Indeterminism posits that events, or specific categories of events, lack causation or are not deterministically caused.
This concept stands in opposition to determinism and is intrinsically linked to chance. It holds significant relevance for the philosophical discourse on free will, particularly within metaphysical libertarianism. Within scientific domains, especially quantum theory in physics, indeterminism suggests that no event is certain and that all outcomes are inherently probabilistic. Key foundational arguments for the universe's indeterministic character often reference Heisenberg's uncertainty principle and the "Born rule," formulated by Max Born. Prominent proponents of indeterminism include Sir Arthur Eddington and Murray Gell-Mann. The French biologist Jacques Monod further advanced this perspective in his essay "Chance and Necessity," while physicist-chemist Ilya Prigogine advocated for indeterminism in complex systems.
Necessary but Insufficient Causation
Adherents of indeterminism are not compelled to negate the existence of causes. Rather, they may contend that existing causes do not restrict future events to a singular trajectory, asserting, for example, that only necessary, but not sufficient, causes operate. The distinction between necessary and sufficient causes is elucidated as follows:
If x constitutes a necessary cause for y, then the manifestation of y unequivocally indicates that x occurred prior. Conversely, the presence of x does not guarantee the subsequent occurrence of y.
If x serves as a sufficient cause for y, then the observation of y suggests that x might have preceded it. Nevertheless, an alternative cause, such as z, could also lead to y. Consequently, the occurrence of y does not necessarily imply the presence of x, z, or any other specific antecedent.
The existence of a necessary cause for every event remains compatible with indeterminism and an open future, given that a necessary condition does not invariably produce a singular, inevitable effect. Indeterministic, or probabilistic, causation is a theoretical possibility, implying that the assertion "everything has a cause" does not unequivocally define indeterminism.
Probabilistic Causation
A deterministic interpretation of causation implies that if A causes B, then A must invariably precede B. However, empirical observations, such as war not always resulting in fatalities or a single instance of smoking not invariably leading to cancer, challenge this strict view. Consequently, many scholars adopt the concept of probabilistic causation. Informally, A probabilistically causes B if the occurrence of A elevates the probability of B. This concept is sometimes understood as a reflection of incomplete knowledge within a deterministic system, while at other times it is interpreted as indicative of an intrinsically indeterministic causal system. (Propensity probability offers a parallel perspective, positing that probabilities possess objective existence rather than merely representing limitations in an observer's knowledge.)
It is demonstrable that the realizations of any non-uniform probability distribution are mathematically equivalent to the application of a deterministic function—specifically, an inverse distribution function—to a random variable that follows a uniform, or "absolutely random," distribution; thus, the probabilities are embedded within the deterministic component. A straightforward illustration involves randomly targeting points within a square and subsequently deterministically designating a larger subsquare as the more probable outcome.
Intrinsic Indeterminism Versus Unpredictability
A fundamental distinction is typically drawn between genuine indeterminism and the mere practical limitation in measuring variables, often termed limits of precision. This differentiation is particularly pertinent in discussions of physical indeterminism, as advanced by various interpretations of quantum mechanics. Nevertheless, certain philosophers contend that indeterminism and unpredictability are synonymous.
Philosophy
Ancient Greek Philosophy
Leucippus
The earliest documented reference to the concept of chance originates from Leucippus, the foundational philosopher of atomism, who stated:
"The cosmos, then, became like a spherical form in this way: the atoms being submitted to a casual and unpredictable movement, quickly and incessantly."
Aristotle
Aristotle delineated four categories of causes—material, efficient, formal, and final. He referred to these as αἰτίαι (aitiai, akin to aetiology), a term signifying the various factors contributing to an event. Aristotle did not endorse the later, more simplistic notion that every event possesses a singular cause.
Within his works, Physics and Metaphysics, Aristotle posited the existence of accidents (συμβεβηκός, sumbebekos) that arose solely from chance (τύχη, tukhe). He observed that neither he nor earlier physicists had incorporated chance into their causal frameworks.
Aristotle significantly diverged from perspectives that positioned chance as a pivotal element in the overarching explanation of phenomena. His reasoning was conceptual: he considered chance events inherently unusual and deficient in specific explanatory characteristics, thus classifying them as distinct from phenomena amenable to comprehensive natural explanations.
Aristotle contrasted his concept of accidental chance with necessity, stating:
"Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause."
"It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not."
Pyrrhonism
Sextus Empiricus, a prominent philosopher, articulated the Pyrrhonist stance on causality:
"...we show the existence of causes are plausible, and if those, too, are plausible which prove that it is incorrect to assert the existence of a cause, and if there is no way to give preference to any of these over others – since we have no agreed-upon sign, criterion, or proof, as has been pointed out earlier – then, if we go by the statements of the Dogmatists, it is necessary to suspend judgment about the existence of causes, too, saying that they are no more existent than non-existent."
Epicureanism
Epicurus contended that atoms, while traversing the void, would occasionally "swerve" (clinamen) from their predetermined trajectories, thereby initiating novel causal sequences. He asserted that these atomic deviations enabled greater human responsibility for actions, a concept incompatible with a purely deterministic causal framework. From an Epicurean perspective, infrequent divine interventions were deemed more acceptable than absolute determinism.
Early Modern Philosophy
In 1729, Jean Meslier's Testament asserted:
"The matter, by virtue of its own active force, moves and acts in blind manner."
Shortly thereafter, Julien Offroy de la Mettrie, in his anonymous 1748 work L'Homme Machine, posited:
"Perhaps, the cause of man's existence is just in existence itself? Perhaps he is by chance thrown in some point of this terrestrial surface without any how and why."
In his 1750 work, Anti-Sénèque [Traité de la vie heureuse, par Sénèque, avec un Discours du traducteur sur le même sujet], the following statement appears:
"Then, the chance has thrown us in life."
During the 19th century, the French philosopher Antoine-Augustin Cournot advanced a novel theory of chance, conceptualizing it as a sequence of non-linear causes. In his 1851 publication, Essai sur les fondements de nos connaissances, he articulated:
"It is not because of rarity that the chance is actual. On the contrary, it is because of chance they produce many possible others."
Modern Philosophy
Charles Peirce
Tychism (from Greek: τύχη, meaning "chance") represents a philosophical thesis introduced by the American philosopher Charles Sanders Peirce during the 1890s. This theory posits that absolute chance, also referred to as spontaneity, constitutes a genuine and active force within the cosmos. It stands in direct opposition to Albert Einstein's frequently cited assertion, "God does not play dice with the universe," and is also regarded as an early philosophical precursor to Werner Heisenberg's uncertainty principle.
Peirce did not assert the absence of universal laws; conversely, he contended that a world entirely governed by chance would be inherently contradictory and thus impossible. He posited that a complete lack of order paradoxically constitutes a form of order. His advocated position is that the universe comprises both regularities and irregularities.
Karl Popper noted that Peirce's theory attracted scant contemporary interest, and that the embrace of indeterminism by other philosophers did not materialize until the emergence of quantum mechanics.
Arthur Holly Compton
In 1931, Arthur Holly Compton championed the concept of human freedom, basing it on quantum indeterminacy. He originated the idea of amplifying microscopic quantum events to introduce an element of chance into the macroscopic world. His rather unconventional mechanism involved imagining sticks of dynamite attached to his amplifier, an anticipation of the Schrödinger's cat paradox.
Responding to criticisms that his theories posited chance as the direct cause of human actions, Compton elucidated the two-stage nature of his concept in a 1955 Atlantic Monthly article. He described an initial phase involving a range of random possible events, followed by the introduction of a determining factor during the act of choice.
A given set of physical conditions is insufficient to precisely determine a future event. These conditions, to the extent they are ascertainable, instead delineate a range of potential occurrences from which a specific event will manifest. When an individual exercises freedom, their act of choice introduces a factor not derived from physical conditions, thereby determining the outcome. This self-determination is known exclusively to the individual. Externally, one perceives only the operation of physical laws in their actions. It is the internal awareness of executing one's intentions that conveys to the actor their freedom.
Compton expressed approval for the emergence of indeterminism in 20th-century science, noting:
In my contemplation of this vital subject, I find myself in a significantly more content state of mind than would have been possible at any earlier phase of scientific development. If the pronouncements of physical laws were presumed accurate, one would have been obliged to infer (as many philosophers did) that the perception of freedom is illusory, or conversely, if [free] choice were considered operative, that the laws of physics ... [were] unreliable. This dilemma has presented an uncomfortable challenge.
Alongside Arthur Eddington in Britain, Compton was among the few distinguished physicists in the English-speaking world during the late 1920s and throughout the 1930s who championed the “liberation of free will” through Heisenberg's indeterminacy principle. Their efforts, however, faced not only physical and philosophical criticism but, more notably, intense political and ideological campaigns.
Karl Popper
In his essay Of Clouds and Clocks, which is part of his book Objective Knowledge, Popper juxtaposed "clouds," his metaphor for indeterministic systems, with "clocks," signifying deterministic ones. He expressed support for indeterminism, articulating:
I believe Peirce was correct in maintaining that all clocks exhibit a considerable degree of cloud-like behavior — even the most precise timepieces. This, I think, constitutes the most significant inversion of the mistaken determinist view that all clouds are merely clocks.
Popper also advocated for propensity probability.
Robert Kane
Kane was a leading contemporary philosopher specializing in free will. Advocating for what is termed "libertarian freedom" within philosophical circles, Kane asserts that "(1) the existence of alternative possibilities (or the agent's power to do otherwise) is a necessary condition for acting freely, and (2) determinism is not compatible with alternative possibilities (it precludes the power to do otherwise)". The fundamental aspect of Kane's argument is rooted not in a defense of alternative possibilities (AP) but in the concept he designates as ultimate responsibility (UR). Therefore, AP constitutes a necessary but insufficient criterion for free will. While the metaphysical existence of genuine alternatives for our actions is requisite, it is not exhaustive; actions could be random without being subject to our control. This control is found in "ultimate responsibility."
Kane's framework posits that ultimate responsibility for creation stems from what he terms "self-forming actions" (SFAs). These SFAs represent instances of indecision where individuals confront conflicting volitions. They constitute the undetermined, regress-stopping voluntary actions or abstentions within an agent's life history, which are essential for ultimate responsibility (UR). UR does not necessitate that every volitional act be undetermined, implying that for every choice, an alternative action was possible. Instead, it only mandates that specific choices and actions, specifically SFAs, remain undetermined, thereby allowing for alternative possibilities. These SFAs are instrumental in shaping an individual's character or nature, subsequently influencing future choices, rationales, and behavioral motivations. Consequently, if an individual has engaged in a character-forming decision (SFA), they bear responsibility for the actions emanating from that developed character.
Mark Balaguer
In his work, Free Will as an Open Scientific Problem, Mark Balaguer presents arguments that align with Kane's perspective. Balaguer contends that, from a conceptual standpoint, free will necessitates indeterminism. He further asserts that the empirical question of whether the brain exhibits indeterministic behavior remains subject to ongoing scientific investigation. Additionally, he has authored "A Scientifically Reputable Version of Indeterministic Libertarian Free Will" on this topic.
Science
Mathematics
Within probability theory, a stochastic process, often referred to as a random process, stands in contrast to a deterministic process or system. Unlike deterministic systems, which model a singular trajectory of evolution over time (e.g., solutions to an ordinary differential equation), stochastic or random processes incorporate an element of indeterminacy in their future progression, characterized by probability distributions. Consequently, even with a known initial state, numerous potential evolutionary paths exist, though some trajectories may possess higher probabilities than others.
Classical and Relativistic Physics
During the early modern era, the notion that Newtonian physics substantiated causal determinism exerted considerable influence. As a result, "physical determinism [...] became the ruling faith among enlightened men; and everybody who did not embrace this new faith was held to be an obscurantist and a reactionary." Nevertheless, "Newton himself may be counted among the few dissenters, for he regarded the solar system as imperfect, and consequently as likely to perish."
Classical chaos is generally not classified as an instance of indeterminism, given its potential manifestation within deterministic systems, exemplified by the three-body problem.
John Earman has posited that the majority of physical theories exhibit indeterminism. For example, Newtonian physics allows for solutions where particles undergo continuous acceleration, extending infinitely outwards. Due to the time-reversibility inherent in these laws, particles could similarly converge inwards without any prior initiating state. Earman refers to these theoretical particles as "space invaders."
John D. Norton has proposed an additional indeterministic scenario, termed Norton's Dome, which describes a particle initially positioned precisely at the apex of a dome.
Branching space-time represents a theoretical framework that integrates indeterminism with the special theory of relativity, a concept initially developed by Nuel Belnap. The equations of general relativity accommodate both indeterministic and deterministic solutions.
Boltzmann
Ludwig Boltzmann is recognized as a foundational figure in statistical mechanics and the contemporary atomic theory of matter. He is notably credited with the discovery that the second law of thermodynamics operates as a statistical principle derived from disorder. Boltzmann also theorized that the observable ordered universe might constitute a mere localized region within a vast, chaotic expanse. The concept of the Boltzmann brain reflects a related philosophical idea.
Evolution and Biology
Darwinian evolution places a greater emphasis on the element of chance inherent in random mutation when contrasted with Herbert Spencer's earlier evolutionary theory. Nevertheless, the necessity of genuine ontological indeterminism for evolution remains a subject of ongoing scholarly debate.
In his 1970 essay, Chance and Necessity, Jacques Monod repudiated the concept of final causation in biology. He contended instead that a combination of efficient causation and "pure chance" results in teleonomy, which he characterized as merely apparent purposefulness.
The Japanese theoretical population geneticist Motoo Kimura emphasizes the significant role of indeterminism in evolutionary processes. According to his neutral theory of molecular evolution, "at the molecular level most evolutionary change is caused by random drift of gene mutants that are equivalent in the face of selection."
Prigogine
In his 1997 publication, The End of Certainty, Prigogine asserts that determinism no longer constitutes a viable scientific principle. He states, "The more we know about our universe, the more difficult it becomes to believe in determinism." This perspective marks a significant divergence from the methodologies of Newton, Einstein, and Schrödinger, all of whom formulated their theories using deterministic equations. Prigogine argues that determinism loses its explanatory efficacy when confronted with phenomena characterized by irreversibility and instability.
Prigogine traces the historical debate surrounding determinism to Darwin, whose efforts to elucidate individual variability within evolving populations inspired Ludwig Boltzmann. Boltzmann subsequently applied this population-based reasoning to explain gas behavior, focusing on populations of particles rather than individual entities. This conceptual shift inaugurated the field of statistical mechanics and revealed that gases undergo irreversible processes. In contrast, deterministic physics traditionally posits that all processes are time-reversible, meaning they can proceed identically both forward and backward through time. Prigogine elucidates that determinism fundamentally negates the concept of an "arrow of time." Without such an arrow, there is no distinct "present" moment, which conventionally follows a determined "past" and precedes an undetermined "future." Instead, all of time is considered a given, with the future being as determined or undetermined as the past. The reintroduction of irreversibility into physics, however, restores the arrow of time. Prigogine cites numerous instances of irreversibility, including diffusion, radioactive decay, solar radiation, weather patterns, and the emergence and evolution of life. Similar to weather systems, living organisms are inherently unstable systems operating far from thermodynamic equilibrium. This inherent instability resists conventional deterministic explanations; instead, due to their acute sensitivity to initial conditions, unstable systems necessitate statistical explanations, relying on probabilistic frameworks.
Prigogine asserts that Newtonian physics has undergone three significant "extensions": first, with the incorporation of the wave function in quantum mechanics; second, through the introduction of spacetime in general relativity; and finally, with the recognition of indeterminism in the study of unstable systems.
Quantum mechanics
Historically, the physical sciences often presumed that any observed unpredictability in a system's behavior stemmed from insufficient fine-grained information. It was believed that a sufficiently detailed investigation would ultimately yield a deterministic theory, exemplified by the notion that "If you knew exactly all the forces acting on the dice, you would be able to predict which number comes up."
However, the advent of quantum mechanics fundamentally undermined this approach by asserting that, at least according to the Copenhagen interpretation, the most elementary constituents of matter occasionally exhibit indeterminate behavior. This indeterminism arises from the collapse of the wave function, where the state of a system upon measurement cannot generally be predicted. Quantum mechanics provides only the probabilities of potential outcomes, which are determined by the Born rule. This non-deterministic behavior during wave function collapse is not exclusive to the Copenhagen interpretation, with its observer-dependence, but is also a feature of objective collapse theories and other theoretical frameworks.
Proponents of determinism, challenging quantum indeterminism, proposed that a novel theoretical framework incorporating additional data, termed hidden variables, could re-establish deterministic outcomes. For example, in 1935, Einstein, Podolsky, and Rosen authored a seminal paper, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?", contending that such a theory was essential for upholding the principle of locality. Subsequently, in 1964, John S. Bell devised a theoretical test for these local hidden variable theories, which Clauser, Horne, Shimony, and Holt later refined into a viable experimental protocol. The conclusive negative findings from Alain Aspect's experiments in the 1980s effectively disproved these theories, contingent upon specific experimental assumptions. Consequently, any interpretation of quantum mechanics, including deterministic reformulations, must either abandon locality or entirely relinquish counterfactual definiteness. David Bohm's theory stands as a prominent illustration of a non-local deterministic quantum theory.
Although the many-worlds interpretation is considered deterministic, experimental outcomes remain unpredictable, as observers cannot foresee which specific "world" they will inhabit. This scenario technically indicates an absence of counterfactual definiteness.
The Heisenberg uncertainty principle, which precludes the simultaneous precise measurement of all a particle's properties, represents a significant implication of quantum indeterminism.
Cosmology
Primordial fluctuations, characterized as density variations in the early universe, are posited as the foundational elements for all cosmic structures. The prevailing explanation for their genesis is rooted in the theory of cosmic inflation. Within the inflationary paradigm, the exponential expansion of the scale factor during inflation caused quantum fluctuations of the inflaton field to extend to macroscopic dimensions. Subsequently, upon exiting the horizon, these fluctuations effectively "froze in." During the subsequent radiation- and matter-dominated epochs, these fluctuations re-entered the horizon, thereby establishing the initial conditions for the formation of cosmic structures.
Neuroscience
Neuroscientists, including Björn Brembs and Christof Koch, propose that thermodynamically stochastic processes within the brain underpin free will, suggesting that even rudimentary organisms like flies exhibit a form of volitional capacity. Analogous concepts have been advanced by philosophers such as Robert Kane.
While acknowledging indeterminism as a fundamental, necessary prerequisite, Björn Brembs asserts that it is far from sufficient for addressing complex concepts such as morality and responsibility.
Other Perspectives
In opposition to proponents of determinism, such as Einstein, Sir Arthur Eddington, an English astronomer, championed indeterminism, positing that physical objects possess an ontologically undetermined component not attributable to epistemological constraints in physicists' comprehension. Consequently, the uncertainty principle would not arise from hidden variables but rather from an inherent indeterminism within nature itself.
David Bohm explores determinism and indeterminism in his work, Causality and Chance in Modern Physics. He theorizes that, given determinism can arise from underlying indeterminism (through the law of large numbers) and indeterminism can emerge from determinism (e.g., from classical chaos), the universe might be conceptualized as comprising alternating strata of causality and chaos.
References
References
Bibliography
- Lejeunne, Denis. 2012. The Radical Use of Chance in 20th Century Art. Rodopi, Amsterdam.
- James, William. The Dilemma of Determinism. Kessinger Publications, 2012.
- Narain, Vir, et al. “Determinism, Free Will, and Moral Responsibility.” TheHumanist.com, 21 Oct. 2014.
Russell, Bertrand. “Elements of Ethics.” Philosophical Essays, 1910.
- Incompatibilist (Nondeterministic) Theories of Free Will from the Stanford Encyclopedia of Philosophy
- Causal Determinism at the Stanford Encyclopedia of Philosophy
- Norton, J.D. Causation as Folk Science.