Chance

Plato's position on chance is worked out in the context of a controversy with those who attribute the order of the cosmos to "nature and chance." In Laws X, the Athenian Stranger argues against those who hold that "fire and water and earth and air all exist by nature and chance, and none of them by art." On this view, soul would be posterior to body, mind would be later than matter, and justice a mere convention. Against it, Plato argues that soul is prior to body, and that self-moving intelligence is the first cause of all things.

In the Timaeus, the visible order of the heavens and the structure of living bodies are accounted for not by chance but by a craftsman, the Demiurge, who fashions matter according to eternal Forms because he is good and desires that all things should be as good as possible. What resists the imposition of form, and remains irregular or unpredictable, is attributed to "necessity," the residual stubbornness of matter. Chance, on this account, is not sovereign but subordinate: it names the portion of natural events not yet fully brought under intelligent order.

The question Plato raises, whether the cosmos is governed by intelligence or by blind necessity and chance, has ethical and political dimensions as well as cosmological ones. If chance rules, the distinctions of justice and piety are merely conventional. If intelligence rules, those distinctions are grounded in the nature of things. Plato's argument in Laws X is addressed to this moral consequence as much as to the cosmological question.

Aristotle accepts Plato's general conclusion that the cosmos is governed by something more than chance, but proposes a more systematic account of what chance is: not merely the residue of what intelligence has not yet organized, but the incidental coincidence of causal lines that were each directed toward something else.

Aristotle analyzes chance in the second book of the Physics, where he asks whether chance belongs among the causes and, if so, what kind of cause it is. Against those who find no place for chance among the causes, he holds that many things "are said both to be and to come to be as a result of chance." Against those who regard chance as inscrutable or divine, he argues that it is simply an incidental cause: the coincidence of two causal lines whose meeting was not aimed at by either.

Aristotle's example is the man who goes to the market to buy fish and there, by chance, meets someone who owes him a debt. Both the going to market and the presence of the creditor are fully caused, each by its own set of causes directed toward its own end. What is lacking is any cause that was directed toward producing the meeting. Chance events are therefore those that "might have happened for the sake of something" but did not happen for that sake; they occur "incidentally." Aristotle distinguishes tuchê, fortune, which belongs to the sphere of deliberate agents, from automaton, spontaneity, which covers chance occurrences in nature and in things without deliberation.

Nature acts, on Aristotle's account, "always or for the most part" by essential causes toward proper ends. Chance belongs to the remaining class of events, those that "come to pass incidentally" by coincidence. Because the causes of chance events are indefinite in number, and not reducible to any single principle, chance remains at the margins of natural science rather than at its center. The relation of this account to Aristotle's account of necessity and contingency is treated more fully under the ideas of Necessity and Contingency and Cause.

Aristotle's account of chance as incidental coincidence of causes, rather than as divine inscrutableness or the total absence of cause, was adopted and developed by Aquinas, who combined it with the Augustinian doctrine of providence. The question of whether contingency and coincidence are compatible with divine foreknowledge and governance is one that medieval theology addressed in direct response to Aristotle's analysis.

Lucretius, following Epicurus, holds that the atoms which constitute all things fall eternally downward through the void by their own weight. If this were their only motion, all atoms would fall in parallel and never meet; no compound bodies could form, and no world could arise. Epicurus, departing from Democritus, posits that atoms swerve slightly and spontaneously from their downward path at uncertain times and places. From this minute and uncaused deviation, collisions occur, bodies form, and the present order of things comes to be.

This swerve, or clinamen, is described by Lucretius as absolutely spontaneous: it happens at no determined time and no determined place, and no further cause accounts for it. It therefore introduces genuine indeterminacy into the physical order, departing from the strictly necessitarian atomism of Democritus, in which all atomic motions follow necessarily from prior states. Lucretius argues that this indeterminacy is required not only to explain the origin of compound bodies, but also to account for the free movements of living creatures: "if all movements are always interlinked, and new motion arises out of old in order fixed," there would be no room for the mind's self-initiated acts.

Lucretius connects the doctrine of the swerve with the Epicurean therapeutic purpose: to free the mind from fear. If the world is the product of atoms moving and colliding without divine design, then natural events require no supernatural explanation, and the gods play no role in human affairs. The question of whether an uncaused swerve can bear the explanatory weight Lucretius places on it, both in cosmology and in the account of freedom, was raised by critics of Epicurean physics from antiquity onward.

Lucretius's account of the swerve as an uncaused, spontaneous deviation represents one of the earliest explicit formulations of physical indeterminism. The question of whether such indeterminism is compatible with any account of natural regularity, and whether it can serve as a foundation for human freedom, remained central to the debate between determinists and libertarians in subsequent philosophy.

Epictetus begins the Discourses with the distinction that governs his entire treatment of fortune and chance. Some things are "up to us" (eph' hēmin): our judgments, impulses, desires, and aversions. These lie within the faculty of rational choice, the prohairesis, which no external force can compel. Other things are not up to us: body, reputation, property, office, the outcomes of our actions in the world. These belong to the domain of what befalls us, and they include everything that goes under the name of fortune or chance. The Stoic's practical program follows from this division: train the rational faculty assiduously; accept what lies outside it as indifferent.

This is not a counsel of passivity toward all things. Epictetus insists on strenuous moral effort, on the daily discipline of examining impulse and desire, on the practice of choosing correctly even in difficult circumstances. The effort is directed inward, however, not toward the management of outcomes. The person who ties happiness to the goods of fortune has made himself hostage to what he cannot govern. The person who has located his good entirely in the rational faculty has found something that neither illness nor poverty nor the loss of reputation can take from him. What Aristotle had included among the constituents of happiness, the external goods of fortune, Epictetus argues are not genuinely goods at all except as occasions for the exercise of virtue.

Epictetus often confronts his students with the implications of this position for grief, fear, and desire. The person who grieves the death of a child has, on the Stoic account, suffered an error of judgment: he has treated as a good something that was never truly his. The child was always only on loan; the loan has been called in; the rational faculty should respond with equanimity. This counsel, which struck many ancient readers as severe, is grounded in a metaphysics that identifies the truly real with what is permanent and rational, and assigns chance no power over what is genuinely ours.

Marcus Aurelius will carry this framework into the experience of an emperor who, unlike Epictetus, could not withdraw from the affairs that depend on fortune. His Meditations return again and again to the Epictetan division, pressing it toward a more explicit cosmological grounding: whether the world is governed by providence or by atoms, submission to what falls is the only rational response, since the rational faculty remains undamaged by either dispensation.

Marcus Aurelius approaches the question of chance from a practical rather than a theoretical direction. He repeatedly presents himself with the following disjunction: either the universe is governed by a rational providence, or it is a concourse of atoms, moving without purpose or design. He finds that the Stoic's conduct need not differ materially between these two possibilities. If providence rules, one should accept what is sent; if atoms rule, one should accept what falls. In neither case is resentment against the event reasonable.

The Stoic metaphysics underlying this position identifies the order of the world with what the Stoics called the logos, the rational principle pervading all things, so that the causal sequence of events is identical with the rational order of nature. On this view, what appears to be chance is only the portion of the causal order whose threads we have not traced. What appears fortuitous is, in the deepest sense, necessary; and submission to what falls is no less appropriate if the universe is after all an atomic concourse without design.

Marcus distinguishes this position from a fatalism that would counsel passivity in all things. He consistently urges the effort of virtue, the exercise of reason, and the discipline of desire, even while insisting on acceptance of what cannot be changed. The practical Stoicism of the Meditations leaves the metaphysical question of chance undecided and proceeds to what follows from either answer. The relationship between Stoic acceptance and the question of human freedom is discussed further under the ideas of Liberty and Fate.

Marcus's practical indifference to the theoretical resolution of the question, combined with his insistence on submission to the causal order whatever its ultimate character, was available to Augustine as both a model and a foil: a model in its counsel against resentment of what happens, and a foil in its failure to distinguish between providential and merely necessary orderings of events.

Plotinus addresses fortune and chance in the third Ennead, particularly in the tractates "On Fate" (III.1) and "On Providence" (III.2–3). His account proceeds from the structure of reality as he has established it: the One, absolutely simple and self-sufficient, is the ultimate source; from it proceeds Intellect, the realm of Forms; from Intellect proceeds Soul, which governs the natural world by animating it with the rational principles inherent in the Forms. At each of these levels, what holds is rational necessity. Chance, as Aristotle had defined it, the incidental concurrence of causes not directed toward that result, can arise only in the domain of matter, where things fall below the clear illumination of Intellect.

What appears to be chance in the sensible world is, at a higher level of description, the expression of the rational order (logos) that Soul impresses on matter. Plotinus compares the cosmos to a great living organism or a drama: what seems arbitrary or accidental in an isolated incident belongs to a larger intelligent design. The atomist account, which treats chance as truly uncaused swerves of fundamental particles, Plotinus rejects as making the universe unintelligible and depriving it of the unity and beauty that, on his view, it evidently displays. The Stoic account, which equates fate with an immanent rational necessity, Plotinus modifies: fate governs the sensible domain, but the soul that has ascended toward Intellect participates in a freedom that is above fate.

This last point is practically important. Epictetus had argued that the rational faculty is always free, in the sense of being immune to fortune's compulsion. Plotinus gives this Stoic claim a metaphysical foundation: the soul's truest activity, contemplation of the intelligible, is genuinely beyond the reach of material contingency. The lower soul, caught up in the body's fortunes, is affected by what happens; the higher soul, oriented toward Intellect, is not. The question of whether such an ascent is possible, and what it requires, connects with the broader discussions of Soul and Happiness.

Augustine will draw on Plotinus's account of providence as rational governance while reconceiving its ultimate source. Where Plotinus identifies the highest principle as the One beyond intellect and beyond personality, Augustine identifies it as the God who speaks, wills, and loves; and where Plotinus sees the human soul's highest activity as contemplation rising above temporal contingency, Augustine sees it as love directed toward the God who governs all things, including contingent ones, by a personal providence that surpasses rational necessity.

Augustine's account of chance and fortune proceeds from his theology of creation and providence. In City of God V, he addresses those who explain events by astrology, by fortune, or by the movements of the stars. Against such accounts he argues that the word "fortune" is merely a name for ignorance: "those causes which are called fortuitous are not a mere name for the absence of causes, but are only latent." What appears to be chance from the human perspective is, from the perspective of divine knowledge, fully known and fully governed.

Augustine holds that everything that happens, from the fall of a tile to the rise and ruin of empires, falls within divine providence. Nothing escapes the eternal present of God's knowledge. This does not mean, however, that Augustine assimilates his position to Stoic determinism. He is careful to maintain that God's foreknowledge of human acts does not abolish their freedom. Contingency survives at the level of secondary causes; it is the human will, acting freely, that God foresees, not a mechanical outcome from prior conditions. The question of how foreknowledge and free will are compatible is treated more fully under the ideas of Will and Liberty.

The practical consequence of Augustine's account is a reconception of historical events. What pagan thought calls fortune, whether good or bad, is for Augustine always within the order of divine pedagogy. The fall of Rome is not a refutation of providence but a lesson addressed to those who had made earthly security their good. The pagan language of fortune, in which events are distributed by a blind goddess, has no place in a created order governed by an omniscient and omnipotent God.

Aquinas will take up Augustine's subordination of chance to providence and combine it with Aristotle's analysis of chance as incidental coincidence, attempting to show that the two accounts are not merely compatible but mutually illuminating: what Aristotle calls chance relative to proximate causes, Aquinas holds to be providentially governed at the level of the first cause.

Aquinas addresses the relation between chance and providence in the Summa Theologica, drawing on both Aristotle's analysis of chance as incidental coincidence and Augustine's insistence that nothing escapes divine governance. His reconciliation distinguishes two levels of consideration. Relative to proximate or secondary causes, chance is genuine: the coincidence of two causal lines is not written into the nature of either line, and no created cause was directed toward producing their meeting. Relative to divine providence, which governs the whole order of causes, there is no chance at all; every concurrence is foreseen and willed.

This distinction is worked out in Summa Theologica I, Q. 22, A. 2, and Q. 103, A. 7. God wills, Aquinas argues, that some effects follow from their causes necessarily and others contingently; he provides for each kind the appropriate sort of cause, necessary causes for necessary effects, defectible and contingent causes for contingent effects. Chance and contingency are therefore not obstacles to providence but instruments of it. The example Aquinas employs is deliberately simple: a master sends two servants to the same place, each ignorant of the other. To the servants, the meeting seems chance; to the master who arranged it, it is plan.

On this account, real contingency in nature and genuine freedom in the will are preserved against accounts that would reduce everything to necessity. Divine governance is also preserved against accounts that would allow anything to escape it. Providence works through the modes of causality, necessary, contingent, and free, rather than replacing them with a uniform necessity. The question of how this reconciliation stands in relation to the Stoic account, which also denies genuine chance while identifying the causal order with divine reason, is one that Aquinas addresses in part through his distinction of free will from natural necessity.

Machiavelli does not engage directly with Aquinas's theological account; he approaches the question of fortune from a purely political perspective, asking how much of political success and failure is determined by fortune and how much by the skill of the agent. The theological question of whether fortune is ultimately governed by providence is, in Machiavelli's discussion, left entirely aside.

Machiavelli's treatment of fortune in The Prince is explicitly practical in aim. He asks how much of what happens in political life must be attributed to fortune and how much to human skill, or virtù, and he proposes a rough accounting: "fortune is the arbiter of one half of our actions, but she still leaves us to direct the other half, or perhaps a little less." This estimate reflects Machiavelli's observation of the many able men who have been overthrown by changing circumstances, and of the few who have managed to maintain their states against adverse fortune.

The comparison Machiavelli employs is that of a flooding river. Fortune is like a river that causes great devastation when it floods, but against which dikes and embankments can be constructed in calm weather to limit the damage. The prince who has prepared against fortune will fare better when it strikes than the one who has trusted entirely to the weather. Machiavelli also observes that fortune tends to favor those whose methods suit the times: the impetuous man prospers when the times call for impetuosity, the cautious man when caution is needed. The difficulty is that men are constitutionally inclined to a particular mode of action and cannot readily change with the times; hence even the most skillful eventually fail.

Machiavelli's account does not address the theological question of whether fortune is governed by providence. The discussion remains entirely within the domain of political analysis: how to reason about what lies within human control, and how to prepare against what does not. The concept of fortune he employs is the traditional personification of luck in human affairs, now described in terms of practical management rather than theological explanation.

Spinoza will later argue that what Machiavelli and the tradition call fortune is simply a name for ignorance: whatever appears contingent is, on a complete account, necessary. Whether the reduction of fortune to ignorance is compatible with Machiavelli's practical analysis, and whether the concept of virtù survives in a fully necessitarian world, are questions the two accounts raise jointly.

Pascal's 1654 correspondence with Fermat on the problem of points, concerning how the stakes should be divided in an interrupted gambling game, lays the mathematical foundation of probability theory. The central move is to treat future contingencies not merely as unknown but as calculable: each outcome can be assigned a determinate probability, and the rational choice among actions can be guided by comparing their expected values. The question is no longer the metaphysical one of whether chance events have hidden causes, but the mathematical and practical one of how to reason correctly when the outcome is genuinely uncertain. This separates the logic of chance from the question of determinism and makes probability an autonomous discipline.

The Pensées extends this framework to the question of religious faith. Pascal's Wager proceeds explicitly from the conditions of uncertainty: we cannot demonstrate by reason whether God exists or not, yet we must live as if we have chosen one side or the other. The wager argument calculates the expected value of each choice. If God exists and we believe, we gain "an infinity of an infinitely happy life"; if God does not exist and we believe, we lose only "finite" goods. Since the potential gain is infinite and the potential loss is finite, reason requires us to wager on belief, even if the probability of God's existence were very small. The argument is unusual in the tradition precisely because it treats the most fundamental question of human existence as a decision problem, governed by the same logic as the division of stakes in a game.

Pascal does not confuse probability with certainty, and he is sharply aware of the limits of reason in the domain of faith. The Wager is not presented as a proof of God's existence but as a practical argument addressed to someone who has not yet found reason sufficient. The broader framework, in which geometry yields certainty and the sciences of contingent fact yield only probability, aligns Pascal with those who, following Aristotle, distinguish strictly between demonstrative knowledge and probable opinion, while going beyond them by giving probability a mathematical structure. The connection between Pascal's account and later developments in scientific inference is discussed further under the ideas of Knowledge and Hypothesis.

Hume will take Pascal's separation of probability from certainty further, extending it from practical decision-making to the natural sciences. Where Pascal retains a domain of geometrical certainty and treats probability as its complement in contingent matters, Hume holds that certainty is available only for relations of ideas, and that all reasoning about matters of fact and real existence proceeds by probability alone. The mathematical theory of probability that Pascal invented becomes, in Hume's hands, the general logic of empirical inquiry.

Spinoza holds that in nature there is nothing contingent: "all things are determined from the necessity of the divine nature to exist and act in a certain manner." From the one infinite substance, God or Nature, everything follows with mathematical necessity, as properties follow from the definition of a geometrical figure. The distinction between necessary and contingent causes, which Aquinas and others had used to accommodate both providence and genuine chance, Spinoza regards as reflecting not a real difference in the order of things but only a deficiency of human knowledge.

In the Appendix to Ethics I, Spinoza diagnoses the belief in chance and contingency as an illusion arising from ignorance of causes. We call a thing contingent when we do not know whether its essence contains a contradiction, or when we cannot trace its causes to a sufficient conclusion. Seen "under the aspect of eternity," the universe admits no gaps; every event follows necessarily from its causes, and those from their causes, back to the eternal necessity of the divine nature.

This thoroughgoing necessitarianism has consequences for ethics. Freedom, for Spinoza, is not the ability to have done otherwise; that is an illusion arising from ignorance of the causes that determine our acts. Freedom is self-determination: understanding the necessity that governs one, so as to be moved by adequate ideas rather than by confused passions. The wise person does not lament what had to happen or hope for what cannot be; he understands the order of causes and acts from that understanding. The implications for the account of human freedom and moral responsibility are discussed further under the ideas of Liberty and Will.

William James will later characterize Spinoza's universe as the "block universe," a world in which genuine novelty and real openness are excluded by the all-encompassing necessity of the whole. His objection will be that such a world cannot make moral striving intelligible, since everything, including every regret and every act of will, is already determined from eternity.

Hume's treatment of chance proceeds from his general skepticism about the idea of necessary connection. Having argued in his account of causation that we never observe any necessary connection between cause and effect, he draws a related conclusion about chance: "though there be no such thing as chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion." Chance, on this account, is not a feature of the world but an expression of ignorance.

Hume's contribution to the discussion consists less in this negative conclusion, which he shares with Spinoza, than in his positive treatment of probability. In Section VI of the Enquiry Concerning Human Understanding, "Of Probability," he analyzes how the mind distributes belief when the evidence is incomplete or mixed. If we throw a die, the mind considers every face equally probable, and belief rises or falls in proportion as the evidence for one outcome or another is assembled by observation and habit. Scientific reasoning, which weighs contrary experiments against one another, operates on the same principle, differing only in the complexity of the evidence.

Hume thereby transfers the discussion of chance from metaphysics to the theory of probability, making the relevant question not whether the world contains genuine contingency but how the mind should proportion its beliefs to the available evidence. Whether this account of probability is adequate to ground scientific inference, or whether it rests on habits of mind that cannot themselves be justified by reason, connects with the broader problem of induction discussed under the ideas of Induction and Knowledge.

William James will argue that Hume's reduction of chance to ignorance, like Spinoza's reduction to necessary consequence, leaves out what is essential: the question of whether there is genuine openness in the world, such that what happens might, in the relevant sense, have been otherwise.

Tolstoy, in the historical and philosophical essays embedded in War and Peace and systematized in the Second Epilogue, takes issue with the use historians make of the concepts of chance and genius. When historians cannot account for the outcome of a battle or the collapse of an empire by reference to the decisions of great men and known causes, they appeal to "chance" as a residual explanation. Tolstoy argues that both "genius" and "chance," as used by historians, "do not denote any really existing thing and therefore cannot be defined. They only denote a certain stage of understanding of phenomena." They mark the point at which the historian stops inquiring, not any genuine feature of the events.

The positive account Tolstoy proposes is one of infinitesimal causes. Every historical event, however large, is the resultant of millions of individual human wills, none of which surveys the whole. The historian who attributes the outcome of a battle to Napoleon's genius or to a fortunate change in the weather has replaced a complex aggregate with an artificial simplicity. What is required instead, Tolstoy suggests, is something like a calculus of history, a method adequate to the infinite complexity of the causes at work. Kutuzov is presented in the novel not because he makes better plans than Napoleon but because he submits to the vast concurrence of forces rather than imagining that his will governs it.

This account is strictly deterministic in the sense that it denies genuine contingency: every event has causes, and the appeal to chance is always an expression of ignorance. It is, however, compatible with a kind of epistemic humility, since the causes are too numerous and too small for any single mind to survey. The relation of this determinism to Tolstoy's moral concerns, particularly his critique of the glorification of military commanders, is discussed further under the ideas of History and War and Peace.

Tolstoy's position that chance is always only ignorance of causes aligns him with Spinoza and Hume on the question of whether genuine contingency exists in the world, though the context and motive of his account differ from theirs. William James will argue against this whole tradition of reducing chance to ignorance, insisting that genuine openness in the future is required for moral seriousness.

William James addresses the question of chance directly in his essay "The Dilemma of Determinism," arguing that the dispute between determinism and indeterminism is not simply a metaphysical question but one with consequences for how we understand moral life. Determinism, which James defines as the doctrine that "those parts of the universe already laid down absolutely appoint and decree what the other parts shall be," leaves no genuine openness in the future. Indeterminism, by contrast, maintains that "possibilities may be in excess of actualities": that the future is genuinely open, and that what happens was not the only thing that could have happened.

James does not claim to demonstrate that indeterminism is true, but argues that it is at least as defensible as determinism, and that its consequences for the moral life are considerably more coherent. If everything, including every act of regret, is necessitated from eternity, then regret is unintelligible: we cannot reasonably regret what had to happen. Indeterminism makes regret intelligible by allowing that the regretted event was one of several genuinely possible outcomes. James insists that chance, in his sense, does not mean causelessness or chaos; it means that at certain junctures more than one future is genuinely possible, that the universe is "concatenated" rather than a fixed "block."

In the Principles of Psychology, James connects indeterminism to the phenomenology of voluntary attention: the mind's effort to hold an idea, to sustain attention in the face of distraction, is offered as evidence that the will is not simply determined by prior states. Whether this phenomenological evidence is adequate to establish genuine indeterminism at the physical or metaphysical level is a question James acknowledges as unresolved. The relation of chance to freedom and to the problem of moral responsibility is discussed further under the ideas of Will and Liberty.

James's insistence that genuine openness in the future is required for moral striving to be real, rather than merely theatrical, connects the metaphysical question of chance with the practical concerns of ethics and religion. Whether the physical indeterminacy discovered by quantum mechanics is the kind of indeterminism James had in mind for freedom remains a question that subsequent philosophy of science and philosophy of action has discussed at length.