C)
may denote individual relatives.
are expressions of pairings of symbols that are not to be interpreted as
variables, at least as I read it.
(The notation is NOT the usual notation for variables for multiplication or
addition. Nor is the subsequent table of extensions...)
Nevertheless, I find the meaning of CP3.220 to clear and straight forward.
It is analogous to the meaning of natural relations among atomic relatives.
"Individual relative" may refer to the Proper Name of an individual chemical
element.
It is also consistent with his later paper on the logic of relatives in
relation to graph theory:
C. S. Peirce (1897 Jan.), "The Logic of Relatives", The Monist, v. VII, n. 2
pp. 161-217.
In short, in CSP's terminology, the nature of addition and of multiplication,
differ for general relatives and individual relatives, vaguely similar to
Boolean notions.
Cheers
Jerry
On Feb 12, 2015, at 3:28 PM, Jon Awbrey wrote:
Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 4
http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-selection-4/
Posted : February 12, 2015 at 4:00 pm
<blockquote>
Chapter 3. The Logic of Relatives (cont.)
§2. Relatives (cont.)
220. Every relative, like every term of singular reference, is general;
its definition describes a system in general terms; and, as general, it
may be conceived either as a logical sum of individual relatives, or as
a logical product of simple relatives. An individual relative refers
to a system all the members of which are individual. The expressions
(A : B)
(A : B : C)
may denote individual relatives. Taking dual individual relatives,
for instance, we may arrange them all in an infinite block, thus,
A:A A:B A:C A:D A:E etc.
B:A B:B B:C B:D B:E etc.
C:A C:B C:C C:D C:E etc.
D:A D:B D:C D:D D:E etc.
E:A E:B E:C E:D E:E etc.
etc. etc. etc. etc. etc. etc.
In the same way, triple individual relatives may be arranged
in a cube, and so forth. The logical sum of all the relatives
in this infinite block will be the relative universe, ∞, where
x ─< ∞,
whatever dual relative x may be. It is needless to distinguish
the dual universe, the triple universe, etc., because, by adding
a perfectly indefinite additional member to the system, a dual
relative may be converted into a triple relative, etc. Thus, for
''lover of a woman'', we may write ''lover of a woman coexisting
with anything''. In the same way, a term of single reference is
equivalent to a relative with an indefinite correlate; thus,
''woman'' is equivalent to ''woman coexisting with anything''.
Thus, we shall have
A = A:A + A:B + A:C + A:D + A:E + etc.
A:B = A:B:A + A:B:B + A:B:C + A:B:D + etc.
</blockquote>
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