Editing Indeterminism

{{short description|Philosophical concept}}
{{For|a similar subject|Indeterminacy (philosophy)}}
{{More citations needed|date=June 2011}}

'''Indeterminism''' is the idea that [[wikt:event|events]] (or certain events, or events of certain types) are not [[causality|caused]], or are not caused [[determinism|deterministically]].

It is the opposite of determinism and related to '''chance'''. It is highly relevant to the philosophical problem of [[free will]], particularly in the form of metaphysical [[Libertarianism (metaphysics)|libertarianism]]. In [[science]], most specifically [[Quantum mechanics|quantum theory]] in [[physics]], indeterminism is the belief that no event is certain and the entire outcome of anything is [[probability|probabilistic]]. [[Heisenberg's uncertainty principle]] and the "[[Born rule]]", proposed by [[Max Born]], are often starting points in support of the indeterministic nature of the universe.<ref>The Born rule itself does not imply whether the observed indeterminism is due to the object, to the measurement system, or both. The [[ensemble interpretation]] by Born does not require fundamental indeterminism and lack of causality.</ref>  Indeterminism is also asserted by [[Sir Arthur Eddington#Indeterminism|Sir Arthur Eddington]], and [[Murray Gell-Mann]]. Indeterminism has been promoted by the French biologist [[Jacques Monod]]'s essay "''[[Chance and Necessity]]''".
The physicist-chemist [[Ilya Prigogine]] argued for indeterminism in [[complex systems]].
<!-- Refs from tychsim paper: Mellor 1990, von Mises 1981, Popper 1972 and 1982, Suppes 1970 and 1984, and Shimony 1993.
MELLOR, H. 1971. The Matter of Chance. Cambridge: Cambridge University Press.
SUPPES, P. 1970. A Probabilistic Theory of Causality. Amsterdam: North Holland.
SUPPES. P. 1984. Probabilistic Metaphysics. Oxford: Blackwell.
SHIMONY, A. 1993. Search For A Naturalistic World View, Vol. II: Natural Science and
Metaphysics. Cambridge: Cambridge University Press.
VON MISES, R. 1981. Probability, Statistics and Truth. New York: Dover.-->

==Necessary but insufficient causation==

{{further|Necessary and sufficient conditions}}
Indeterminists do not have to deny that causes exist. Instead, they  can maintain that the only causes that exist are of a type that do not constrain the future to a single course; for instance, they can maintain that only necessary and not sufficient causes exist. The necessary/sufficient distinction works as follows:

If ''x'' is a necessary cause of ''y''; then the presence of ''y''  implies that ''x'' definitely preceded it.  The presence of ''x'', however, does not imply that ''y'' will occur.

If ''x'' is a sufficient cause of ''y'', then the presence of ''y'' implies that ''x'' may have preceded it. (However, another cause ''z'' may alternatively cause ''y''. Thus the presence of ''y'' does not imply the presence of ''x'', or ''z'', or any other suspect.)

It is possible for everything to have a [[necessary cause]], even while indeterminism holds and the future is open, because a necessary condition does not lead to a single inevitable effect. Indeterministic (or probabilistic) causation is a proposed possibility, such that "everything has a cause" is not a clear statement of indeterminism.

==Probabilistic causation==

{{main|Probabilistic causation}}

Interpreting [[causality|causation]] as a [[Causal determinism|deterministic]] relation means that if ''A'' causes ''B'', then ''A'' must always be followed by ''B''. In this sense, however, war does not always cause deaths (see [[Cyberwarfare]]), nor does a singular moment of [[Tobacco smoking|smoking]] always cause [[cancer]]. As a result, many turn to a notion of [[probabilistic causation]].  Informally, ''A'' '''probabilistically''' causes ''B'' if ''A''<nowiki>'</nowiki>s occurrence increases the probability of ''B''.  This is sometimes interpreted to reflect the imperfect knowledge of a deterministic system  but other times interpreted to mean that the causal system under study has an inherently indeterministic nature. ([[Propensity probability]] is an analogous idea, according to which probabilities have an objective existence and are not just limitations in a subject's knowledge).<ref>[http://plato.stanford.edu/entries/probability-interpret/ Stanford Encyclopedia of Philosophy: ''Interpretations of Philosophy'']</ref>

It can be proved that realizations of any [[probability distribution]] other than the [[uniform distribution (continuous)|uniform]] one are mathematically equal to applying a (deterministic) function (namely, an [[inverse distribution function]]) on a random variable following the latter (i.e. an "absolutely random" one<ref>The uniform distribution is the most "agnostic" distribution, representing lack of any information. [[Laplace]] in his theory of probability was apparently the first one to notice this. Currently, it can be shown using definitions of [[Entropy (information theory)|entropy]].</ref>); the probabilities are contained in the deterministic element. A simple form of demonstrating it would be shooting randomly within a square and then (deterministically) interpreting a relatively large subsquare as the more probable outcome.

==Intrinsic indeterminism versus unpredictability==

A distinction is generally made between indeterminism and the mere inability to measure the variables (limits of precision). This is especially the case for physical indeterminism (as proposed by various [[interpretations of quantum mechanics]]). Yet some philosophers have argued that indeterminism and unpredictability are synonymous.<ref>{{cite book|author=Popper, K| title=Of Clouds and Clocks: an approach to the rationality and the freedom of man, included in Objective Knowledge|year=1972|page=220|publisher=Oxford Clarendon Press|quote=Indeterminism—or, more precisely physical indeterminism—is merely the doctrine that not all events in the physical world are predetermined with absolute precision}}</ref>

==Philosophy<!--'Chance (philosophy)' redirects here-->==
===Ancient Greek philosophy===

====Leucippus====
The oldest mention of the concept of '''chance'''<!--boldface per WP:R#PLA; 'Chance (philosophy)' redirects here--> is by the earliest philosopher of [[atomism]], [[Leucippus]], who said:
<blockquote>"The cosmos, then, became like a spherical form in this way: the atoms being submitted to a casual and unpredictable movement, quickly and incessantly".<ref>"ὁ τοίνυν κόσμος συνέστη περικεκλασμένῳ σχήματι ἐσχηματισμένος τὸν τρόπον τοῦτον. τῶν ἀτόμων σωμάτων ἀπρονόητον καὶ τυχαίαν ἐχόντων τὴν κίνησιν συνεχῶς τε καὶ τάχιστα κινουμένων" [[Hermann Alexander Diels|H.Diels-W.Kranz]] ''Die Fragmente der Vorsokratiker'', Berlin Weidmann 1952, 24, I, 1</ref></blockquote>

====Aristotle====
{{main|Four causes}}
[[Aristotle]] described four possible causes (material, efficient, formal, and final). Aristotle's word for these causes was αἰτίαι (''aitiai'', as in ''[[wikt:aetiology|aetiology]]''), which translates as causes in the sense of the multiple factors responsible for an event. Aristotle did not subscribe to the simplistic "every event has a (single) cause" idea that was to come later.

In his ''[[Physics (Aristotle)|Physics]]'' and ''[[Metaphysics (Aristotle)|Metaphysics]]'', Aristotle said there were [[Accident (philosophy)|accidents]] (συμβεβηκός, ''[[sumbebekos]]'') caused by nothing but chance (τύχη, ''tukhe''). He noted that he and the early physicists found no place for chance among their causes.

{{quote|We have seen how far Aristotle distances himself from any view which makes chance a crucial factor in the general explanation of things. And he does so on conceptual grounds: chance events are, he thinks, by definition unusual and lacking certain explanatory features: as such they form the complement class to those things which can be given full natural explanations.<ref name="Hankinson">{{cite book |chapter=Causes |title=Blackwell Companion to Aristotle |last=Hankinson |first=R.J. |year=2009 |page=223}}</ref>|R.J. Hankinson |"Causes" in ''Blackwell Companion to Aristotle ''}}

Aristotle opposed his accidental chance to necessity:
<blockquote>
    Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause.<ref>Aristotle, ''[[Metaphysics (Aristotle)|Metaphysics]]'', Book V, 1025a25</ref>
</blockquote>
<blockquote>
    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.<ref>Aristotle, ''[[Metaphysics (Aristotle)|Metaphysics]]'', Book VI, 1027a29-33</ref>
</blockquote>

====Pyrrhonism====
The philosopher [[Sextus Empiricus]] described the [[pyrrhonism|Pyrrhonist]] position on causes as follows:

<blockquote>...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, [[criteria of truth|criterion]], or proof, as has been pointed out earlier – then, if we go by the statements of the [[Dogma]]tists, it is necessary to [[epoche|suspend judgment]] about the existence of causes, too, saying that they are no more existent than non-existent<ref>[[Sextus Empiricus]] ''Outlines of Pyrrhonism'' Book III Chapter 5</ref></blockquote>

====Epicureanism====
[[Epicurus]] argued that as atoms moved through the void, there were occasions when they would "swerve" (''[[clinamen]]'') from their otherwise determined paths, thus initiating new causal chains. Epicurus argued that these swerves would allow us to be more responsible for our actions, something impossible if every action was deterministically caused. For [[Epicureanism]], the occasional interventions of arbitrary gods would be preferable to strict determinism.

===Early modern philosophy===
In 1729 the<small> </small>''Testament'' of [[Jean Meslier]] states:

<blockquote>"The matter, by virtue of its own active force, moves and acts in blind manner".<ref>Meslier, J. ''The Testament''.</ref> </blockquote>

Soon after [[Julien Offroy de la Mettrie]] in his ''L'Homme Machine.'' (1748, anon.) wrote:

<blockquote>"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''". </blockquote>

In his ''Anti-Sénèque'' [''Traité de la vie heureuse, par Sénèque, avec un Discours du traducteur sur le même sujet'', 1750] we read:

<blockquote>"Then, the chance has thrown us in life".<ref>Jde La Mettrie, J.O.:''Anti-Sénèque''</ref></blockquote>

In the 19th century the French Philosopher [[Antoine-Augustin Cournot]] theorized ''chance'' in a new way, as series of not-linear causes. He wrote in ''Essai sur les fondements de nos connaissances'' (1851):

<blockquote>"It is not because of rarity that the chance is actual. On the contrary, it is because of chance they produce many possible others."<ref>Cournot, A.A: ''Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique'', § 32.</ref> </blockquote>

===Modern philosophy===

====Charles Peirce====
[[Tychism]] ({{langx|el|τύχη}} "chance") is a thesis proposed by the American philosopher [[Charles Sanders Peirce]] in the 1890s.<ref>Peirce, C. S.:  ''The Doctrine of Necessity Examined'', [[The Monist]], 1892
</ref> It holds that absolute [[chance (philosophy)|chance]], also called spontaneity, is a real factor operative in the universe. It may be considered both the direct opposite of [[Albert Einstein]]'s oft quoted dictum that: "[[God does not play dice]] with the universe" and an early philosophical anticipation of [[Werner Heisenberg]]'s [[uncertainty principle]].

Peirce does not, of course, assert that there is ''no'' law in the universe. On the contrary, he maintains that an absolutely chance world would be a contradiction and thus impossible.
Complete lack of order is itself a sort of order. The position he advocates is rather that there are in the universe both regularities and irregularities.

[[Karl Popper]] comments<ref>Popper, K: ''Of Clouds and Cuckoos'', included in ''Objective Knowledge'', revised, 1978, p231.</ref> that Peirce's theory received little contemporary attention, and that other philosophers did not adopt indeterminism until the rise of quantum mechanics.

====Arthur Holly Compton====
In 1931, [[Arthur Holly Compton]] championed the idea of human freedom based on [[quantum indeterminacy]] and invented the notion of amplification of microscopic quantum events to bring [[Randomness|chance]] into the macroscopic world. In his somewhat bizarre mechanism, he imagined sticks of dynamite attached to his amplifier, anticipating the [[Schrödinger's cat]] paradox.<ref>SCIENCE, 74, p. 1911, August 14, 1931.</ref>

Reacting to criticisms that his ideas made chance the direct cause of our actions, Compton clarified the two-stage nature of his idea in an ''Atlantic Monthly'' article in 1955. First there is a range of random possible events, then one adds a determining factor in the act of [[choice]].

<blockquote>A set of known physical conditions is not adequate to specify precisely what a forthcoming event will be. These conditions, insofar as they can be known, define instead a range of possible events from among which some particular event will occur. When one exercises freedom, by his act of choice he is himself adding a factor not supplied by the physical conditions and is thus himself determining what will occur. That he does so is known only to the person himself. From the outside one can see in his act only the working of physical law. It is the inner knowledge that he is in fact doing what he intends to do that tells the actor himself that he is free.<ref>"Science and Man’s Freedom", in ''The Cosmos of Arthur Holly Compton'', 1967, Knopf, p. 115</ref>
</blockquote>

Compton welcomed the rise of indeterminism in 20th century science, writing:

<blockquote>
In my own thinking on this vital subject I am in a much more satisfied state of mind than I could have been at any earlier stage of science. If the statements of the laws of physics were assumed correct, one would have had to suppose (as did most philosophers) that the feeling of freedom is illusory, or if [free] choice were considered effective, that the laws of physics ... [were] unreliable. The dilemma has been an uncomfortable one.<ref>Commpton, A.H. ''The Human Meaning of Science'' p. ix</ref>
</blockquote>Together with Arthur Eddington in Britain, Compton was one of those rare distinguished physicists in the English speaking world of the late 1920s and throughout the 1930s arguing for the “liberation of free will” with the help of Heisenberg’s  indeterminacy principle, but their efforts had been met not only with physical and philosophical criticism but most primarily with fierce political and ideological campaigns.<ref>{{Citation|last=Kožnjak|first=Boris|title=The Earliest Missionaries of 'Quantum Free Will': A Socio-Historical Analysis|volume=6|date=2018|work=Free Will & Action|pages=131–154|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-319-99295-2_10|isbn=9783319992945|series=Historical-Analytical Studies on Nature, Mind and Action}}</ref>

====Karl Popper====
In his essay ''Of Clouds and Clocks'', included in his book ''Objective Knowledge'', [[Karl Popper|Popper]]
contrasted "clouds", his metaphor for indeterministic systems, with "clocks", meaning deterministic ones.
He sided with indeterminism, writing
<blockquote>
I believe Peirce was right in holding that all clocks are clouds to some considerable degree — even the most precise of clocks. This, I think, is the most important inversion of the mistaken determinist view that all clouds are clocks<ref>Popper, K: ''Of Clouds and Cuckoos'', included in ''Objective Knowledge'', revised, 1978, p215.</ref>
</blockquote>

Popper was also a promoter of [[propensity probability]].

====Robert Kane====
Kane is one of the leading contemporary philosophers on [[free will]].<ref name = "KaneFreeWill">Kane, R. (ed.) ''Oxford Handbook of Free Will''</ref><ref>[http://www.informationphilosopher.com/solutions/philosophers/kane/ Information Philosophers] "Robert Kane is the acknowledged dean of the libertarian philosophers writing actively on the free will problem."</ref>  Advocating what is termed within philosophical circles "[[Libertarianism (metaphysics)|libertarian]] freedom", Kane argues 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)".<ref>Kane (ed.): ''Oxford Handbook of Free Will'', p. 11.</ref>  It is important to note that the crux of Kane's position is grounded not in a defense of alternative possibilities (AP) but in the notion of what Kane refers to as ultimate responsibility (UR).  Thus, AP is a necessary but insufficient criterion for free will.  It is necessary that there be ([[Metaphysics|metaphysically]]) real alternatives for our actions, but that is not enough; our actions could be random without being in our control.  The control is found in "ultimate responsibility".

What allows for ultimate responsibility of creation in Kane's picture are what he refers to as "self-forming actions" or SFAs — those moments of indecision during which people experience conflicting wills.  These SFAs are the undetermined, regress-stopping voluntary actions or refrainings in the life histories of agents that are required for UR.  UR does not require that ''every'' act done of our own free will be undetermined and thus that, for every act or choice, we could have done otherwise; it requires only that certain of our choices and actions be undetermined (and thus that we could have done otherwise), namely SFAs.  These form our character or nature; they inform our future choices, reasons and motivations in action.  If a person has had the opportunity to make a character-forming decision (SFA), he is responsible for the actions that are a result of his character.

====Mark Balaguer====
[[Mark Balaguer]], in his book ''Free Will as an Open Scientific Problem''<ref>{{Cite web |url=http://ndpr.nd.edu/review.cfm?id=19727 |title=Notre Dame Reviews: ''Free Will as an Open Scientific Problem'' |access-date=2011-07-26 |archive-date=2010-05-27 |archive-url=https://web.archive.org/web/20100527203918/http://ndpr.nd.edu/review.cfm?id=19727 |url-status=dead }}</ref> argues similarly to Kane. He believes that, conceptually,  free will requires indeterminism, and the question of whether the brain behaves indeterministically is open to further [[empirical]] research. He has also written on this matter "A Scientifically Reputable Version of Indeterministic Libertarian Free Will".<ref>{{cite web|url=http://turingc.blogspot.pt/2012/07/mark-balaguer-scientifically-reputable.html|title=Mark Balaguer: A Scientifically Reputable Version of Indeterministic Libertarian Free Will|website=turingc.blogspot.pt|date=2012-07-06}}</ref>

==Science==
{{see also|Philosophy of physics#Indeterminism|label 1=Philosophy of physics and indeterminism}}

===Mathematics===
{{Probability fundamentals}}

In [[probability theory]], a [[stochastic process]], or sometimes random process, is the counterpart to a deterministic process (or [[deterministic system]]). Instead of dealing with only one possible reality of how the process might evolve over time (as is the case, for example, for solutions of an [[ordinary differential equation]]), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.

===Classical and relativistic physics===
The idea that [[Newtonian physics]] proved causal determinism was highly influential in the early modern period.
"Thus 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".<ref>Popper, K: ''Of Clouds and Cuckoos'', included in ''Objective Knowledge'', revised, 1978, p212.</ref> However: "Newton himself may be counted among the few dissenters, for he regarded the solar system as ''imperfect'', and consequently as likely to perish".<ref>Popper, 1978, citing, Henry Pemberton's ''A View of Sir Isaac Newton's Philosophy''</ref>

[[Classical chaos]] is not usually considered an example of indeterminism, as it can occur in deterministic systems such as the [[three-body problem]].

[[John Earman]] has argued that most physical theories are indeterministic.<ref>[http://www.ucl.ac.uk/~uctytho/Determinism.pdf Earman, J. ''Determinism: What We Have Learned, and What We Still Don't Know'']</ref><ref>[http://plato.stanford.edu/entries/determinism-causal/#StaDetPhy The Stanford Encyclopedia of Philosophy: ''Causal Determinism'']</ref> For instance, Newtonian physics admits solutions where particles accelerate continuously, heading out towards infinity. By the [[time reversibility]] of the laws in question, particles could also head inwards, unprompted by any pre-existing state. He calls such hypothetical particles "[[space invaders (classical physics)|space invaders]]".

John D. Norton has suggested another indeterministic scenario, known as [[Norton's Dome]], where a particle is initially situated on the exact apex of a dome.<ref>[http://plato.stanford.edu/entries/determinism-causal/ Stanford Encyclopedia of Philosophy ''Causal Determinism'']</ref>

[[Branching space-time]] is a theory uniting indeterminism and the [[special theory of relativity]]. The idea was originated by [[Nuel Belnap]].<ref>{{Cite web |url=http://confer.uj.edu.pl/branching/ |title=Conference on Branching Space Time |access-date=2011-07-27 |archive-url=https://web.archive.org/web/20110930083210/http://confer.uj.edu.pl/branching/ |archive-date=2011-09-30 |url-status=dead }}</ref> The equations of [[general relativity]] admit of both indeterministic and deterministic solutions.

===Boltzmann===

[[Ludwig Boltzmann]] was one of the founders of [[statistical mechanics]] and the modern [[atomic theory of matter]]. He is remembered for his discovery that the [[second law of thermodynamics]] is a statistical law  stemming from [[Chaos theory|disorder]]. He also speculated that the ordered universe is only a small bubble in a larger sea of chaos. The [[Boltzmann brain]] is a similar idea.

===Evolution and biology===
[[Darwinian evolution]] has an enhanced reliance on the chance element of [[random mutation]] compared to the earlier evolutionary theory of [[Herbert Spencer]]. However, the question of whether evolution requires genuine ontological indeterminism is open to debate<ref>{{Cite web |url=http://philosophy.ucdavis.edu/millstein/papers/Millstein_agnosticism.pdf |title=Millstein, R.L.: ''Is the Evolutionary Process Deterministic or Indeterministic'' |access-date=2011-07-28 |archive-url=https://web.archive.org/web/20110930131133/http://philosophy.ucdavis.edu/millstein/papers/Millstein_agnosticism.pdf |archive-date=2011-09-30 |url-status=dead }}</ref>

In the essay ''[[Chance and Necessity]]'' (1970) Jacques Monod rejected the role of [[final causation]] in [[biology]], instead arguing that a mixture of [[efficient causation]] and "pure chance" lead to [[teleonomy]], or merely ''apparent'' purposefulness.

The Japanese theoretical population geneticist [[Motoo Kimura]] emphasises the role of indeterminism in evolution.  According to [[neutral theory of molecular evolution]]: "at the molecular level most evolutionary change is caused by [[random drift]] of [[mutation|gene mutants]] that are equivalent in the face of selection.<ref>Kimura, M. ''The neutral theory of molecular evolution'', (''The Science'', No. 1, 1980, p. 34)</ref>

===Prigogine===

In his 1997 book, ''The End of Certainty'', Prigogine contends that determinism is no longer a viable scientific belief. "The more we know about our universe, the more difficult it becomes to believe in determinism." This is a major departure from the approach of [[Isaac Newton|Newton]], [[Albert Einstein|Einstein]] and [[Erwin Schrödinger|Schrödinger]], all of whom expressed their theories in terms of deterministic equations. According to Prigogine, determinism loses its explanatory power in the face of [[irreversibility]] and [[instability]].<ref>End of Certainty by Ilya Prigogine pp. 162–85 Free Press; 1 edition (August 17, 1997) {{ISBN|978-0-684-83705-5}} [https://books.google.com/books?id=-VI8093PJuUC&pg=PA183]</ref>

Prigogine traces the dispute over determinism back to [[Charles Darwin|Darwin]], whose attempt to explain individual variability according to evolving populations inspired [[Ludwig Boltzmann]] to explain the behavior of gases in terms of populations of particles rather than individual particles.<ref>End of Certainty by Ilya Prigogine pp. 19–21 Free Press; 1 edition (August 17, 1997) {{ISBN|978-0-684-83705-5}} [https://books.google.com/books?id=-VI8093PJuUC&pg=PA19]</ref> This led to the field of [[statistical mechanics]] and the realization that gases undergo irreversible processes. In deterministic physics, all processes are time-reversible, meaning that they can proceed backward as well as forward through time. As Prigogine explains, determinism is fundamentally a denial of the [[arrow of time]]. With no arrow of time, there is no longer a privileged moment known as the "present," which follows a determined "past" and precedes an undetermined "future." All of time is simply given, with the future as determined or undetermined as the past. With irreversibility, the arrow of time is reintroduced to physics. Prigogine notes numerous examples of irreversibility, including [[diffusion]], [[radioactive decay]], [[solar radiation]], [[weather]] and the emergence and evolution of [[life]]. Like weather systems, organisms are unstable systems existing far from [[thermodynamic equilibrium]]. Instability resists standard deterministic explanation. Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of [[probability]].

Prigogine asserts that [[Newtonian physics]] has now been "extended" three times, first with the use of the wave function in [[quantum mechanics]], then with the introduction of spacetime in [[general relativity]] and finally with the recognition of indeterminism in the study of unstable systems.

===Quantum mechanics===
{{main|Quantum indeterminacy}}
At one time, it was assumed in the physical sciences that if the behavior observed in a system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result in a deterministic theory ("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]] removed the underpinning from that approach, with the claim that (at least according to the [[Copenhagen interpretation]]) the most basic constituents of matter at times behave [[quantum indeterminism|indeterministically]]. This comes from the [[wave function collapse|collapse of the wave function]], in which the state of a system upon [[measurement problem|measurement]] cannot in general be predicted.  Quantum mechanics only predicts the probabilities of possible outcomes, which are given by the [[Born rule]]. Non-deterministic behavior in wave function collapse is not only a feature of the Copenhagen interpretation, with its [[observer (quantum mechanics)|observer]]-dependence, but also of [[objective collapse theories|objective collapse]] and [[Interpretations of quantum mechanics#Comparisons|other theories]].

Opponents of quantum indeterminism suggested that determinism could be restored by formulating a new theory in which additional information, so-called [[hidden variable (physics)|hidden variables]],<ref>[https://web.archive.org/web/20110319153807/http://www.cosmosmagazine.com/features/online/4137/how-much-free-will-do-we-have Cosmos Magazine: ''How Much Free Will Do We Have'']</ref> would allow definite outcomes to be determined. For instance, in 1935, Einstein, Podolsky and Rosen wrote a paper titled ''"[[EPR paradox|Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?]]"'' arguing that such a theory was in fact necessary to preserve the [[principle of locality]].
In 1964, [[John S. Bell]] was able to define [[Bell's theorem|a theoretical test]] for these local hidden variable theories, which was reformulated as a workable experimental test through the work of [[CHSH inequality|Clauser, Horne, Shimony and Holt]]. The negative result of the 1980s [[Aspect experiment|tests]] by [[Alain Aspect]] ruled such theories out, provided certain [[Loopholes in Bell test experiments|assumptions]] about the experiment hold. Thus any [[interpretation of quantum mechanics]], including deterministic reformulations, must either reject [[Principle of locality|locality]] or reject [[counterfactual definiteness]] altogether. [[David Bohm]]'s [[Bohmian quantum mechanics|theory]] is the main example of a non-local deterministic quantum theory.

The [[many-worlds interpretation]] is said to be deterministic, but experimental results still cannot be predicted: experimenters do not know which 'world' they will end up in. Technically, [[counterfactual definiteness]] is lacking.

A notable consequence of quantum indeterminism is the [[Heisenberg uncertainty principle]], which prevents the simultaneous accurate measurement of all a particle's properties.

===Cosmology===
[[Primordial fluctuations]] are density variations in the early universe which are considered the seeds of all [[large-scale structure of the cosmos|structure]] in the universe. Currently, the most widely accepted explanation for their origin is in the context of [[cosmic inflation]]. According to the inflationary paradigm, the exponential growth of the [[scale factor]] during inflation caused [[quantum fluctuation]]s of the inflaton field to be stretched to macroscopic scales, and, upon leaving the [[Observable universe#Horizons|horizon]], to "freeze in".
At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the [[initial conditions]] for [[structure formation]].

===Neuroscience===
[[Neuroscientist]]s such as [[Björn Brembs]] and [[Christof Koch]] believe thermodynamically [[stochastic processes]] in the brain are the basis of [[free will]], and that even very simple organisms such as [[flies]] have a form of free will.<ref name="bbc.co.uk">[https://www.bbc.co.uk/news/science-environment-11998687 BBC Science: ''Free Will Similar in Animals, Humans—But Not So Free'']</ref> Similar ideas are put forward by some philosophers such as [[indeterminism#Robert Kane|Robert Kane]].

Despite recognizing indeterminism to be a very low-level, necessary prerequisite, Björn Brembs says that it's not even close to being sufficient for addressing things like morality and responsibility.<ref name="bbc.co.uk"/>

===Other views===
Against [[Albert Einstein|Einstein]] and others who advocated [[determinism]], indeterminism—as championed by the English astronomer [[Sir Arthur Eddington]]—says that a physical object has an [[ontology|ontologically]] undetermined component that is not due to the [[epistemology|epistemological]] limitations of physicists' understanding. The [[uncertainty principle]], then, would not necessarily be due to [[Hidden variable theory|hidden variables]] but to an indeterminism in nature itself.<ref>{{Cite book
| publisher = University of Notre Dame Press
| isbn = 978-0-268-02595-3
| last = de Koninck
| first = Charles
| author-link=Charles De Koninck
| title = The writings of Charles de Koninck
| location = Notre Dame, Ind. 
| year = 2008
| oclc = 615199716
| chapter = The philosophy of Sir Arthur Eddington and The problem of indeterminism
}}</ref>

Determinism and indeterminism are examined in ''Causality and Chance in Modern Physics''  by [[David Bohm]]. He speculates that, since determinism can emerge from underlying indeterminism (via the [[law of large numbers]]),<ref> In this regard, by recognizing chance (contingency) in the reality, the rationality of the empirical law of large numbers can be shown. See: D’AMICO Rosario. Chance and The Statistical Law of Large Numbers. Journal of Mathematical Economics and Finance, [S.l.], v. 7, n. 2, p. 41-53, dec. 2021. ISSN 2458-0813. Available at:

https://journals.aserspublishing.eu/jmef/article/view/6879
</ref> and that indeterminism can emerge from determinism (for instance, from [[classical chaos]]), the universe could be conceived of as having alternating layers of causality and chaos.<ref>[https://www.amazon.com/Causality-Chance-Modern-Physics-David/dp/0812210026 Bohm, D: ''Causality and Chance in Modern Physics'', pp. 29–33 ]</ref>

==See also==
{{cols}}
* [[Catastrophism]]
* [[Chance (disambiguation)]]
* [[Interpretations of quantum mechanics]]: [[Interpretations_of_quantum_mechanics#Comparisons|Comparisons chart]]
* [[Free will]]
* [[Incompatibilism]]
* [[Luck]]
* [[Nondeterminism (disambiguation)]]
* [[Randomness]]
* [[Uncertainty]]
{{colend}}

==References==
{{Reflist|30em}}

==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, thehumanist.com/magazine/november-december-2014/philosophically-speaking/determinism-free-will-and-moral-responsibility.
Russell, Bertrand. “Elements of Ethics.” Philosophical essays, 1910.

==External links==
* [http://plato.stanford.edu/entries/incompatibilism-theories/ Incompatibilist (Nondeterministic) Theories of Free Will] from the Stanford Encyclopedia of Philosophy
* [http://www.philosophyprofessor.com/philosophies/indeterminism.php indeterminism] from the Philosophy Professor
* [http://plato.stanford.edu/entries/determinism-causal/ Causal Determinism at the Stanford Encyclopedia of Philosophy]
* [http://www.philosophersimprint.org/003004/ Norton, J.D. ''Causation as Folk Science'']

{{Determinism}}
{{Evolutionary psychology}}

[[Category:Free will]] 
[[Category:Randomness]]
[[Category:Determinism]]