Thanks Ben,
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.
Jim W
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Subject: [peirce-l] Re: The roots of speech-act theory in the New List
Jim,
> [Jim Willgoose] The proposition "She is possibly pregnant" is easily understood by all. I overstated my case. (nor is their a potential contradiction) But I think it masks a problem for the theory of cognition, and furthermore, not all ordinary expressions are as clear as they might be. So, we might try to rephrase some expressions if they do not fit the theory. It appears here that "possibility" reflects a state of ignorance with respect to the predicate. How far can the theory be extended and still work? The abstracted quality "pregnancy" can be identified. But can "possible pregnancy" be identified? I think your response would be "so much the worse for the theory." As you said previously, it is not rich enough. As for the matter of my particular interpretation of "possibility" being nowhere near shouting distance of ordinary Engish, that may be a virtue. Consider that a definite, actual stove cannot have contrary predicates. So, there is only one individual under consideration regardless of our ignorance of the predicate. The statements cannot both be true and in that sense they are inconsistent with each other. In any case, do you think some of your examples can be handled by Peirce's theory of cognition?
A possible pregnancy could be idenitified as being in respect of signs positive but inconclusive about pregnancy. In the given case, there would need to be an understood threshhold, even if only a vague one, for what the mind counts as representing a significant degree of possibility, as in practical affairs wherein one signifies that one is momentarily departing from just such a practical understood norm by saying something like, "well, it's _theoretically_ possible but...," etc. I don't know to what extent modal logics have dealt with these issues or instead leave them to the user along with the standard advice to be consistent across the given case.
Note that any problem with the idea of a possible pregnancy is also part of a problem with a flat-out modal proposition such as "Possibly there is a pregnant woman" or any propostion of the form "Possibly[Ex(Gx&Hx)]. In any non-empty universe, certain Ex, there is something. So it's a question of the possibility of Hx&Gx. If one goes even simpler, "Possibly[ExHx], then in any non-empty universe the same question about a "possibly H" will be raised.
Theories of probability and statistics are among the ways of dealing with possibility more variegatedly. There's also fuzzy logic, or at least a fuzzified modal logic (I presume), in order to deal with ways to formalize the informality and vagueness involved with talking about things like "maybe pregnant," "oh just possibly pregnant," etc.
I don't see why you consider "possibly black" and "possibly non-black" contrary. They seem for all the world to be _subcontrary_ -- it seems that of a given subject they can both be true but they can't both be false. "Necessarily black" and "necessarily non-black" -- those seem contrary, since it seems that of a given subject they can both be false but can't both be true.
Boldface: *3 any-pair-wise contraries*, collectively exhausting the options (usually one would say "exhausting the possibilities" but the word "possible" itself appears in the table, so, in order to avoid confusion....)
Italics: _3 any-pair-wise subcontaries_, whose negatives collectively exhaust the options.
~ ~ ~ _necessary or impossible_ ~ ~ ~
*necessary* ~ ~ ~ ~ ~ ~ *impossible*
~ ~ ~ ~ ~ ~ ~ ~ ~ >|< ~ ~ ~ ~ ~ ~ ~ ~
_possible_ ~ ~ ~ ~ ~ ~ ~ _unnecessary_ (=possible non-)
~ ~ *possible and unnecessary* ~ ~
| _necessary or impossible_ |
*necessary* | *impossible* | X |
| possible or impossible |
_possible_ | _unnecessary_ | *possible & unnecessary* |
Boldface: *4 any-pair-wise contraries*, collectively exhausting the options.
Italics: _4 any-pair-wise subcontaries_, whose negatives collectively exhaust the options.
Table pattern in familiar case (Boolean quantification).
| I iff A | *I&A* | *O&E* | F |
| _AvE_ | A | E | *A&E* |
| _IvO_ | I | O | *I&O* |
| T | _IvA_ | _OvE_ | I iff O |
| not contingent | *necessarily true* | *necessarily false* | X |
| _not contingently true_ | necessarily true or contingently false |
false | *contingently false* |
| _not contingently false_ | true | necessarily false or contingently true |
*contingently true* |
| true or false | _possibly true_ | _possibly false_ | contingent |
Rearranged a little, but table has same overall oppositional properties:
| necessarily true or contingently false |
*necessarily true | *contingently false* | X |
| _not contingently true_ | not contingent | false | *necessarily false* |
| _possibly true_ | true | contingent | *contingently true* |
| true or false | _not contingently false_ | _possibly false_ | necessarily false or contingently true |
> [Jim] How far can the theory be extended and still work? [....] As you said previously, it is not rich enough.
I didn't say that Peirce's theory isn't rich enough, although the idea that in some general sense it isn't rich enough is an obvious implication of what I've been saying. More specifically, the stove example isn't rich enough, and I mean that it isn't rich enough for expository purposes -- the "whetherhood" that I'm discussing is there in the idea that the stove is _affirmatively_ black, but such whetherhood is not brought into relief, it's just too "vanilla." Likewise such relationships as "another than" are only weakly presented.
> [Jim] In any case, do you think some of your examples can be handled by Peirce's theory of cognition?
I haven't been discussing a general _theory_ by Peirce about cognition. If I were familiar with such a theory, I might end up thinking that it is more adequate than his categorial and semiotic threefolds, just as I do think in regard to his pragmaticism with its definitive ideas about clarification by appeal to relevant experience. Whether one holds that his theorized category scheme is adequate for a complete cognition may depend at least partly on such questions as whether one accepts that selfsameness/otherness and the selfsames/others themselves comprise a single category -- the very daring and, I think, mistaken, conflation of 'dyadic' mathematical relations with thisness/reaction/resistance--, while accident & its attribution are in two different categories (though in the Peircean context perhaps one should think of the attribution of quality to reaction/resistance). But I've gone over these and related issues more extensively in recent posts.
Best,
Ben Udell
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