Hello Ben.
Not all of these examples seem to fit the #580 case. The first problem is that
if 222 is an open variable ("a man commits suicide")
is identical to the other man, which Peirce leaves as an option, then the rule
of passage itself is questionable. Secondly, the rule of passage for a
conditional statement from an existentially quantified formula to an open
formula is a universal quantifier binding both. Thus, "any man either doesn't
go bankrupt or he commits suicide." But I cannot tell why the outer line of
identity is "null and void." It appears that you cannot connect the line
through "suicide" if the two men are identical. Thus, back to the first
problem. Importantly, I am changing quantifiers and not simply adding or
subtracting the same one. Secondly, I am curious about the previous role of "a
man." Jim W
Date: Sat, 17 Jan 2015 18:20:03 -0500
From: bud...@nyc.rr.com
To: peirce-l@list.iupui.edu
Subject: Re: Contradictories, contraries, etc. WAS Re: [PEIRCE-L] Natural
Propositions : Chapter 8 - On the philosophical nature of semiosis?
Jim, list,
Expository examples in everyday language are usually open to
logical criticism. If 'these beans' lack reference, then
Peirce's examples of inference modes don't work any more than my
examples with 'John'.
As to the rules of passage in terms of graphs, here are some
examples. Note that 'Z' plays the same role as
'bankrupt'.
See "An Improvement on the Gamma graphs" (1906), CP 4.573-580,
see 580
http://www.existentialgraphs.com/peirceoneg/improvement_on_the_gamma_Graphs.htm
. There you'll see the graph equivalences that bothered Peirce.
Best, Ben
On 1/17/2015 5:41 PM, Jim Willgoose wrote:
Curious. The formula "S is P" or "S is not P" do
not seem to carry enough information to decide the question.
On the other hand, if "John" lacks reference, the statements
"John is blue " and John is not blue" are consistent. (trivial
empty) Further, one may tempted to treat these as Universals;
(or singleton classes). But then, the existent singleton class
inclusive of "every John" doesn't seem to obey the rule of
contrary, namely, "may both be false," unless there are two
Johns. Aristotle's definition of a contradiction seems to me to
exclude this. The square of opposition is always fun to play
with. I sometimes like to consider that "everything exists" so
it works alright. BTW, waiting to see how you use the "rules of
passage" in terms of graphs.
Jim W
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