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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