[peirce-l] Re: The roots of speech-act theory in the New List

[Benjamin Udell]

Jim,   >[Jim Willgoose] There is a difference between treating possibility epistemically or treating it ontologically.  "Possibly black' and "possibly non-black" are (sub) contraries, indeterminate with respect to a state of information. But since we are considering "this stove," and not allowing multiple reference for "this," we know that both statements cannot be true for a definite individual. Particular propositions, for Peirce, obey both the laws of non-contradiction and excluded middle. ( 1st order Form: (poss. Bs  & poss -Bs ) Notice that I do not use the quantifier "E" since "this stove" denotes a definite individual.  ("s" is an individual variable and "B" is a predicate letter.) These two propositions are not "compossible, although they are severally possible." (Peirce's language) However, 2nd order Form creates a problem. EF(Fs & -Fs) Which property? Here "F" is an indefinite predicate variable. Should not all substitutions for "F" be identical regardless of whether we can identify the property? Maybe not. Peirce said in the gamma graphs that for ordinary purposes, "qualities may be treated as individuals." If there is  no definite property, then the proposition is vague rather than false. Identity is critical even for possible states of information.   Maybe there's a necessary difference at a simple logical level between epistemic and ontological treatments of possibility, but such difference isn't evident to me.   You don't provide a reference or a quote, but presumably Peirce is referring to the components of "(Bs & ~Bs)" as non-compossible and as severally (separately) possible, but is _not_ referring to a form like "(poss. Bs  & poss. -Bs)" at all. It would be strange, I think, if he did. Yet Peirce's technical conception of propositions and predicates and their treatment differs enough from the contemporary, that, well, who knows? So I ask for a quote from him. Somehow you seem to be thinking that "poss.Bs" is the negative of "poss.~Bs".   The same issues are involved with the "(Fs & ~Fs)" in "EF(Fs & ~Fs)."    I don't know what your assumptions are about the 1st-order syntactical status of "poss.", but it's as if you're treating "poss." in "poss. Bs" as a predicate, whereas one needs to treat it as a functor (like the negative sign) and to treat the resultant "poss. Bs" as function of "Bs" rather than as "Bs" itself with some added predicated description "possible." This is the same as one treats "~Bs" as a function of "Bs" rather than as "Bs" with some added predicated description "negative." The appropriate 2nd-order counterpart is not "EF(Fs & ~Fs)" but "EF(poss.Fs & poss.~Fs). But I'm just guessing at your assumption. However it does seem that, however you're treating "poss.", it's not as a functor like "not".   Best, Ben Udell, http://tetrast.blogspot.com/ --- Message from peirce-l forum to subscriber archive@mail-archive.com