The Structure of Possibility
William L. Reese
I call your attention to ten theses concerning possibility which seem to me to be defensible:
I shall now comment on (1) through (6), and (10).
(1) Unable to think of any conditions which would falsify, or even qualify, I take it to be necessarily true. For simplicitys sake alone, I insist on the necessity of its possibility in an immediately preceding time, while not denying that it may also have been possible in a longer stretch of time prior to its having become actual. It would be reasonable to believe this longer stretch of time to be the normal case. Also, its possibility may be necessary, even though the likelihood of its actualization is merely probable, and however slightly probable. We are interested in determining the nature of this possible prior to its actualization. We approach the question through consideration of three relevant definitions of the possible suggested by Bruce Aune. Aune never uses the term possibility in his definitions, believing the term to suggest that the possible is an entity; and his program of ontological reduction is devoted to redescribing abstracta out of existence.
We shall consider Aunes definitions without preserving the niceties of his program, at least partly because of our belief that, on analysis, there is an end to redescription, and possibilities do turn out to be entities, although of an unusual kind. From now on I shall use the terms possible and possibility as synonyms, employing either or both, somewhat randomly.
(2) Aunes first definition, that of the logically possible, defined as "the proposition that p does not imply a contradiction," says to me that the logically possible is, first of all, a conception. As a conception, there is no question but that it exists within the mind. I do not know that Aune would agree. However it may be for him, Berkeleys distinction between what exists within, and without, the mind works for me. Nor do I believe that the mind-brain problem need arise here. I do note that no analysis of the brain waves which may be charted when one thinks of Platos idea of justice can yield that idea, or any idea, of justice. From the intensional side of things, at least, mental activity is made up of conceptions. I think that is all I need, even if extensionally it is composed of brain waves, passing through neural connections, and the like.
That the logically possible exists within the mind is convenient for getting on with the task of separating apparent logical possibilities, which harbor contradictions, from genuine logical possibilities which do not. Existence within the mind allows one to probe for the condition of consistency. While consistency is no guarantee that qualifying logical possibilities have an extramental existence (as actualities), no one expects to find contradictions existing outside the mind. Some believe that they do not exist even within the mind, that a so-called contradiction within the mind is not a single mental entity, but two opposed entities, which we insist on jamming together, even though we never quite succeed in thinking them together. Their apparent togetherness is the result of the mind quickly strobing between two conceptions which are inconsistent with each other. When we find, however, that an apparent possibility is logically possible, we accept it as a candidate for existing also outside the mind. (Such finding is, of course, provisional in the sense that anything we take to be logically possible might contain a lurking contradiction; but everyone agrees, I think, that the inconsistent has the negative purchase on actuality suggested here.)
Have logical possibilities, i.e., consistencies, a positive purchase on actuality corresponding to the negative purchase of inconsistencies; that is to say, are they also ontologically possible, as inconsistencies are ontologically impossible? We shall consider this question in the context of the three interpretations of the possible commonly offered in the history of philosophy. The three are: (a) The possible is a mere name (nominalism). (b) The possible is a mental entity and that alone (conceptualism). (c) The possible is an ontological entity, real although not (yet) actual (philosophic realism in my 1952 designation).
(3) The condition of consistency eliminates the first of the three interpretations on the following grounds: Were the possible a mere name, and that alone, its manner of existence would be that of a flatus vocis, and that alone. But a flatus vocis is something actual, a puff of air, and not something possible. If the possible were only an actual flatus vocis and nothing more then a possible flatus vocis would be a contradiction, since it is nothing actual, and therefore likewise not anything that is logically possible. Since a possible puff of air is not a name, it could not be a mere name and that alone.
If the possible is not a mere name but a mental entity, it is some form of abstractum and the locution possibility with its entitative suggestiveness becomes entirely appropriate.
Although the argument is framed in terms of possibility in general, we apply it in the first instance to logical possibility, the only type of possibility now before us. It remains to be seen whether we can advance beyond "logical possibility." If not, then all possibility is logical possibility, and that alone. For the moment we say merely:
(4) Were the possible a mental entity and that alone, it would be no more than a mental possibility. Were it to exist as an entity in the mind then, on the interpretation in (2) above (that contradictions do not exist, strictly speaking, within the mind), it is a genuine logical possibility. If, however, it exists in the mind alone, then in actualizing, the most it could become is a mental actuality. But a mental actuality, having no extramental reference, has not actualized, after all, and remains a mental possibility, i.e., there is no difference in meaning between the phrases "mental possibility" and "mental actuality."
Nominalists and conceptualists, when speaking of possibilities actualizing, while confining their existence to the mind, seem to be claiming that these actualizing logical possibilities leap out of the mind into actuality. That would seem to be a miracle. Most of us mean, I suggest, that logical possibilities somehow image ontological possibilities, or they are, at the same time, logical and ontological; and it is their latter aspect which, already outside the mind, turns into actualities. The same argument can be made with "logical possibility." Were a logical possibility, pure and simple, to actualize it would become a logical actuality. But either "logical actuality" has the same meaning as "logical possibility," or else a "logical actuality" is the same as an "ontological possibility." There is an issue here, however, which we shall access below.
(5) The parenthetical "yet" in the fifth proposition signifies that only ontological possibilities become actual; it is not meant to imply that every ontological possibility becomes actual.
If (3) and (4) are acceptable, the only way to move from logical possibility to actuality is through ontological possibility whose actualization can produce something in the actual world. The point of (3) is that consistency is the sufficient condition of logical possibility. As sufficient condition of logical possibility it is also, and inevitably, a necessary condition for ontological possibility (since nothing inconsistent in itself could be either ontologically possible or a condition of ontological possibility). Is logical possibility also a sufficient condition for ontological possibility? If so, then (a) logical possibilities are eo ipso ontological as well. If (a) is accepted, then logical possibilities have a positive purchase on ontology, paralleling the negative purchase of inconsistency (aka, impossibility). If consistency is merely a necessary condition of ontological possibility, then (b) at least one further condition must be added to logical possibility in order to reach ontological possibility. A further condition is readily at hand. Consistency with the laws of nature (external consistency) may serve as a second condition, supplementing the first condition of logical possibility (internal consistency). If nothing else, internal and external consistency make a nice pair.
(6) Certainly, what is not consistent with the laws of nature cannot become actual. If inconsistency with the laws of nature leads to impossibility might not internal and external consistency be joint conditions for possibility; and perhaps, if there are no further conditions, for actuality as well? Let us call the expansion of (6) to include external consistency (6b). In (6b) the idea of a unicorn is logically possible because internally consistent (let us suppose this to be the case); but not ontologically possible because inconsistent with the laws of nature. The contrapositive, "What is consistent with the laws of nature can become actual" would seem to follow. If it does then, since it can become actual it would seem, by (1), to have been antecedently possible. From the possible worlds standpoint, which we adopt only for the sake of the example, in some possible worlds the laws of nature are consistent with the unicorn idea. In those worlds the unicorn is both logically and ontologically possible. In worlds like ours the unicorn is only a logical possibility. In the worlds of Peirce and Whitehead where the laws of nature change, evolving and devolving, the unicorn idea might well be merely logically possible in some periods of time, while both logically and ontologically possible in others. In all periods of time it would be logically possible unless, of course, its idea contains a (lurking) contradiction.
But there is a counter-argument to the above. Consider the discovery of the top quark at the Fermi Laboratory in Santa Fe, New Mexico, in the spring of 1995. As heavy as an atom of gold, the top quark existed 10 billion years ago, under the early conditions of the universe, and had not existed since, so far as anyone knows, until the time of the experiment. Then, under conditions of intense energy produced by a particle accelerator the top quark appeared once again. Where had it been in between? The natural response is to say that in between it had remained an ontological possibility which lacked the conditions necessary for its actualization. Heisenberg made exactly that response to the question where an electron is between orbits. It retreats, he suggested, into possibility, and reactualizes in a different orbit. If this is so, is (6b) refuted, on the grounds that we must take ontological possibility, no less than logical possibility, to be independent of the laws of nature at any given time? One might express the point by saying that ontology is deeper than cosmology.
Should ontology be deeper than cosmology, logical and ontological possibility are on the same footing, internal consistency becomes a sufficient condition for ontological possibility, with external consistency neither necessary nor sufficient for either one. In our example the actualization of the quark was inconsistent with the present course of nature, although consistent with an earlier course, now replicated in the particle accelerator. One response is to say that the laws of nature are not different in the two cases; but that a change in conditions, i.e., in energy level, allowed the quark to actualize. But how are we to think of conditions, courses of nature, and laws of nature? Does a course of nature include only the conditions prevailing at a certain time, or both those conditions and the laws governing them? And how are we to distinguish between conditions and laws? Does an inoperant law of nature remain a law, while inoperant? Does the law hold even when the condition, which would make it operant, is not present? We could say that inoperant laws do not exist, operant laws do exist, and the shift between operant and inoperant is what Peirce and Whitehead meant by the habit-taking feature of the universe. Our hold on these terms is so tenuous, however, that it is difficult to determine what belongs to (6) and what to (6b); and since the added condition in (6b) did not turn out to be helpful in the top quark example, we have no reason not to remain with (6).
In keeping with (6) we have to say that the idea of the unicorn, if logically possible, is also ontologically possible, although in some given stretch of the universe, perhaps in many or most such stretches, the conditions allowing its actualization are not present.
(10) We can now say that where actual things have the form of the present (they are what they are and the principle of excluded middle applies to them), the mode of reality of an ontological possibility, real although not (yet) actual, is that of the "may be," a "may be which also may not be." The first is determinate; the second only quasi-so, depending upon its degree of nascency. We can also say that every actuality is related to a cluster of further possibilities; and that these relate to still further possibilities. Where an entity in the modality of the present, the "is," will be determinate, an entity sharing the modality of the future will have a forked nature, one fork for "may be," the other for "may not be." Since every fork forks in turn, the future branches into a pattern of possibilities beyond possibilities.
Aune urges that: "There could be a presumption in favor of accepting a certain general theory [of abstract entities] only if the theory is relatively clear and determinate. But no such theory is actually in hand for abstract entities. We have the words abstract entity, but almost no theory to back them up." I deny that statement. The more than 200 references to eternal objects in the index to Whiteheads Process and Reality outline an extensive theory of such objects which, at the very least, refresh the interpretation I am pursuing. A page later (p. 75) Aune claims that abstracta are "fundamentally mysterious." There is certainly something to that. While I dont pretend that they are, or should be, commonplace my contention is that the fundamental mysteries of Platos language with respect to participating in, partaking of, or exemplifying the forms are considerably reduced when the line of truth is toppled forward into the stream of time so that the forms coincide with possibilities. Such a move would endorse the "horizontal platonism" which Robert Pollock finds in modern pragmatism of the non-revisionist sort.
Unlike vertical platonism, its horizontal form participates in the flow of time. Since actual things have the form of the present, it seems reasonable to follow Peirce and Whitehead, giving possibilities the form of the future. Starting with any actual entity in the present, the possible branches in the following manner:
One might consider this to be too simple since, at times, one is aware of, e.g., 4 possibilities:
And some, although not Whitehead, have urged that a multi-valued logic is needed to handle the future. On reflection, however, decision may be considered to be 2-valued. When I am considering A, the decisions are:
and the negated possibility, e.g. not-A, covers all of the remaining possibilities. If I have rejected A, the decision becomes B or not-B. The A or not-A pattern continues through increasing determination until some increasingly nascent possibility is translated into actuality. The process represented by forking follows an iteration into actuality of Peirces triadic structure:
When considering A,B,C, or D, one is really considering A or not-A, B or not-B, C or not-C, D or not-D, in a triadic pattern gradually becoming more determinate. Our interest, quite often, extends not to the chain, but centers on A or not-A: "Will there be a sea fight tomorrow, or not?" We simply prescind A or not-A from the chain of possibilities which might occur as alternatives to a sea fight. When we think of A,B,C, and D as equally possible, we have jammed 4 triads into a single tetrad. This is a decision that the chain of triads can be safely ignored for the sake of highlighting A,B,C, and D.