Howard, list,
Peirce said /"there is some one individual of which one or other of two
predicates is true"/ ABOUT a specific proposition that he was
discussing. So you need to read that specific proposition in order to
understand what Peirce meant by "there is some one individual" etc.:
"There is some married woman who will commit suicide in case her husband
fails in business." which, Peirce finds, turns out to be equivalent to
"if every married man fails in business some married woman will commit
suicide".
A material implication, a.k.a. conditional proposition, _/de inesse/_,
is a non-exclusive disjunction between the negation of the antecedent
and the affirmation of the consequent. In other words,
'/p/→/q/' is formally equivalent to '~/p/ or /q/'.
So in my examples I could just have said that 'there is something
non-round or blue' is formally equivalent to 'there is something
non-round or there is something blue'. But the exposition is less
complicated if one simply gets rid of the 'non-'s. In the statement of
the general principle, Peirce, too, simplified to a characterization in
terms of non-exclusive disjunction. This may have thrown you off.
Now, Peirce discusses the general issue in two places that I've been
discussing in previous posts in this or the previous thread:
"Prolegomena to an Apology for Pragmaticism" CP 4 paragraph 569,
the section of the paragraph discussing Figure 210
Direct link to paragraph 569, once there, scroll down a little
http://www.existentialgraphs.com/peirceoneg/prolegomena.htm#Paragraph569
"On an Improvement on the Gamma Graphs" CP 4 paragraph 580,
sentence beginning "Let us assert that there is a man A and a man B...."
a little above Figures 222 and 223
Direct link to paragraph 580, then scroll down a little:
http://www.existentialgraphs.com/peirceoneg/improvement_on_the_gamma_Graphs.htm#Paragraph580
Best, Ben
On 2/16/2015 7:52 PM, Howard Pattee wrote:
Ben and list,
I don't see that any of your examples correspond to Peirce's first
clause: /"there is some one individual of which one or other of two
predicates is true."/ My point was that this statement does not imply
a second individual. Even if you assume that this "one individual" is
a member of a larger set of individuals, the predicates apply only to
that "one individual". Peirce's statement would give no justification
for applying one or both predicates to any other individual.
Peirce's second clause: /"there either is some individual of which one
/[predicate] /is true or else there is some individual of which the
other is true,"/ suggests more than one individual for which one or
the other predicate is true, or at least it allows that possibility,
which Peirce's first clause does not. So I still do not see how these
statements could be conceptually or logically equivalent.
I agree with you that the ambiguity is in words like "something," but
Peirce says, "There is some one individual . . ." You say, "*A*:
'There is something round or blue'. In normal language the concept of
"one individual" is not equivalent to "something". I don't know the
logical concept of a "veiled constant" but I know that "something" can
be a pronoun or a noun (or an adverb). As a pronoun it is
indeterminate. The opposite of this indeterminate "pronoun-something"
is, as you say, "nothing." But the opposite of "noun-something" is not
"nothing" but "not that one individual something." A negation of
Peirce's "one individual" should not be "nothing" but should be "not
that one individual." Therefore, I would say that your negations of
your statements *A* and *B* are not equivalent.
I don't know the context of this issue, so I have no idea why Peirce
felt the need to make these two lexically (at least) different
statements appear logically equivalent. Perhaps there were good reasons.
Howard
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