Possibility

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POSSIBILITY

The subject of possibility is a central topic in philosophy. It was frequently discussed in the history of philosophy, and it is actively debated by contemporary philosophers.

Historical Developments

aristotle

The first comprehensive treatment of possibility occurs in the work of Aristotle. Aristotle's writing on this subject is difficult and confusing, but he seems to have held that the idea of possibility is derivative from that of necessity and negation, "It is possible that P" meaning "It is not necessary that not-P" (see On Interpretation 13.22b). Necessity of this basic kind is absolute necessity, and like absolute possibility it is applicable to sentences or propositions (logoi ). According to his Posterior Analytics (4.21), a necessary proposition truly predicates something of a thing's essence; an example would be "A man is a rational being." A possible proposition, one that may be asserted to be such by a proposition containing the words "It is possible that ," attributes an accident to a thing, an accident being a character that, because it is not excluded by a thing's essence, may or may not belong to it, as being seated may or may not belong to a man or woman. Because Aristotle held that what belongs to a thing's essence is given by a "real" definition, necessary propositions for him are either real definitions or logical consequences of such definitions.

Formal possibility

Although Aristotle's explicit remarks on absolute necessity relate to his theory of essences, he also uses a formal notion of necessity and, thus, of possibility, as when he argues that "Necessarily, every S is L" follows from "Necessarily, every M is L" and "Necessarily, every S is M." That the necessity and, correlatively, the possibility involved here is not the same as the real necessity and possibility just discussed is evident from the fact that the necessity of the conclusion "Every S is L" (and the impossibility of "Some S is not L") is justified wholly by the logical connection signified by "Every is " and by the sub-occurrences of "necessarily" in the modal syllogism. Important as this type of necessity and possibility obviously is to his theory of modal syllogisms, Aristotle does not seem to have reached the point of formulating its meaning explicitly. (See the discussion of Aristotle's modal syllogisms in The Development of Logic [1963] by William Kneale and Martha Kneale.) There can be little doubt, however, that this formal notion of necessity is rooted in the necessity of the first principles of all reasoning, such as the principle of contradiction. These principles cannot be demonstrated, Aristotle said, because all demonstration presupposes them (see Posterior Analytics 1.3.72b). They are known immediately and intuitively, and they cannot be consistently questioned.

Relative possibility

In the Prior Analytics (1.19.23a) Aristotle distinguishes absolute from relative necessity, and he implicitly makes a similar distinction for possibility in various passages of the Organon (for instance, in De Sophisticis Elenchis 4.166a22166a30). Just as a proposition that does not state an absolute necessity may be considered necessary relative to certain other propositions (as a contingent statement constituting the conclusion of a valid deductive argument may be considered necessary relative to the truth of the premises), so a proposition like "Jones is walking" may be considered impossible relative to the proposition "Jones is sitting," and "Jones is sitting" may be considered possible relative to "Jones is not running." Although this distinction is intuitively clear, Aristotle does not explicitly say whether relative necessity and relative possibility are to be understood by reference to the sort of real absolute necessity and possibility discussed earlier or whether, as is likely, they are to be understood in relation to the formal notions that he sometimes uses but does not explicitly define.

Potentiality

Another sort of possibility discussed by Aristotle is potentiality, for certain possibilities can be said to exist as potentialities of concrete things. The possibility of a person's reading this or that may be understood in relation to a potentiality (we would say an ability) that the person has. For Aristotle a person who can read is a potential reader. Although the notion of potentiality is basic to Aristotle's metaphysics, he thought it could be understood only by analogy: "As a man who is building is to one who knows how to build, as waking is to sleeping, that which sees to that which has sight but has eyes shut, that which is shaped out of matter to its matter, the finished product to the raw material, so in general is actuality to potentiality" (Metaphysics 1048b).

megrians and stoics

A definition of possibility widely accepted in the Hellenistic period was that of Diodorus Cronus of Megara, who said, "The possible is that which either is or will be true" (Kneale and Kneale 1963, p. 117f). This identification of possibility with, in effect, present and future actuality was challenged by the Stoics (for example, by Chrysippus), who defined real possibility as "that which is not prevented by any thing from happening even if it does not happen" (Kneale and Kneale 1963, p. 123). Because the Stoics tended to be strict determinists, holding that whatever happens is necessitated by something else, they typically argued that our assessment of nonactuals as possibles could be based only on ignorance, for any conceivable occurrence that does not take place at some time or other is presumably prevented from taking place by the course of nature. Thus, their conception of real possibility developed into a conception of what is now known as epistemic possibility, or possibility as consistency with our knowledge.

Because the Stoics were especially interested in formal logic, they had another conception of possibility, however. According to this conception, necessary propositions (that is, necessary sentences) are those that are always true, such as the propositions of logic and mathematics. Possible propositions are those that are sometimes true. Since today's utterance of "A sea battle will occur tomorrow" is sometimes true according to the Stoics, then even though the course of nature may determine its truth with respect to tomorrow, the fact it states still belongs to the category of the possible (in the sense of sometimes true). It is perhaps worth adding that some commentatorsfor instance, Jaakko Hintikka (1959)find this conception of possibility in Aristotle as well.

neoplatonists

The next distinctive conception of possibility, which turned out to be of great importance in medieval and modern philosophy, was worked out by the Neoplatonistsalthough it can be said to have its roots in Plato. According to this tradition, possibilities are not facts or states of affairs (that is, items properly expressed by sentences or propositions) but beings or essences that belong to Nous or Intelligence, the "first emanation of the One." Aristotle had spoken of potential beings inherent in various mattersfor instance, a statue of Hermes existing potentially in a chunk of marblebut the idea of a possible being, which cannot be understood in relation to what substances or matter will become under certain conditions or when operated on in a certain way, is evidently new.

Admittedly, the idea may in a sense be traced back to Plato, for a possible being thus conceived is essentially something thinkable or intelligible, and Plato identified the intelligible with the world of Ideas or Forms. But Plato's Ideas were always general rather than specific, of humanity rather than of Socrates, and this means that the only possibilities, in this sense, that Plato could accommodate were kinds or species. Such Neoplatonists as Plotinus admitted Ideas of individual souls, and these, being nongeneral, may be regarded as the prototypes of the possible beings that occur in the theories of later philosophers such as Leibniz.

An extremely important aspect of the Neoplatonist treatment of possibles is that all possible beings were held to be actualized; possibility and actuality were regarded, that is, as precisely coextensive. The basic reason for this was that the infinite perfection or "goodness" of the One, which "overflows" into the emanation constituting the world of diverse actuality, requires that every possible being be brought into existence or actualized. This principle of plenitude among actualities was thought to be necessary according to the nature of things, because it is an essential feature of the One's perfection "to produce otherness" and "necessarily to do this in the maximum degree" (Lovejoy 1936, p. 66).

The Neoplatonic conception of possibles as Ideas in a divine mind that, owing to the perfection of that mind, are necessarily actualized was a recurrent and problematic theme in medieval philosophy. As A. O. Lovejoy pointed out in The Great Chain of Being (1936), medieval writers tended to conceive the love or goodness of the Christian God (in whose mind the Ideas were now said to exist) as an "immeasurable and inexhaustible energy," a love of which "the only beneficiaries were not actual sentient creatures or already existing moral agents, but Platonic ideas, conceived figuratively as aspirants for the grace of actual existence" (p. 68).

abelard

Abelard, writing in the early twelfth century, was led to maintain that what can be is the same as what can be produced by God and that "it is intrinsically impossible for God to do (or make) or to leave undone (or unmade) anything other than the things that he actually does at some time do or omit to do; or to do anything in any other manner at any other time than that in which it actually is done" (Lovejoy 1936, p. 71).

aquinas

Because Abelard's view of possibility and actuality seemed not only to deny God's divine freedom but also, in implying that the created world was so good that it could not be better, to "make the creation equal to the Creator," it was regarded as heretical (Lovejoy 1936, p. 73). Accordingly, other Schoolmen, who like Aquinas agreed that "all things preexist in God by their types (rationes )," had to maintain that the creation involved a selection among the ideas. In this view not all possibles are actual, and what is actual is not necessary: There are, that is, possible beings that God could have created but did not create, and he did not have to create the things that he did create. To square this claim with God's goodness, Aquinas found it necessary to invoke the Aristotelian distinction between absolute and relative necessity and possibility. Although it is absolutely possible for God, good as he is, to have created things other than what he did create, it may nevertheless be admitted that, relative to his choice, which was "becoming to" rather than necessary to his goodness, the existence of what is actual is necessary and could not be otherwise. That is, relative to this premise, it is impossible for anything to exist that does not sooner or later actually exist.

Even granting the distinction between absolute and relative possibility, it might be objected that Aquinas is still imposing a limit on God's freedom. If what actually exists is determined by God's selection from a class of possibilities, it would appear that God could not, in an absolute sense, have created anything not belonging to this class. In reply to this Aquinas maintained that what is absolutely impossible is self-contradictory and that what is self-contradictory is contrary to God's nature, repugnant to being, and therefore not an object at all. ("So it is better to say that what involves a contradiction cannot be done rather than God cannot do it," Summa Theologica 1.25.34.) In making this reply, Aquinas may seem to be introducing a formal notion of absolute possibility of the sort defended in more recent times. Yet, as with Aristotle, the category of possibility in question is grounded not in linguistic or purely logical considerations but wholly in intelligible essences ("intelligible forms"). In other words, the definitions relevant to ascertaining the consistency or intelligibility of a term or idea are "real" rather than nominal or analytical, which means that the possibility in question is the absolute kind espoused by Aristotle, not the formal or conceptual sort allowed by most modern philosophers.

hobbes

In the modern period we find in Hobbes a view that not only contrasts vividly with the typical medieval one but which, confused as it is, is occasionally defended by philosophers of the twenty-first century. Hobbes's view contrasts with the medieval one because he held that conceivable beings are not necessarily possible beings. If a being is conceivable, the only conclusion Hobbes would draw is that words standing for it are not gibberish. To be possible, the necessary conditions for a thing's existence must be satisfied. Hobbes therefore contended that every possible being, event, or state of affairs is actual at some time or another: "If it shall never be produced, then those things will never concur which are requisite for the production of it" (Elements of Philosophy 10.4). Because for Hobbes whatever exists does so by virtue of necessary causes, we can call something possible (or contingent), as opposed to necessary, in his opinion only when we do not know the cause that will produce it. This view plainly goes back to that of the Stoics, for it implies that the only legitimate possibilities that are not also necessities are epistemic possibilitiesthat is, things or states of affairs whose existence is consistent with our knowledge at a given time.

descartes

Descartes's approach to possibility is important mainly because it is essentially psychologistic: what is possible is what is clearly and distinctly conceivable. Descartes admitted that if the idea of a thing involves a contradiction, the thing is impossible, but he held that its impossibility is owing to the fact that contradictory ideas cannot be clearly and distinctly conceived. This latter criterion is basic for Descartes because some impossibilities do not, in his view, involve contradictions. As he saw it, there are a priori truths that are necessary and guaranteed to be true by the goodness of God but whose denials, which state impossibilities, are consistent. To know firsthand whether a given ideafor instance, the idea of a circular polygondoes represent a possibility, one must therefore be able to form a clear and distinct idea of it. If one is able to form such an idea, one has God's assurance that it represents a real possibility, the sort of thing that God could actualize if he chose to do so.

spinoza

According to Spinoza, "A thing is said to be impossible either because the essence of the thing itself or its definition involves a contradiction, or because no external cause exists determinate to the production of such a thing" (Spinoza, Ethics, 1, prop. 33, note I). Because Spinoza in effect adopted the Neoplatonic principle of plenitude, he held that if the idea of a thing does not involve a contradiction, it must be actual, for all self-consistent beings are determined to exist, and necessarily exist, by the very nature of reality, which he calls "God":

[Accordingly, a] thing cannot be called contingent unless with reference to a deficiency of our knowledge. For if [and here Spinoza introduces the notion of epistemic possibility] we do not know that the essence of a thing involves a contradiction, or if we actually know it involves no contradiction, and nevertheless can affirm nothing with certainty about its existence because the order of causes is concealed from us, that thing can never appear to us as necessary or impossible, and therefore we call it either contingent or possible (Spinoza, Ethics, 1, prop. 33, note I).

leibniz

To general readers, Leibniz is best known for his metaphysical optimism, the doctrine that this is the best of all possible worlds. He conceived of a possible world as a maximal collection of absolutely possible beings each of which is "compossible" with the other beings contained in that world; the totality is maximal in the sense that it contains everything compossible with its contents. Two things are compossible, Leibniz said, when it is absolutely possible for them to exist together; and something is absolutely possible, for him, when God's conception of it is free from contradiction. Because Leibniz held that God's concept of a thing includes all facts about it, including such apparently accidental facts as that it once crossed a certain river in Peru or that it once was bitten by a dog called "Rover," he concluded that if a thing is absolutely possible, it is so only relative to its place in a possible world, one including certain possible rivers, perhaps, and certain possible dogs. A possible being is strictly a being, therefore, whose existence is compossible with the members of a possible world. This conception comprehends the less restrictive idea, common in recent metaphysics, that a possible thing or state of affairs is one that "exists at," or belongs to, some possible world.

Like Aristotle, Leibniz drew a distinction between absolute and relative possibility. (Leibniz used the term "hypothetical" here instead of "relative," but his distinction was the same as Aristotle's.) Because God created the best of all possible worlds, any existing thing that is not, like God, an absolutely necessary being depends on God's creative choice. A thing that is absolutely possible but dependent this way on God's creative choice is hypothetically necessary: its nonexistence is hypothetically impossible, ruled out by the choice God actually made. Everything that has occurred, will occur, or is now occurring is necessary in this hypothetical sense, according to Leibniz. But hypothetical necessity is not the same as absolute necessity, he insisted; Diodorus Cronus (see above) erred in not recognizing this important fact. All human behavior is hypothetically necessary, but it is not thereby inevitable in an absolute sense. This is why one can rightly maintain that free choice remains possible for human beings. A free action, for Leibniz, is one that results from a "rationally spontaneous" choice; its originating principles lie within the agent. Free actions spring from motives and other causes, but these "incline without necessitating," he said; absolutely necessity is not imposed upon them (see Mates 1986, p. 119)

hume

The British empiricists, typically rejecting the claims of conceptualism as defended by most epistemic rationalists, seemed to embrace more fully the idea that possibility is a matter of logical consistency. In remarking that, "The contrary of every matter of fact is still possible, because it can never imply a contradiction," Hume appears firmly committed to a view of logical possibility. But in adding to the quoted sentence, "And is conceived by the mind with the same facility and distinctness," Hume discloses his tacit commitment to a psychologistic conception of possibility (what is possible is what is conceivable), which was held by Descartes and is often assumed even today. (See Hume's Enquiry concerning Human Understanding, 4.1.)

kant

In Kant there is not only a clear identification of a priori possibility but an explicit distinction between logical and physical (or nomological) possibility. For philosophers like Spinoza, who identified the logical with the real order, there was plainly no sense in this distinction, and there was little place for it in the philosophies of the Greek and medieval thinkers. It is, however, essential to the contemporary outlook. Kant expresses the distinction a bit clumsily thus:

A concept is always possible [he means "represents a possibility"] if it is not self-contradictory. This is the logical criterion of possibility, and through it objects are distinguished from the nihil negativum. But it may nonetheless be an empty concept, unless the objective reality of the synthesis through which the concept is generated has been specifically proved; and such proof rests on principles of possible experience, and not on the principle of analysis (the law of contradiction). This is a warning against arguing directly from the logical possibility of concepts to the real possibility of things. (Critique of Pure Reason, A597/B625, note)

[Thus, the possibility of such things as] a special fundamental power of our mind to intuit the future (not merely, say, to deduce it), or, finally, a faculty of our mind to stand in a community of thoughts with other men (no matter how distant they may be)these are concepts the possibility of which is entirely groundless, because it cannot be grounded in experience and its known laws, and without this it is an arbitrary combination of thoughts that, although it contains no contradiction, still can make no claim to objective reality, thus to the possibility of the sort of object that one would here think. (Critique of Pure Reason A223/B270)

To ascertain that such things are empirically (as opposed to merely logically) possible, we must ascertain whether the nature of things so described agree with the formal conditions of actual experience.

Contemporary Developments

Not all the conceptions of possibility discussed in the previous section on the history of philosophy are equally acceptable to contemporary philosophers, and new conceptions are topics of current debate. Generally speaking, possibility is now discussed in relation to two principal subjects: basic metaphysics, which takes some kind of absolute possibility as fundamental, and the compatibility of freedom and determinism, which introduces possibilities of other kinds. The conceptions of possibility now considered tenable by most philosophers (there is disagreement on this) can be identified by reference to these two subjects.

basic metaphysics

Until the 1970s, most analytic philosophers described absolute a priori possibilities as "logical possibilities" and identified them, as Leibniz did, by reference to logical consistency: An absolute possibility is something that can be exhaustively described without contradiction. In logic a contradiction has the form of "p and not-p" however; and this syntactical structure is not explicit in many statements that fail to express genuine possibilities: it is not present, for instance, in "Some bachelors are married" or "Mary is both taller and shorter than Sally." To expose the contradictions implicit in these statements one must make use of definitions and conceptual truths such as "For any x and y, if x is taller than y then x is not shorter than y." Conceptual truths and statements true by definition were called "analytic" truths, and the full range of absolute possibilities was generally conceded to be identifiable only by reference to them. An absolute possibility was then said to be expressed by a statement that is consistent with all relevant analytic truths. According to this conception, a statement that is not so consistent would fail to express a genuine possibility.

This way of identifying absolute possibilities was undermined by Saul Kripke in lectures given in 1970 and subsequently published under the title Naming and Necessity (1980). Kripke's criticism featured two striking examples. The first involved what most philosophers would call an analytic truth pertinent to the standard meter located in Paris. The truth is that the rod is one meter long. Although this truth is a consequence of an arbitrarily chosen standard specifying what is to count as a meter in length, and thus would be acknowledged to be analytic by most philosophers, it is not necessary because the rod in question does not of necessity possess its current length: it could have a different one. This latter possibility is genuine, but it is identified by reflection on how the rod might change, what might happen if, say, it were heatednot by the consistency of "The rod is not a standard meter long" with the truth that the length it now has equals one meter. The analytic consistency conception of absolute possibility does not give the right result in this kind of case.

Kripke's second example concerned the identity of Hesperus and Phosphorus, the morning star and the evening star. The statement that Hesperus = Phosphorus is not an analytic truth; it was discovered to be true by empirical investigation. The two "stars" turned out to be a single planet, Venus, seen in the sky at different times and presumed to be different. The fact that the statement is not an analytic truth does not prove that it is not necessary, however. It is in fact necessary because it concerns a single planet, and that planet, like everything else, is necessarily self-identical. Because the identity of Hesperus and Phosphorous had to be discovered empirically, the necessity of their identity had to be inferred from the fact of their identity. If "a" and "b" are used "rigidly," as Kripke said, to pick out the same objects in actual as well as counterfactual situations, then the following principle provides a basis for the inference: If a = b then it is necessary that a = b. Because the necessity of "a" being "b" is equivalent to the impossibility of a not being b, a certain possibility is ruled out by our empirical investigation: We learn that it is not possible for a to differ from b. This impossibility is not known a priori by the discovery that some statement (or proposition) is self-contradictory or analytically inconsistent.

In developing his metaphysical views, Kripke drew a distinction between de dicto and de re necessity and possibility. A de dicto possibility is in effect the possible truth of some proposition; it is expressed in words by a sentence beginning "It is possible that " A de re possibility, by contrast, is attached to a particular thing, such as a person or chair. We are concerned with such possibilities, Kripke said, when we wonder whether a certain person might have done this or that in some counterfactual situation. Kripke spoke of "contingent properties" in describing such possibilities. A property is contingent for a thing when the thing may or may not possess it in some situation or other. Such a property contrasts with a necessary or "essential" one, this being a property that a thing possesses in every situation, actual and counterfactual, in which it may exist. De re possibilities correspond to Aristotle's potentialities; de re necessities correspond to his "actualities," or the components, as he conceived them, of a thing's "form" or essence.

Kripke emphasized that the notions of necessity and possibility he discussed belong to metaphysics, not epistemology, and he sometimes spoke of them as metaphysical necessity and metaphysical possibility (see Kripke 1980, p.19). In commenting on the formal semantics he invented for the logic of statements affirming such necessities and possibilities, Kripke used Leibniz's notion of a possible world. A statement, S, is necessary with respect to the actual world, Kripke said, just when S is true with respect to all possible worldsmore exactly, all worlds that are possible relative to the actual world. S is possible with respect to the actual world (it is, for members of this world, possible that S) just when S is true with respect to some possible worldwith some world that is possible relative to the actual world. Kripke spoke of worlds possible "relative to" the actual world because different assumptions may be made about this relativity, and these different assumptions are associated with modal principles that are characteristic of different systems of modal logic (see Kripke 1971).

Although Kripke informally used the notion of a possible world in describing the truth-condition for statements affirming metaphysical possibilities and necessities, he did not believe that such statements were understandable only in relation to possible worlds or that the framework of possible worlds provides a reductive analysis of modal discourse. In fact, to avoid philosophical confusions and anxieties regarding possible worlds, he recommended that "possible state (or history) of the world" or "counterfactual situation" might provide a preferable terminology (see Kripke 1980, pp. 18f). As far as modal knowledge is concerned, he seems to believe that intuitiveness (or perhaps intuitive obviousness) is basic. As he put it in Naming and Necessity (1980), "Some philosophers think that something's having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself. I really don't know, in a way, what more conclusive evidence one can have about anything, ultimately speaking" (p. 42). In speaking of intuitive content this way Kripke appears to favor an epistemically rationalist (or Cartesian) view of modal knowledge, but he did not discuss the matter in greater detail, and it remains uncertain what the details of his view actually are.

An influential writer about possibility who appears to regard possible worlds and the possible individuals that compose them as basic realities is David Lewis (1986). Lewis believes that all possible worlds actually exist but that only one world, at least from our perspective, is actual: our world. Like Leibniz, Lewis holds that the possible individuals of other possible worlds do not include the individuals of our world; in fact, he thinks the individuals of different worlds cannot be shared. When we consider a counterfactual possibility involving a person belonging to our worldGeorge W. Bush, saythe possibility is grounded in (or actually involves) a counterpart to that person, a being relevantly similar to him, belonging to another possible world. Lewis accepts this counterpart theory because he thinks a given thing cannot have incompatible features. If a thing belonged to two different worlds, the worlds would overlap in it, and this could happen only if the thing's nonrelational features were exactly the same in both worlds: A thing cannot possibly differ from itself. Lewis ably defends his position against a multitude of objections in On the Plurality of Worlds (1986), and he also provides a non-Cartesian account of how he thinks we can have genuine knowledge of worlds that, although existing, are possible rather than actual.

freedom and determinism

The conceptions of possibility relevant to this topic are brought to mind by the question, "If the world is a deterministic system, is it possible for human beings to do anything that they do not actually do?" Not every responsible philosopher agrees that this question requires an affirmative answer if human beings can reasonably be considered capable of acting of their own free will, but the question is commonly asked and different kinds of possibility are mentioned in answering it (see Austin 1961).

Possibility as ability

This kind of possibility corresponds to Aristotle's potentiality. We often have this sort of possibility in mind when we wonder what a person is capable of doing, and what he or she could do in specific circumstances. Can Tom do fifty push-ups? Can he do that many after a big meal? What is relevantly possible here? The basic idea pertinent in answering these questions is that of an ability or capacity. To have an ability or capacity a person must be capable of doing something; and to be thus capable is to be such that if conditions are of the right kind, appropriate behavior will occur. In discussions involving human freedom the abilities under consideration are voluntary: they are abilities that a person can manifest "at will." If Sally has the ability to swim, then she will normally succeed in swimming if she is immersed in water and attempts to swim. The qualification "normal" is important here because a failure to swim would not be evidence of an inability to swim if one's legs were encased in concrete. Success is required only in "favorable" conditions.

Sometimes we are concerned with what a person can do in special conditions, which may be far from what are considered favorable. Can Tom swim in a rough sea? Can Betty solve an algebra problem when her roommate's stereo is pounding in her ears, when she is seething with irritable frustration? The relevant test here is success under the specified conditions. In a particular case the test to be satisfied is specified by a conditional statement in the subjunctive mood: If conditions C were to obtain and the subject attempted to exercise the relevant capacity, the subject would succeed in the attempt.

The most important recent work on the logic of subjunctive conditionals is contained in Davis Lewis's book Counterfactuals (1973). Lewis gives the truth-conditions for these statements by reference to possible worlds. A statement of the form "If it were the case that p, it would be the case that q" is true, according to Lewis, just when q is true at the possible worlds that satisfy p and are otherwise most similar to the actual world. (There may or may not be a single most similar p-world.) Thus, to decide whether Tom could do fifty push-ups after a certain meal, one in effect has to decide, Lewis says, whether a possible world in which he (or his "counterpart") does fifty push-ups after such a meal would be minimally different from the actual world, or whether it would require him to have undergone a course of training, say, that he did not experience in the actual world. Because the negation, according to Lewis, of the conditional "If A were to happen, B would happen" is "If A were to happen, B might not happen," one can use his theory to identify another kind of possibility, which might be called a "contingent" possibility. Suppose it is false both that if A were to happen, B would happen and that A does happen. Under these circumstances it could be said that B's not happening is a contingent possibility.

Relative or Hypothetical Possibility

A conception of possibility ultimately vital to the subject of human freedom is that of what is possible given the laws of nature and the occurrence of remotely prior causal factors. Aristotle and Leibniz both acknowledged this conception, but the idea that it represents a genuine kind of possibility is often questioned by contemporary philosophers. Benson Mates (1986), in his commentary on Leibniz, says that the distinction between absolute and hypothetical necessity (and therefore between absolute and hypothetical possibility) seems to originate in a confusion of "Necessarily, if P then Q" and "If P, then necessarily Q." There is no doubt that this confusion is often made, but it was certainly not made by Leibniz, who explicitly distinguished statements of these kinds and accused Diodorus Cronos, who denied that any possibility could fail to be a necessity, of confusing hypothetical necessity with absolute necessity (see Mates 1986, pp. 117ff).

Peter van Inwagen (1983, 2000), wishing to avoid the confusion Mates mentioned, introduced a new modal operator in formulating an argument against the compatibility of freedom and determinism. The formula "Np" containing his special operator "N" is to be understood as meaning "p [is true] and no one has or ever had any choice as to whether p." If "O" is a modal operator representing a kind of necessity, there is no doubt that an argument having "Op" and "O(if p then q)" as premises and "Oq" as a conclusion is valid. Accordingly, van Inwagen formulates a corresponding argument featuring his operator "N" and argues that it is valid. The remotely prior causes C occurred and no one now has or ever had any choice about their occurrence; hence "N(C)." Similarly, the laws of nature hold true and no one has or ever had any choice about this fact. The laws also imply that if C then B, where B is a representative item of behavior in a deterministic world. Because this implication is necessary and something no one has or ever had any choice about, van Inwagen concludes that N(B)that B occurs and no one has or ever had any choice about it: an alternative to B is out of the question.

Van Inwagen's argument has been seriously criticized since his book was published in 1983, and he has gone on to sketch a new argument to express his sense of the "sheer inescapablity" of determined behavior (see van Inwagen 2000). But it is obvious that the sheer inescapability of B is tantamount to the fact that it is relatively (or hypothetically) necessary in Leibniz's sense, and van Inwagen's conclusion "N(B)" amounts to nothing more than an assertion that B is a logical consequence of natural laws and the occurrence of initial conditions (or previous causes) that cannot be altered when B occurs. Van Inwagen's worry about human freedom depends, in effect, on the relative impossibility of behavior that does not occur. So this sense of possibility is vital to the freedom-determinism issue, at least as philosophers such as van Inwagen understand it.

See also Analytic and Synthetic Statements; Modal Logic.

Bibliography

possibility in the history of philosophy

Aquinas, Thomas. Basic Writings of Saint Thomas Aquinas, edited by Anton C. Pegis. 2 vols. New York: Random House, 1945.

Aristotle. The Complete Works of Aristotle: The Revised Oxford Translation, edited by Jonathan Barnes. 2 vols. Princeton, NJ: Princeton University Press, 1984.

Copleston, Frederick. A History of Philosophy. 8 vols. London. 19591965.

Descartes, René. The Philosophical Writings of Descartes. Translated and edited by John Cottingham, Robert Stoothoff, and Dugald Murdoch. 2 vols. Cambridge, U.K.: Cambridge University Press, 1984.

Hintikka, Jaakko. "Necessity, Universality, and Time in Aristotle." Adjatus 20 (1959): 6590.

Hobbes, Thomas. Hobbes: Selections, edited by Frederick J. E. Woodbridge. New York: Scribners, 1930.

Hume, David. Enquiry concerning Human Understanding. 3rd ed., edited by L. A. Selby-Bigge. Revised by P. H. Nidditch. Oxford: Clarendon Press, 1975.

Kant, Immanuel. Critique of Pure Reason. Translated and edited by Paul Guyer and Allen Wood. Cambridge, U.K.: Cambridge University Press, 1998.

Kneale, William, and Martha Kneale. The Development of Logic. Oxford: Clarendon Press, 1963.

Leibniz, Gottfried von. Leibniz: Selections, edited by Philip P. Wiener. New York: Scribners, 1951.

Lovejoy, A. O. The Great Chain of Being: A Study of the History of an Idea. Cambridge, MA: Harvard University Press, 1936.

Mates, Benson. The Philosophy of Leibniz: Metaphysics and Language. New York: Oxford University Press, 1986.

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possibility in contemporary philosophy

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