Determinism

To the Determinist, the universe is like clockwork

Determinism (specifically causal determinism) is the concept that events within a given paradigm are bound by causality in such a way that any state is, to some large degree, determined by prior states.

Hence "determinism" is the name of a broader philosophical view that conjectures that every event, including human cognition, behaviour, decision, and action is causally determined (completely predictable) by previous events. In philosophical arguments, the concept of determinism in the domain of human action is often contrasted with free will. The argument called indeterminism (otherwise "nondeterminism") negates causality as a factor and contradicts deterministic argument.

Determinists believe the universe is fully governed by causal laws resulting in only one possible state at any point in time. With numerous historical debates, many varieties and philosophical positions on the subject of determinism exist, most prominently the free will debates involving compatibilism and incompatibilism. Predeterminism proposes there is an unbroken chain of prior occurrences back to the origin of the universe.

Determinism should not be confused with Self-determination of human actions by reasons, motives, and desires, or with predestination, which specifically factors the existence of God into its tenets.

Certainty series
Agnosticism
Belief
Certainty
Doubt
Determinism
Epistemology
Estimation
Fallibilism
Fatalism
Justification
Nihilism
Probability
Skepticism
Solipsism
Truth
Uncertainty

Contents

Varieties of determinism

Causal (or Nomological) determinism [1] generally assumes that every event has an antecedent cause in an infinite causal chain going back to Aristotle's Prime Mover or the beginning of the universe. Determinists believe that there is nothing uncaused or self-caused (causa sui). Research in quantum mechanics complicates this position further (see 'Arguments' section below). Such determinism is sometimes illustrated by the thought experiment of Laplace's demon.

Many philosophical theories of determinism frame themselves with the idea that reality follows a sort of predetermined path

Logical determinism or Determinateness is the notion that all propositions, whether about the past, present, or future, are either true or false. A belief in Causal Determinism along with this Logical Determinism together define what is called 'Hard Determinism' (discussed further below). Note that one can support Causal Determinism without necessarily supporting Logical Determinism (depending on one's views on the nature of time) and vice versa. The problem of free will is especially salient now with Logical Determinism: how can choices be free, given that propositions about the future already have a truth value in the present (i.e. it is already determined as either true or false)? This is referred to as the problem of future contingents.[1] Often synonymous with Logical Determinism are the ideas behind Spatio-temporal Determinism or Eternalism: the view of special relativity. J. J. C. Smart, a proponent of this view, uses the term "tenselessness" to describe the simultaneous existence of past, present, and future. In physics, the "block universe" of Hermann Minkowski and Albert Einstein assumes that time is simply a fourth dimension that already exists (like the three spatial dimensions). In other words, all the other parts of time are real, just like the city blocks up and down one's street, although we only ever perceive one part of time.

Historical determinism is the stance in explaining history, or advocating a political position, that events are historically predetermined (and/or currently constrained) by various forces. Historical Determinism is may be synonymous with Causal Determinism. It is associated with the dialectical idealism of G.W.F. Hegel.

Necessitarianism is a metaphysical principle that denies all mere possibility; there is exactly one way for the world to be. Leucippus claimed there were no uncaused events. "Nothing occurs at random, but everything for a reason and by necessity." The focus, then, is on a sort of teleology. This view is similar, and often synonymous, with fatalism.[2] Fatalism is the simple idea that everything is fated to happen, so that humans have no control over their future. Notice that fate has arbitrary power. Fate also need not follow any causal or otherwise deterministic laws.

Even without a full understanding of microscopic physics, we can predict the distribution of 1000 coin tosses

Theological determinism or predestination is the concept that there is a God who determines all that humans will do, either by knowing their actions in advance, via some form of omniscience[3] or by decreeing their actions in advance.[4] The problem of free will, in this context, is the problem of how our actions can be free if there is a being who has determined them for us ahead of time.

Adequate determinism is the thesis that quantum indeterminacy can be ignored for most macroscopic events, since random quantum events "average out" in the limit of large numbers of particles, where the laws of quantum mechanics asymptotically approach the laws of classical mechanics.

Determined by nature or nurture

Looking at a sculpture after some time, one does not ask whether we are seeing the effects of the starting materials OR environmental influences - the two interact

Some deterministic theories frame themselves as an answer to the Nature or Nurture debate, suggesting that one will entirely determine behaviour. As scientific understanding has grown, the strongest versions of these theories have been widely rejected as single cause fallacy.[5] In other words, the modern deterministic theories attempt to explain how the interaction of both nature and nurture is entirely predictable. The concept of heritability has been helpful to make this distinction.

Biological determinism, sometimes called Genetic determinism, is the idea that each of our behaviors, beliefs, and desires are fixed by our genetic nature.

Behavioral determinism is the idea that all actions are reflex reactions established by operant or classical conditioning from the environment. This Nurture-focused determinism was developed to an extreme by John B. Watson and B. F. Skinner.

Cultural determinism or social determinism is the nurture-focused theory that it the culture in which we are raised that determines who we are.

Environmental determinism is also known as climatic or geographical determinism. It holds the view that the physical environment, rather than social conditions, determines culture. Supporters often also support Behavioral determinism. Key proponents of this notion have included Ellen Churchill Semple, Ellsworth Huntington, Thomas Griffith Taylor and possibly Jared Diamond, although his status as an environmental determinist is debated.[6]

Factor priority

A technological determinist might suggest that technology, like the internet, is the greatest factor shaping human civilization.

Other 'deterministic' theories actually seek only to highlight the importance of a particular factor in predicting the future. These theories often use the factor as a sort of guide or constraint on the future. They need not suppose that complete knowledge of that one factor would allow us to make perfect predictions.

Psychological determinism can mean that humans must act according to reason, but it can also be synonymous with some sort of Psychological egoism. The latter is the view that humans will always act according to their perceived best interest.

Linguistic determinism claims that our language determines (at least limits) the things we can think and say and thus know. The Sapir-Whorf hypothesis argues that individuals experience the world based on the grammatical structures they habitually use.

Economic determinism is the theory which attributes primacy to the economic structure over politics in the development of human history. It is associated with the dialectical materialism of Karl Marx.

Technological determinism is a reductionist theory that presumes that a society's technology drives the development of its social structure and cultural values. Media determinism, a subset of technological determinism, is a philosophical and sociological position which posits the power of the media to impact society. Two leading media determinists are the Canadian scholars Harold Innis and Marshall McLuhan.

Free will and determinism

Main article: Free will
A table showing the different positions related to free will and determinism

Philosophers have argued that either Determinism is true or Indeterminism is true, but also that 'Free will' either exists or it does not. This creates four possible positions. Compatibilism refers to the view that free will is, in some sense, compatible with Determinism. The three 'Incompatibilist' positions, on the other hand, deny this possibility. They instead suggest there is a dichotomy between determinism and free will (only one can be true).

To the Incompatibilists, one must choose either free will or Determinism, and maybe even reject both. The result is one of three positions:

Thus, although Determinists may be Compatibilists, calling someone a 'Determinist' is often used to denote the 'Hard Determinist' position.

The Standard argument against free will, according to philosopher J. J. C. Smart focuses on the implications of Determinism for 'free will' [7]. He suggests that, if determinism is true, all our actions are predicted and we are not free; if indeterminism is true, our actions are random and still we do not seem free.

Implications

Some determinists argue that materialism does not present a complete understanding of the universe, because while it can describe determinate interactions among material things, it ignores the minds or souls of conscious beings.

A number of positions can be delineated:

  1. Immaterial souls exist and exert a non-deterministic causal influence on bodies. (Traditional free-will, interactionist dualism).[8][9]
  2. Immaterial souls exist, but are part of deterministic framework.
  3. Immaterial souls exist, but exert no causal influence, free or determined (epiphenomenalism, occasionalism)
  4. Immaterial souls are all that exist (Idealism).
  5. Immaterial souls do not exist — there is no mind-body dichotomy, and there is a Materialistic explanation for intuitions to the contrary.

Another topic of debate is the implication that Determinism has on morality. Hard determinism is particularly criticized for making moral judgements impossible.

History

Some of the main philosophers who have dealt with this issue are Marcus Aurelius, Omar Khayyám, Thomas Hobbes, Baruch Spinoza, Gottfried Leibniz, David Hume, Baron d'Holbach (Paul Heinrich Dietrich), Pierre-Simon Laplace, Arthur Schopenhauer, William James, Friedrich Nietzsche, Albert Einstein, Niels Bohr, and, more recently, Victoria DiMarco, John Searle, Suraj Manjunath, Jai Ramachandran, Michael He, Ted Honderich, and Daniel Dennett.

Mecca Chiesa notes that the probabilistic or selectionistic determinism of B.F. Skinner comprised a wholly separate conception of determinism that was not mechanistic at all.[10] Mechanistic determinism assumes that every event has an unbroken chain of prior occurrences, but a selectionistic or probabilistic model does not.[11][12]

In Eastern tradition

The idea that the entire universe is a deterministic system has been articulated in both Eastern and non-Eastern religion, philosophy, and literature.

A shifting flow of probabilities for futures lies at the heart of theories associated with the Yi Jing (or I Ching, the Book of Changes). Probabilities take the center of the stage away from things and people. A kind of "divine" volition sets the fundamental rules for the working out of probabilities in the universe, and human volitions are always a factor in the ways that humans can deal with the real world situations one encounters. If one's situation in life is surfing on a tsunami, one still has some range of choices even in that situation. One person might give up, and another person might choose to struggle and perhaps to survive. The Yi Jing mentality is much closer to the mentality of quantum physics than to that of classical physics, and also finds parallelism in voluntarist or Existentialist ideas of taking one's life as one's project.

The followers of the philosopher Mozi made some early discoveries in optics and other areas of physics, ideas that were consonant with deterministic ideas.

In the philosophical schools of India, the concept of precise and continual effect of laws of Karma on the existence of all sentient beings is analogous to western deterministic concept. Karma is the concept of "action" or "deed" in Indian religions. It is understood as that which causes the entire cycle of cause and effect (i.e., the cycle called saṃsāra) originating in ancient India and treated in Hindu, Jain, Sikh and Buddhist philosophies. Karma is considered predetermined and deterministic in the universe, with the exception of a human, who through free will can influence the future. See Karma in Hinduism.

In Western tradition

In the West, the Ancient Greek atomists Leucippus and Democritus were the first to anticipate determinism when they theorized that all processes in the world were due to the mechanical interplay of atoms, but this theory did not gain much support at the time. Determinism in the West is often associated with Newtonian physics, which depicts the physical matter of the universe as operating according to a set of fixed, knowable laws. The "billiard ball" hypothesis, a product of Newtonian physics, argues that once the initial conditions of the universe have been established, the rest of the history of the universe follows inevitably. If it were actually possible to have complete knowledge of physical matter and all of the laws governing that matter at any one time, then it would be theoretically possible to compute the time and place of every event that will ever occur (Laplace's demon). In this sense, the basic particles of the universe operate in the same fashion as the rolling balls on a billiard table, moving and striking each other in predictable ways to produce predictable results.

Whether or not it is all-encompassing in so doing, Newtonian mechanics deals only with caused events, e.g.: If an object begins in a known position and is hit dead on by an object with some known velocity, then it will be pushed straight toward another predictable point. If it goes somewhere else, the Newtonians argue, one must question one's measurements of the original position of the object, the exact direction of the striking object, gravitational or other fields that were inadvertently ignored, etc. Then, they maintain, repeated experiments and improvements in accuracy will always bring one's observations closer to the theoretically predicted results. When dealing with situations on an ordinary human scale, Newtonian physics has been so enormously successful that it has no competition. But it fails spectacularly as velocities become some substantial fraction of the speed of light and when interactions at the atomic scale are studied. Before the discovery of quantum effects and other challenges to Newtonian physics, "uncertainty" was always a term that applied to the accuracy of human knowledge about causes and effects, and not to the causes and effects themselves.

Newtonian mechanics as well as any following physical theories are results of observations and experiments, and so they describe "how it all works" within a tolerance. However, old western scientists believed if there are any logical connections found between an observed cause and effect, there must be also some absolute natural laws behind. Belief in perfect natural laws driving everything, instead of just describing what we should expect, led to searching for a set of universal simple laws that rule the world. This movement significantly encouraged deterministic views in western philosophy.[13]

Modern perspectives

In biology

Although it was once thought by scientists that any indeterminism in quantum mechanics occurred at too small a scale to influence biological or neurological systems, there is evidence that nervous systems are indeterministic,[14] and it has been argued that "[classical] physical determinism is out: the future is not fully determined by the current facts".[15]

Cause and effect

Since the early twentieth century when astronomer Edwin Hubble first hypothesized that redshift shows the universe is expanding, prevailing scientific opinion has been that the current state of the universe is the result of a process described by the Big Bang. Many theists and deists claim that it therefore has a finite age, pointing out that something cannot come from nothing. The big bang does not describe from where the compressed universe came; instead it leaves the question open. Different astrophysicists hold different views about precisely how the universe originated (Cosmogony). The philosophical argument here would be that the big bang triggered every single action, and possibly mental thought, through the system of cause and effect.

Generative processes

Some proponents of emergentist or generative philosophy, cognitive sciences and evolutionary psychology, argue that free will does not exist.[16][17] They suggest instead that an illusion of free will is experienced due to the generation of infinite behaviour from the interaction of finite-deterministic set of rules and parameters. Thus the unpredictability of the emerging behaviour from deterministic processes leads to a perception of free will, even though free will as an ontological entity does not exist.[16][17] Certain experiments looking at the Neuroscience of free will can be said to support this possibility.

As an illustration, the strategy board-games chess and Go have rigorous rules in which no information (such as cards' face-values) is hidden from either player and no random events (such as dice-rolling) happen within the game. Yet, chess and especially Go with its extremely simple deterministic rules, can still have an extremely large number of unpredictable moves. By this analogy, it is suggested, the experience of free will emerges from the interaction of finite rules and deterministic parameters that generate infinite and unpredictable behaviour. Yet, if all these events were accounted for, and there were a known way to evaluate these events, the seemingly unpredictable behaviour would become predictable.[16][17]

In mathematical models

Many mathematical models of physical systems are deterministic. This is true of most models involving differential equations (notably, those measuring rate of change over time). Mathematical models that are not deterministic because they involve randomness are called stochastic. Because of sensitive dependence on initial conditions, some deterministic models may appear to behave non-deterministically; in such cases, a deterministic interpretation of the model may not be useful due to numerical instability and a finite amount of precision in measurement. Such considerations can motivate the consideration of a stochastic model even though the underlying system is governed by deterministic equations.[18][19][20]

Arguments

Compatibilism is the acceptance of both Free Will and Determinism. The negation of determinism is called Indeterminism.

Quantum mechanics and classical physics

Since the beginning of the 20th century, quantum mechanics has revealed previously concealed aspects of events. Newtonian physics, taken in isolation rather than as an approximation to quantum mechanics, depicts a universe in which objects move in perfectly determinative ways. At human scale levels of interaction, Newtonian mechanics makes predictions that are agreed with, within the accuracy of measurement. Poorly designed and fabricated guns and ammunition scatter their shots rather widely around the center of a target, and better guns produce tighter patterns. Absolute knowledge of the forces accelerating a bullet should produce absolutely reliable predictions of its path, or so it was thought. However, knowledge is never absolute in practice and the equations of Newtonian mechanics can exhibit sensitive dependence on initial conditions, meaning small errors in knowledge of initial conditions can result in arbitrarily large deviations from predicted behavior.

At atomic scales the paths of objects can only be predicted in a probabilistic way. The paths may not be exactly specified in a full quantum description of the particles; "path" is a classical concept which quantum particles do not exactly possess. The probability arises from the measurement of the perceived path of the particle. In some cases, a quantum particle may trace an exact path, and the probability of finding the particles in that path is one. The quantum development is at least as predictable as the classical motion, but it describes wave functions that cannot be easily expressed in ordinary language. In double-slit experiments, photons are fired singly through a double-slit apparatus at a distant screen and do not arrive at a single point, nor do the photons arrive in a scattered pattern analogous to bullets fired by a fixed gun at a distant target. Instead, the light arrives in varying concentrations at widely separated points, and the distribution of its collisions with the target can be calculated reliably. In that sense the behavior of light in this apparatus is deterministic, but there is no way to predict where in the resulting interference pattern an individual photon will make its contribution (see Heisenberg Uncertainty Principle).

Some have argued[21] that, in addition to the conditions humans can observe and the laws we can deduce, there are hidden factors or "hidden variables" that determine absolutely in which order photons reach the detector screen. They argue that the course of the universe is absolutely determined, but that humans are screened from knowledge of the determinative factors. So, they say, it only appears that things proceed in a merely probabilistically determinative way. In actuality, they proceed in an absolutely deterministic way. Although matters are still subject to some measure of dispute, quantum mechanics makes statistical predictions which would be violated if some local hidden variables existed. There have been a number of experiments to verify those predictions, and so far they do not appear to be violated, though many physicists believe better experiments are needed to conclusively settle the question. (See Bell test experiments.) It is possible, however, to augment quantum mechanics with non-local hidden variables to achieve a deterministic theory that is in agreement with experiment. An example is the Bohm interpretation of quantum mechanics.

On the macro scale it can matter very much whether a bullet arrives at a specific point at a specific time; there are analogous quantum events that have macro- as well as quantum-level consequences. It is easy to contrive situations in which the arrival of an electron at a screen at a certain point and time would trigger one event and its arrival at another point would trigger an entirely different event. (See Schrödinger's cat.)

Chaotic radioactivity is the next explanatory challenge for physicists supporting determinism

All uranium found on earth is thought to have been synthesized during a supernova explosion that occurred roughly 5 billion years ago. Even before the laws of quantum mechanics were developed to their present level, the radioactivity of such elements has posed a challenge to determinism due to its unpredictability. One gram of uranium-238, a commonly occurring radioactive substance, contains some 2.5 x 1021 atoms. Each of these atoms are identical and indistinguishable according to all tests known to modern science. Yet about 12600 times a second, one of the atoms in that gram will decay, giving off an alpha particle. The challenge for determinism is to explain why and when decay occurs, since it does not seem to depend on external stimulus. Indeed, no extant theory of physics makes testable predictions of exactly when any given atom will decay.

The time dependent Schrödinger equation gives the first time derivative of the quantum state. That is, it explicitly and uniquely predicts the development of the wave function with time.

i\hbar\frac{\partial\psi(x,t)}{\partial t} = - \frac{\hbar^2}{2m} \frac{\partial^2\psi(x,t)}{\partial x^2}+V(x)\psi

So if the wave function itself is reality (rather than probability of classical coordinates), quantum mechanics can be said to be deterministic. Since we have no practical way of knowing the exact magnitudes, and especially the phases, in a full quantum mechanical description of the causes of an observable event, this turns out to be philosophically similar to the "hidden variable" doctrine.

According to some, quantum mechanics is more strongly ordered than Classical Mechanics, because while Classical Mechanics is chaotic, quantum mechanics is not. For example, the classical problem of three bodies under a force such as gravity is not integrable, while the quantum mechanical three body problem is tractable and integrable, using the Faddeev Equations. This does not mean that quantum mechanics describes the world as more deterministic, unless one already considers the wave function to be the true reality. Even so, this does not get rid of the probabilities, because we can't do anything without using classical descriptions, but it assigns the probabilities to the classical approximation, rather than to the quantum reality.

Asserting that quantum mechanics is deterministic by treating the wave function itself as reality implies a single wave function for the entire universe, starting at the origin of the universe. Such a "wave function of everything" would carry the probabilities of not just the world we know, but every other possible world that could have evolved. For example, large voids in the distributions of galaxies are believed by many cosmologists to have originated in quantum fluctuations during the big bang. (See cosmic inflation and primordial fluctuations.) If so, the "wave function of everything" would carry the possibility that the region where our Milky Way galaxy is located could have been a void and the Earth never existed at all. (See large-scale structure of the cosmos.)

First cause

Intrinsic to the debate concerning determinism is the issue of first cause. Deism, a philosophy articulated in the seventeenth century, holds that the universe has been deterministic since creation, but ascribes the creation to a metaphysical God or first cause outside of the chain of determinism. God may have begun the process, Deism argues, but God has not influenced its progression. This perspective illustrates a puzzle underlying any conception of determinism:

Assume: All events have causes, and their causes are all prior events. There is no cycle of events such that an event (possibly indirectly) causes itself.

The picture this gives us is that Event AN is preceded by AN-1, which is preceded by AN-2, and so forth.

Under these assumptions, two possibilities seem clear, and both of them question the validity of the original assumptions:

(1) There is an event A0 prior to which there was no other event that could serve as its cause.
(2) There is no event A0 prior to which there was no other event, which means that we are presented with an infinite series of causally related events, which is itself an event, and yet there is no cause for this infinite series of events.

Under this analysis the original assumption must have something wrong with it. It can be fixed by admitting one exception, a creation event (either the creation of the original event or events, or the creation of the infinite series of events) that is itself not a caused event in the sense of the word "caused" used in the formulation of the original assumption. Some agency, which many systems of thought call God, creates space, time, and the entities found in the universe by means of some process that is analogous to causation but is not causation as we know it. This solution to the original difficulty has led people to question whether there is any reason for there only being one divine quasi-causal act, whether there have not been a number of events that have occurred outside the ordinary sequence of events. Others argue that this is simply redefining the question.

Another possibility is that the "last event" loops back to the "first event" causing an infinite loop. If you were to call the Big Bang the first event, you would see the end of the Universe as the "last event". In theory, the end of the Universe would be the cause of the beginning of the Universe. You would be left with an infinite loop of time with no real beginning or end. This theory eliminates the need for a first cause, but does not explain why there should be a loop in time.

Immanuel Kant carried forth this idea of Leibniz in his idea of transcendental relations, and as a result, this had profound effects on later philosophical attempts to sort these issues out. His most influential immediate successor, a strong critic whose ideas were yet strongly influenced by Kant, was Edmund Husserl, the developer of the school of philosophy called phenomenology. But the central concern of that school was to elucidate not physics but the grounding of information that physicists and others regard as empirical. In an indirect way, this train of investigation appears to have contributed much to the philosophy of science called logical positivism and particularly to the thought of members of the Vienna Circle, all of which have had much to say, at least indirectly, about ideas of determinism.

See also

  • Genetic determinism
  • Ilya Prigogine
  • Interpretation of quantum mechanics
  • Neuroscience of free will
  • Open Theism
  • Philosophical interpretation of classical physics
  • Predestination
  • Radical behaviorism
  • Social determinism
  • Theological determinism
  • Technological Determinism
  • Voluntarism

Notes

  1. ↑ 1.0 1.1 http://plato.stanford.edu/entries/incompatibilism-arguments/
  2. ↑ Leucippus, Fragment 569 - from Fr. 2 Actius I, 25, 4
  3. ↑ Fischer, John Martin (1989) God, Foreknowledge and Freedom. Stanford, CA: Stanford University Press. ISBN 1-55786-857-3
  4. ↑ Watt, Montgomery (1948) Free-Will and Predestination in Early Islam. London:Luzac & Co.
  5. ↑ de Melo-Martín I (2005). "Firing up the nature/nurture controversy: bioethics and genetic determinism". J Med Ethics 31 (9): 526–30. doi:10.1136/jme.2004.008417. PMID 16131554. 
  6. ↑ Andrew, Sluyter. "Neo-Environmental Determinism, Intellectual Damage Control, and Nature/Society Science". Antipode 4 (35). 
  7. ↑ J. J. C. Smart, "Free-Will, Praise and Blame,"Mind, July 1961, p.293-4.
  8. ↑ By 'soul' in the context of (1) is meant an autonomous immaterial agent that has the power to control the body but not to be controlled by the body (this theory of determinism thus conceives of conscious agents in dualistic terms). Therefore the soul stands to the activities of the individual agent's body as does the creator of the universe to the universe. The creator of the universe put in motion a deterministic system of material entities that would, if left to themselves, carry out the chain of events determined by ordinary causation. But the creator also provided for souls that could exert a causal force analogous to the primordial causal force and alter outcomes in the physical universe via the acts of their bodies. Thus, it emerges that no events in the physical universe are uncaused. Some are caused entirely by the original creative act and the way it plays itself out through time, and some are caused by the acts of created souls. But those created souls were not created by means of physical processes involving ordinary causation. They are another order of being entirely, gifted with the power to modify the original creation. However, determinism is not necessarily limited to matter; it can encompass energy as well. The question of how these immaterial entities can act upon material entities is deeply involved in what is generally known as the mind-body problem. It is a significant problem which philosophers have not reached agreement about
  9. ↑ Free Will (Stanford Encyclopedia of Philosophy)
  10. ↑ Chiesa, Mecca (2004) Radical Behaviorism: The Philosophy & The Science.
  11. ↑ ibid
  12. ↑ Ringen, J. D. (1993). Adaptation, teleology, and selection by consequences. Journal of Applied Behavior Analysis. 60,3–15. [1]
  13. ↑ Swartz, Norman (2003) The Concept of Physical Law / Chapter 10: Free Will and Determinism ( http://www.sfu.ca/philosophy/physical-law/)
  14. ↑ Lewis, E.R.; MacGregor, R.J. (2006). "On Indeterminism, Chaos, and Small Number Particle Systems in the Brain". Journal of Integrative Neuroscience 5: 223–247. doi:10.1142/S0219635206001112. http://www.eecs.berkeley.edu/~lewis/LewisMacGregor.pdf. 
  15. ↑ Koch, Christof (September 2009). "Free Will, Physics, Biology and the Brain". In Murphy, Nancy; Ellis, George; O'Connor, Timothy. Downward Causation and the Neurobiology of Free Will. New York, USA: Springer. ISBN 978-3642032042. 
  16. ↑ 16.0 16.1 16.2 Kenrick, D. T., Li, N. P., & Butner, J. 2003; Nowak A., Vallacher R.R., Tesser A., Borkowski W., 2000;
  17. ↑ 17.0 17.1 17.2 Epstein J.M. and Axtell R. 1996; Epstein J.M. 1999
  18. ↑ Werndl, Charlotte (2009). Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?. Studies in History and Philosophy of Modern Physics 40, 232-242.
  19. ↑ Werndl, Charlotte (2009). Deterministic Versus Indeterministic Descriptions: Not That Different After All?. In: A. Hieke and H. Leitgeb (eds), Reduction, Abstraction, Analysis, Proceedings of the 31st International Ludwig Wittgenstein-Symposium. Ontos, 63-78.
  20. ↑ J. Glimm, D. Sharp, Stochastic Differential Equations: Selected Applications in Continuum Physics, in: R.A. Carmona, B. Rozovskii (ed.) Stochastic Partial Differential Equations: Six Perspectives, American Mathematical Society (October 1998) (ISBN 0-8218-0806-0).
  21. ↑ Albert Einstein insisted that, "I am convinced God does not play dice" in a private letter to Max Born, 4 December 1926, Albert Einstein Archives reel 8, item 180

References and bibliography

External links