formulasearchengine - User contributions [en]

P–n diode

2015-01-08T07:09:40Z

117.214.209.188: /* Forward bias */

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Schmitt trigger

2014-01-26T11:47:04Z

117.214.245.102: /* Fundamental idea */

In [[mathematics]], there is an ample supply of [[duality of categories|categorical dualities]] between certain [[category theory|categories]] of [[topological space]]s and categories of [[partially ordered set]]s. Today, these dualities are usually collected under the label '''Stone duality''', since they form a natural generalization of [[Stone's representation theorem for Boolean algebras]]. These concepts are named in honor of [[Marshall Stone]]. Stone-type dualities also provide the foundation for [[pointless topology]] and are exploited in [[theoretical computer science]] for the study of [[Semantics of programming languages|formal semantics]].

This article gives pointers to special cases of Stone duality and explains a very general instance thereof in detail.

==Overview of Stone-type dualities==
Probably the most general duality which is classically referred to as "Stone duality" is the duality between the category '''Sob''' of [[sober space]]s with [[continuous function]]s and the category '''SFrm''' of spatial [[complete Heyting algebra|frames]] with appropriate frame homomorphisms. The [[dual (category theory)|dual category]] of '''SFrm''' is the category of [[complete Heyting algebra|locales]] denoted by '''SLoc'''. The [[equivalence of categories|categorical equivalence]] of '''Sob''' and '''SLoc''' is the basis for the mathematical area of [[pointless topology]], that is devoted to the study of '''Loc''' – the category of all locales of which '''SLoc''' is a full subcategory. The involved constructions are characteristic for this kind of duality, and are detailed below.

Now one can easily obtain a number of other dualities by restricting to certain special classes of sober spaces:

* The category '''CohSp''' of [[coherent space|coherent]] sober spaces (and coherent maps) is equivalent to the category '''CohLoc''' of [[coherent locale|coherent (or spectral) locales]] (and coherent maps), on the assumption of the [[Boolean prime ideal theorem]] (in fact, this statement is equivalent to that assumption). The significance of this result stems from the fact that '''CohLoc''' in turn is dual to the category '''DLat''' of [[distributivity (order theory)|distributive]] [[lattice (order)|lattices]]. Hence, '''DLat''' is dual to '''CohSp''' – one obtains [[Stone's representation theorem for distributive lattices]].

* When restricting further to coherent sober spaces which are [[Hausdorff space|Hausdorff]], one obtains the category '''Stone''' of so-called [[Stone space]]s. On the side of '''DLat''', the restriction yields the subcategory '''Bool''' of [[Boolean algebra (structure)|Boolean algebras]]. Thus one obtains [[Stone's representation theorem for Boolean algebras]].

* Stone's representation for distributive lattices can be extended via an equivalence of coherent spaces and [[Priestley space]]s (ordered topological spaces, that are [[compact space|compact]] and totally order-disconnected). One obtains a representation of distributive lattices via ordered topologies: [[Priestley's representation theorem for distributive lattice]]s.

Many other Stone-type dualities could be added to these basic dualities.

== Duality of sober spaces and spatial locales ==
This section motivates and explains one of the most basic constructions of Stone duality: the duality between topological spaces which are ''sober'' and frames (i.e. [[complete Heyting algebra]]s) which are ''spatial''. This classical piece of mathematics requires a substantial amount of abstraction that usually tends to puzzle beginners. It should therefore be considered as graduate level mathematics. Some prior exposure to the basics of [[category theory]] is recommended, although a deep understanding of the concepts of adjunction and duality may well arise from examples such as the result below. Furthermore, concepts of [[topology]] and [[order theory]] are naturally involved as well, where the latter is probably more important for a thorough understanding.

=== The lattice of open sets ===
The starting point for the theory is the fact that every topological space is characterized by a set of points ''X'' and a system Ω(''X'') of [[open set]]s of elements from ''X'', i.e. a subset of the [[powerset]] of ''X''. It is known that Ω(''X'') has certain special properties: it is a [[complete lattice]] within which [[supremum|suprema]] and finite [[infimum|infima]] are given by set unions and finite set intersections, respectively. Furthermore, it contains both ''X'' and the [[empty set]]. Since the [[order embedding|embedding]] of Ω(''X'') into the powerset lattice of ''X'' [[limit preserving (order theory)|preserves]] finite infima and arbitrary suprema, Ω(''X'') inherits the following distributivity law:

:<math>x \wedge \bigvee S = \bigvee \{\, x \wedge s : s \in S \,\}, </math>

for every element (open set) ''x'' and every subset ''S'' of Ω(''X''). Hence Ω(''X'') is not an arbitrary complete lattice but a ''complete Heyting algebra'' (also called ''frame'' or ''locale'' – the various names are primarily used to distinguish several categories that have the same class of objects but different morphisms: frame morphisms, locale morphisms and homomorphisms of complete Heyting algebras). Now an obvious question is: To what extent is a topological space characterized by its locale of open sets?

As already hinted at above, one can go even further. The category '''Top''' of topological spaces has as morphisms the continuous functions, where a function ''f'' is continuous if the [[inverse image]] ''f'' −1(''O'') of any open set in the [[codomain]] of ''f'' is open in the [[domain of a function|domain]] of ''f''. Thus any continuous function ''f'' from a space ''X'' to a space ''Y'' defines an inverse mapping ''f'' −1 from Ω(''Y'') to Ω(''X''). Furthermore, it is easy to check that ''f'' −1 (like any inverse image map) preserves finite intersections and arbitrary unions and therefore is a ''morphism of frames''. If we define Ω(''f'') = ''f'' −1 then Ω becomes a [[contravariant functor]] from the category '''Top''' to the category '''Frm''' of frames and frame morphisms. Using the tools of category theory, the task of finding a characterization of topological spaces in terms of their open set lattices is equivalent to finding a functor from '''Frm''' to '''Top''' which is [[adjoint functors|adjoint]] to Ω.

=== Points of a locale ===
The goal of this section is to define a functor pt from '''Frm''' to '''Top''' that in a certain sense "inverts" the operation of Ω by assigning to each locale ''L'' a set of points pt(''L'') (hence the notation pt) with a suitable topology. But how can we recover the set of points just from the locale, though it is not given as a lattice of sets? It is certain that one cannot expect in general that pt can reproduce all of the original elements of a topological space just from its lattice of open sets – for example all sets with the [[indiscrete topology]] yield (up to isomorphism) the same locale, such that the information on the specific set is no longer present. However, there is still a reasonable technique for obtaining "points" from a locale, which indeed gives an example of a central construction for Stone-type duality theorems.

Let us first look at the points of a topological space ''X''. One is usually tempted to consider a point of ''X'' as an element ''x'' of the set ''X'', but there is in fact a more useful description for our current investigation. Any point ''x'' gives rise to a continuous function ''p''''x'' from the one element topological space 1 (all subsets of which are open) to the space ''X'' by defining ''p''''x''(1) = ''x''. Conversely, any function from 1 to ''X'' clearly determines one point: the element that it "points" to. Therefore the set of points of a topological space is equivalently characterized as the set of functions from 1 to ''X''.

When using the functor Ω to pass from '''Top''' to '''Frm''', all set-theoretic elements of a space are lost, but – using a fundamental idea of category theory – one can as well work on the [[function space]]s. Indeed, any "point" ''p''''x'': 1 → ''X'' in '''Top''' is mapped to a morphism Ω(''p''''x''): Ω(''X'') → Ω(1). The open set lattice of the one-element topological space Ω(1) is just (isomorphic to) the two-element locale 2 = { 0, 1 } with 0 < 1. After these observations it appears reasonable to define the set of points of a locale ''L'' to be the set of frame morphisms from ''L'' to 2. Yet, there is no guarantee that every point of the locale Ω(''X'') is in one-to-one correspondence to a point of the topological space ''X'' (consider again the indiscrete topology, for which the open set lattice has only one "point").

Before defining the required topology on pt(''X''), it is worthwhile to clarify the concept of a point of a locale further. The perspective motivated above suggests to consider a point of a locale ''L'' as a frame morphism ''p'' from ''L'' to 2. But these morphisms are characterized equivalently by the inverse images of the two elements of 2. From the properties of frame morphisms, one can derive that ''p'' −1(0) is a lower set (since ''p'' is [[monotone]]), which contains a greatest element ''a''''p'' = V ''p'' −1(0) (since ''p'' preserves arbitrary suprema). In addition, the [[ideal (order theory)|principal ideal]] ''p'' −1(0) is a [[ideal (order theory)|prime ideal]] since ''p'' preserves finite infima and thus the principal ''a''''p'' is a [[prime (order theroy)|meet-prime element]]. Now the set-inverse of ''p'' −1(0) given by ''p'' −1(1) is a [[filter (mathematics)|completely prime filter]] because ''p'' −1(0) is a principal prime ideal. It turns out that all of these descriptions uniquely determine the initial frame morphism. We sum up:

A point of a locale ''L'' is equivalently described as:
* a frame morphism from ''L'' to 2
* a principal prime ideal of ''L''
* a meet-prime element of ''L''
* a completely prime filter of ''L''.

All of these descriptions have their place within the theory and it is convenient to switch between them as needed.

=== The functor pt ===
Now that a set of points is available for any locale, it remains to equip this set with an appropriate topology in order to define the object part of the functor pt. This is done by defining the open sets of pt(''L'') as

:φ(''a'') = { ''p'' ∈ pt(''L'') | ''p''(''a'') = 1 },

for every element ''a'' of ''L''. Here we viewed the points of ''L'' as morphisms, but one can of course state a similar definition for all of the other equivalent characterizations. It can be shown that setting Ω(pt(''L'')) = {φ(''a'') | ''a'' ∈ ''L''} does really yield a topological space (pt(''L''), Ω(pt(''L''))). It is common to abbreviate this space as pt(''L'').

Finally pt can be defined on morphisms of '''Frm''' rather canonically by defining, for a frame morphism ''g'' from ''L'' to ''M'', pt(''g''): pt(''M'') → pt(''L'') as pt(''g'')(''p'') = ''p'' o ''g''. In words, we obtain a morphism from ''L'' to 2 (a point of ''L'') by applying the morphism ''g'' to get from ''L'' to ''M'' before applying the morphism ''p'' that maps from ''M'' to 2. Again, this can be formalized using the other descriptions of points of a locale as well – for example just calculate (''p'' o ''g'') −1(0).

=== The adjunction of Top and Loc===
As noted several times before, pt and Ω usually are not inverses. In general neither is ''X'' [[homeomorphism|homeomorphic]] to pt(Ω(''X'')) nor is ''L'' [[order isomorphism|order-isomorphic]] to Ω(pt(''L'')). However, when introducing the topology of pt(''L'') above, a mapping φ from ''L'' to Ω(pt(''L'')) was applied. This mapping is indeed a frame morphism. Conversely, we can define a continuous function ψ from ''X'' to pt(Ω(''X'')) by setting ψ(''x'') = Ω(''p''''x''), where ''p''''x'' is just the characteristic function for the point ''x'' from 1 to ''X'' as described above. Another convenient description is given by viewing points of a locale as meet-prime elements. In this case we have ψ(''x'') = ''X'' \ Cl{''x''}, where Cl{''x''} denotes the topological closure of the set {''x''} and \ is just set-difference.

At this point we already have more than enough data to obtain the desired result: the functors Ω and pt define an adjunction between the categories '''Top''' and '''Loc''' = '''Frm'''op, where pt is right adjoint to Ω and the [[natural transformation]]s ψ and φop provide the required unit and counit, respectively.

=== The duality theorem ===
The above adjunction is not an equivalence of the categories '''Top''' and '''Loc''' (or, equivalently, a duality of '''Top''' and '''Frm'''). For this it is necessary that both ψ and φ are isomorphisms in their respective categories.

For a space ''X'', ψ: ''X'' → pt(Ω(''X'')) is a homeomorphism [[if and only if]] it is [[bijective]]. Using the characterization via meet-prime elements of the open set lattice, one sees that this is the case if and only if every meet-prime open set is of the form ''X'' \ Cl{''x''} for a unique ''x''. Alternatively, every join-prime closed set is the closure of a unique point, where "join-prime" can be replaced by [[irreducible (order theory)|(join-) irreducible]] since we are in a distributive lattice. Spaces with this property are called '''sober'''.

Conversely, for a locale ''L'', φ: ''L'' → Ω(pt(''L'')) is always surjective. It is additionally injective if and only if any two elements ''a'' and ''b'' of ''L'' for which ''a'' is not less-or-equal to ''b'' can be separated by points of the locale, formally:

: if not ''a'' ≤ ''b'', then there is a point ''p'' in pt(''L'') such that p(''a'') = 1 and p(''b'') = 0.

If this condition is satisfied for all elements of the locale, then the locale is '''spatial''', or said to have enough points. (See also [[well-pointed category]] for a similar condition in more general categories.)

Finally, one can verify that for every space ''X'', Ω(''X'') is spatial and for every locale ''L'', pt(''L'') is sober. Hence, it follows that the above adjunction of '''Top''' and '''Loc''' restricts to an equivalence of the full subcategories '''Sob''' of sober spaces and '''SLoc''' of spatial locales. This main result is completed by the observation that for the functor pt o Ω, sending each space to the points of its open set lattice is right adjoint to the [[inclusion functor]] from '''Sob''' to '''Top'''. For a space ''X'', pt(Ω(''X'')) is called its '''soberification'''. The case of the functor Ω o pt is symmetric but a special name for this operation is not commonly used.

==References==
* Burris, Stanley N., and H.P. Sankappanavar, H. P., 1981. ''[http://www.thoralf.uwaterloo.ca/htdocs/ualg.html A Course in Universal Algebra.]'' [[Springer-Verlag]]. ISBN 3-540-90578-2. (available free online at the website mentioned)
* P. T. Johnstone, ''Stone Spaces'', Cambridge Studies in Advanced Mathematics 3, [[Cambridge University Press]], Cambridge, 1982. ISBN 0-521-23893-5.
* {{cite book | editor1-last=Pedicchio | editor1-first=Maria Cristina | editor2-last=Tholen | editor2-first=Walter | title=Categorical foundations. Special topics in order, topology, algebra, and sheaf theory | series=Encyclopedia of Mathematics and Its Applications | volume=97 | location=Cambridge | publisher=[[Cambridge University Press]] | year=2004 | isbn=0-521-83414-7 | zbl=1034.18001 }}
* {{cite book | last=Vickers | first=Steven | authorlink=Steve Vickers (computer scientist) | title=Topology via logic | series=Cambridge Tracts in Theoretical Computer Science | volume=5 | location=Cambridge | publisher=[[Cambridge University Press]] | year=1989 | isbn=0-521-36062-5 | zbl=0668.54001 }}
* [http://paultaylor.eu/ASD/ Abstract Stone Duality]

[[Category:Topology]]
[[Category:Order theory]]
[[Category:Duality theories]]

Data stream

2014-01-25T18:39:15Z

117.214.96.109: /* Formal definition */

{{pp-protected|expiry=2014-02-27 15:46:56|small=yes}}{{About|the general notion of determinism in philosophy}}
{{Distinguish|Fatalism|Predeterminism|Predictability|Theological determinism}}
{{Certainty}}

'''Determinism''' is the philosophical position that for every event exist conditions that could cause no other event. "There are many determinisms, depending upon what pre-conditions are considered to be determinative of an event."<ref name=Doyle>A list of a dozen varieties of determinism is provided in {{cite book |title=Free Will: The Scandal in Philosophy |author=Bob Doyle |pages=145–146 ''ff'' |isbn=0983580200 |year=2011 |publisher=I-Phi Press |url=http://books.google.com/books?id=SeA_gFfHMgoC&pg=PA145}}</ref> Deterministic theories throughout the history of philosophy have sprung from diverse and sometimes overlapping motives and considerations. Some forms of determinism can be [[empirically]] tested with ideas from physics and its [[philosophy of physics|philosophy]]. Opposing determinism is some kind of [[indeterminism]] (otherwise called ''nondeterminism''). Determinism is often contrasted with [[free will]].<ref name=Franklin>For example, see {{cite book |title=Freewill and determinism: a study of rival conceptions of man |author=Richard Langdon Franklin |year=1968 |publisher=Routledge & K. Paul |url=http://books.google.com/books?id=51wIAQAAIAAJ}}</ref>

Determinism often is taken to mean ''causal determinism,' which in physics is known as cause-and-effect. It is the concept that [[Event (philosophy)|event]]s within a given [[paradigm]] are so [[causality|causally]] bound that prior states of any object or event completely determine its later states. This meaning can be distinguished from other varieties of determinism mentioned below.

Other debates often concern the scope of determined systems, with some maintaining that the entire universe is a single determinate system and others identifying other more limited determinate systems (or [[multiverse]]). Numerous historical debates involve many philosophical positions and varieties of determinism, some concerning determinism and [[free will]], technically denoted as [[compatibilistic]] (allowing the two to coexist) and [[incompatibilistic]] (denying their coexistence is a possibility).

Determinism should not be confused with [[Self-determination (philosophy)|self-determination]] of human actions by reasons, motives, and desires. Determinism rarely requires that perfect [[prediction]] be practically possible.

==Varieties==
{{Expert-subject|Philosophy|date=July 2011}}
Below appear some of the more common viewpoints meant by, or confused with "determinism".

[[File:Willow path.jpg|thumb|right|140px|Many philosophical theories of determinism frame themselves with the idea that reality follows a sort of predetermined path]]

* Causal determinism is "the idea that every event is necessitated by antecedent events and conditions together with the laws of nature".<ref name=stanfordcausaldeterminism>{{cite encyclopedia|last=Hoefer |first=Carl | title=Causal Determinism | encyclopedia=The Stanford Encyclopedia of Philosophy (Winter 2009 edition) |date=Apr 1, 2008 |editor=Edward N. Zalta, ed |url=http://plato.stanford.edu/archives/win2009/entries/determinism-causal/}}</ref> However, causal determinism is a broad enough term to consider that "one's deliberations, choices, and actions will often be necessary links in the causal chain that brings something about. In other words, even though our deliberations, choices, and actions are themselves determined like everything else, it is still the case, according to causal determinism, that the occurrence or existence of yet other things depends upon our deliberating, choosing and acting in a certain way".<ref name=stanfordmoralresponsibility>{{cite encyclopedia|last=Eshleman |first=Andrew |editor=Edward N. Zalta, ed |title=Moral Responsibility | encyclopedia=The Stanford Encyclopedia of Philosophy| edition=Winter 2009 |date=Nov 18, 2009 | url=http://plato.stanford.edu/archives/win2012/entries/moral-responsibility/}}</ref> Causal determinism proposes that there is an unbroken chain of prior occurrences stretching back to the origin of the universe. The relation between events may not be specified, nor the origin of that universe. Causal determinists believe that there is nothing uncaused or [[causa sui|self-caused]]. [[Historical determinism]] (a sort of [[path dependence]]) can also be synonymous with causal determinism. - Causal determinism has also been considered more generally as the idea that everything that happens or exists is caused by antecedent conditions.<ref name=StanfordIncompatibilism>[http://plato.stanford.edu/entries/incompatibilism-arguments/ Arguments for Incompatibilism (Stanford Encyclopedia of Philosophy)]</ref> In the case of nomological determinism, these conditions are considered events also, implying that the future is determined completely by preceding events - a combination of prior states of the universe and the laws of nature.<ref name=stanfordcausaldeterminism>{{cite encyclopedia|last=Hoefer |first=Carl |editor=Edward N. Zalta | title=Causal Determinism | encyclopedia=The Stanford Encyclopedia of Philosophy| edition=Spring 2010 | year=2010 | url=http://plato.stanford.edu/archives/win2009/entries/moral-responsibility}}</ref> Yet they can also be considered metaphysical of origin (such as in the case of theological determinism).<ref name=stanfordmoralresponsibility />

** [[Nomological determinism]] is the most common form of causal determinism. It is the notion that the past and the present dictate the future entirely and necessarily by rigid natural laws, that every occurrence results inevitably from prior events. [[Quantum mechanics]] and various [[interpretations of quantum mechanics|interpretations]] thereof pose a serious challenge to this view. Nomological determinism is sometimes illustrated by the [[thought experiment]] of [[Laplace's demon]].<ref name=laplace>
[[Laplace]] posited that an omniscient observer knowing with infinite precision all the positions and velocities of every particle in the universe could predict the future entirely. For a discussion, see {{cite book |title=The Big Questions: A Short Introduction to Philosophy |author=Robert C. Solomon, Kathleen M. Higgins |url=http://books.google.com/books?id=ekh2AKqXdqgC&pg=PA232 |page=232 |isbn=0495595152 |publisher=Cengage Learning |chapter=Free will and determinism|year=2009 |edition=8th}} Another view of determinism is discussed by {{cite book |title=The Structure of Science: Problems in the Logic of Scientific Explanation |author=Ernest Nagel |url=http://books.google.com/books?id=u6EycHgRfkQC&pg=PA285 |pages =285–292 |chapter=§V: Alternative descriptions of physical state |quote=a theory is deterministic if, and only if, given its state variables for some initial period, the theory logically determines a unique set of values for those variables for any other period. |isbn=0915144719 |year=1999 |publisher=Hackett |edition=2nd }}
</ref> Nomological determinism is sometimes called 'scientific' determinism, although that is a misnomer. [[Physical determinism]] is generally used synonymously with nomological determinism (its opposite being [[Indeterminism|physical indeterminism]]).

** [[Necessitarianism]] is very related to the causal determinism described above. It is a [[Metaphysics|metaphysical]] principle that denies all mere possibility; there is exactly one way for the world to be. [[Leucippus]] claimed there were no uncaused events, and that everything occurs for a reason and by necessity.<ref>Leucippus, Fragment 569 - from Fr. 2 Actius I, 25, 4</ref>

* [[Predeterminism]] is the idea that all events are determined in advance.<ref name="McKewan">{{cite encyclopedia |last=McKewan |first=Jaclyn |editor=H. James Birx"|encyclopedia=Encyclopedia of Time: Science, Philosophy, Theology, & Culture |title=Predeterminism |url=http://dx.doi.org/10.4135/9781412963961.n191 |accessdate=20 December 2012 |year=2009 |publisher=SAGE Publications, Inc. |doi=10.4135/9781412963961.n191 |pages=1035–1036}}</ref><ref>{{cite encyclopedia |encyclopedia=Oxford Dictionaries |title=Predeterminism |url=http://oxforddictionaries.com/definition/english/predeterminism |accessdate=20 December 2012 |date=April 2010 |publisher=Oxford Dictionaries}}. See also {{cite encyclopedia |encyclopedia=Collins English Dictionary |title=Predeterminism |url=http://www.collinsdictionary.com/dictionary/english/predeterminism |accessdate=20 December 2012 |publisher=Collins}}</ref> The concept of predeterminism is often argued by invoking causal determinism, implying that there is an unbroken [[chain of prior occurrences]] stretching back to the origin of the universe. In the case of predeterminism, this chain of events has been pre-established, and human actions cannot interfere with the outcomes of this pre-established chain. Predeterminism can be used to mean such pre-established causal determinism, in which case it is categorised as a specific type of determinism.<ref name="McKewan" /><ref>{{cite web |url=http://philosophy.lander.edu/ethics/notes-determinism.html |title=Some Varieties of Free Will and Determinism |author= |date=09.10.09 |work=Philosophy 302: Ethics |publisher=philosophy.lander.edu |accessdate=19 December 2012| quote=Predeterminism: the philosophical and theological view that combines God with determinism. On this doctrine events throughout eternity have been foreordained by some supernatural power in a causal sequence.}}</ref> It can also be used interchangeably with causal determinism - in the context of its capacity to determine future events.<ref name="McKewan" /><ref>See for example {{cite journal |author=Hooft, G. |title=How does god play dice? (Pre-)determinism at the Planck scale |quote=Predeterminism is here defined by the assumption that the experimenter's 'free will' in deciding what to measure (such as his choice to measure the x- or the y-component of an electron's spin), is in fact limited by deterministic laws, hence not free at all |journal=arXiv preprint hep-th/0104219 |year=2001}}, and {{cite journal |author=Sukumar, CV |title=A new paradigm for science and architecture |quote=Quantum Theory provided a beautiful description of the behaviour of isolated atoms and nuclei and small aggregates of elementary particles. Modern science recognized that predisposition rather than predeterminism is what is widely prevalent in nature. |journal=City |volume=1 |issue=1-2 |pages=181–183 |year=1996| publisher=Taylor & Francis}}</ref> Despite this, predeterminism is often considered as independent of causal determinism.<ref>{{cite journal |author=Borst, C. |title=Leibniz and the compatibilist account of free will |quote=Leibniz presents a clear case of a philosopher who does not think that predeterminism requires universal causal determinism |journal=Studia leibnitiana |pages=49-58 |year=1992 |publisher=JSTOR}}</ref><ref name=Society1971>{{cite book|author=Far Western Philosophy of Education Society|title=Proceedings of the Annual Meeting of the Far Western Philosophy of Education Society|url=http://books.google.com/books?id=spkpAQAAMAAJ|accessdate=20 December 2012|year=1971|publisher=Far Western Philosophy of Education Society.|page=12|quote="Determinism" is, in essence, the position which holds that all behavior is caused by prior behavior. "Predeterminism" is the position which holds that all behavior is caused by conditions which predate behavior altogether (such impersonal boundaries as "the human conditions," instincts, the will of God, inherent knowledge, fate, and such).}}</ref> The term predeterminism is also frequently used in the context of biology and hereditary, in which case it represents a form of [[biological determinism]].<ref>{{cite encyclopedia |encyclopedia=Merriam-Webster Dictionary |title=Predeterminism |url=http://www.merriam-webster.com/dictionary/predeterminism |accessdate=20 December 2012 |publisher=Merriam-Webster, Incorporated}} See for example {{cite journal |author=Ormond, A.T. |title=Freedom and psycho-genesis |quote=The problem of predeterminism is one that involves the factors of heredity and environment, and the point to be debated here is the relation of the present self that chooses to these predetermining agencies |journal=Psychological Review |volume=1 |issue=3 |pages=217 |year=1894 |publisher=Macmillan & Company}}, and {{cite journal |author=Garris, M.D. and others |title=A Platform for Evolving Genetic Automata for Text Segmentation (GNATS) |quote=However, predeterminism is not completely avoided. If the codes within the genotype are not designed properly, then the organisms being evolved will be fundamentally handicapped. |journal=Science of Artificial Neural Networks |volume=1710 |pages=714–724 |year=1992| publisher=Citeseer}}</ref>

* [[Fatalism]] is normally distinguished from "determinism".<ref name=SEPDeterminism>[http://plato.stanford.edu/entries/determinism-causal/ SEP, Causal Determinism]</ref> Fatalism is the idea that everything is fated to happen, so that humans have no control over their future. [[Fate]] has arbitrary power, and need not follow any causal or otherwise deterministic [[law]]s.<ref name=StanfordIncompatibilism>[http://plato.stanford.edu/entries/incompatibilism-arguments/ Arguments for Incompatibilism (Stanford Encyclopedia of Philosophy)]</ref> Types of Fatalism include hard [[theological determinism]] and the idea of [[predestination]], where there is a [[God]] who determines all that humans will do. This may be accomplished either by knowing their actions in advance, via some form of [[omniscience]]<ref name = "Fischer">Fischer, John Martin (1989) ''God, Foreknowledge and Freedom''. Stanford, CA: Stanford University Press. ISBN 1-55786-857-3</ref> or by decreeing their actions in advance.<ref name="Watt">Watt, Montgomery (1948) ''Free-Will and Predestination in Early Islam''. London:Luzac & Co.</ref>

* [[Theological determinism]] is a form of determinism which states that all events that happen are pre-ordained, or [[predestination|predestined]] to happen, by a [[monotheism|monotheistic]] [[deity]], or that they are [[destiny|destined]] to occur given its [[omniscience]]. Two forms of theological determinism exist, here referenced as strong and weak theological determinism.<ref name=JordanTate2004>{{cite book|author1=Anne Lockyer Jordan|author2=Anne Lockyer Jordan Neil Lockyer Edwin Tate|author3=Neil Lockyer|coauthors=Edwin Tate|title=Philosophy of Religion for A Level OCR Edition|url=http://books.google.com/books?id=uBVuNip8qjkC|accessdate=22 December 2012|date=25 June 2004|publisher=Nelson Thornes|isbn=978-0-7487-8078-5|page=211}}</ref> The first one, strong theological determinism, is based on the concept of a [[creator deity]] dictating all events in history: "everything that happens has been predestined to happen by an omniscient, omnipotent divinity".<ref name=Iannone2001>{{cite book|author=A. Pabl Iannone|title=Dictionary of World Philosophy|url=http://books.google.com/books?id=7wBmBO3vpE4C|accessdate=22 December 2012|year=2001|publisher=Taylor & Francis|isbn=978-0-415-17995-9|page=194|chapter=determinism|quote=theological determinism, or the doctrine of predestination: the view that everything which happens has been predestined to happen by an omniscient, omnipotent divinity. A weaker version holds that, though not predestined to happen, everything that happens has been eternally known by virtue of the divine foreknowledge of an omniscient divinity. If this divinity is also omnipotent, as in the case of the Judeo-Christian religions, this weaker version is hard to distinguish from the previous one because, though able to prevent what happens and knowing that it is going to happen, God lets it happen. To this, advocates of free will reply that God permits it to happen in order to make room for the free will of humans.}}</ref> The second form, weak theological determinism, is based on the concept of divine foreknowledge - "because [[God]]'s omniscience is perfect, what God knows about the future will inevitably happen, which means, consequently, that the future is already fixed".<ref name=Huyssteen2003>{{cite book|author=Wentzel Van Huyssteen|title=Encyclopedia of science and religion|url=http://books.google.com/books?id=HIcYAAAAIAAJ|accessdate=22 December 2012|volume=1|year=2003|publisher=Macmillan Reference|isbn=978-0-02-865705-9|page=217|chapter=theological determinism|quote=Theological determinism constitutes a fifth kind of determinism. There are two types of theological determinism, both compatible with scientific and metaphysical determinism. In the first, God determines everything that happens, either in one all-determining single act at the initial creation of the universe or through continuous divine interactions with the world. Either way, the consequence is that everything that happens becomes God's action, and determinism is closely linked to divine action and God's omnipotence. According to the second type of theological determinism, God has perfect knowledge of everything in the universe because God is omniscient. And, as some say, because God is outside of time, God has the capacity of knowing past, present, and future in one instance. This means that God knows what will happen in the future. And because God's omniscience is perfect, what God knows about the future will inevitably happen, which means, consequently, that the future is already fixed.}}</ref> There exist slight variations on the above categorisation. Some claim that theological determinism requires [[predestination]] of all events and outcomes by the divinity (i.e. they do not classify the weaker version as 'theological determinism' unless libertarian free will is assumed to be denied as a consequence), or that the weaker version does not constitute 'theological determinism' at all.<ref name=VanArragon2010>{{cite book|author=Raymond J. VanArragon|title=Key Terms in Philosophy of Religion|url=http://books.google.com/books?id=JyTohO1AMzwC|accessdate=22 December 2012|date=21 October 2010|publisher=Continuum International Publishing Group|isbn=978-1-4411-3867-5|page=21|quote=Theological determinism, on the other hand, claims that all events are determined by God. On this view, God decree that everything will go thus-and-so and ensure that everything goes that way, so that ultimately God is the cause of everything that happens and everything that happens is part of God's plan. We might think of God here as the all-powerful movie director who writes script and causes everything to go accord with it. We should note, as an aside, that there is some debate over what would be sufficient for theological determinism to be true. Some people claim that God's merely knowing what will happen determines that it will, while others believe that God must not only know but must also cause those events to occur in order for their occurrence to be determined.}}</ref> With respect to free will, "theological determinism is the thesis that God exists and has infallible knowledge of all true propositions including propositions about our future actions", more minimal criteria designed to encapsulate all forms of theological determinism.<ref name=stanfordincompatibilismarguments>{{cite encyclopedia|last=Vihvelin |first=Kadri |editor=Edward N. Zalta | title=Arguments for Incompatibilism | encyclopedia=The Stanford Encyclopedia of Philosophy| edition=Spring 2011 | year=2011 | url=http://plato.stanford.edu/archives/spr2011/entries/incompatibilism-arguments}}</ref> Theological determinism can also be seen as a form of causal determinism, in which the antecedent conditions are the nature and will of God.<ref name=stanfordmoralresponsibility>{{cite encyclopedia|last=Eshleman |first=Andrew |editor=Edward N. Zalta | title=Moral Responsibility | encyclopedia=The Stanford Encyclopedia of Philosophy| edition=Winter 2009 | year=2009 | url=http://plato.stanford.edu/archives/spr2010/entries/determinism-causal}}</ref>

* Logical determinism or Determinateness is the notion that all propositions, whether about the past, present, or future, are either [[Law of excluded middle|true or false]]. Note that one can support Causal Determinism without necessarily supporting Logical Determinism and vice versa (depending on one's views on the nature of [[time]], but also [[randomness]]). 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]].
[[File:Iimatyas.jpg|thumb|right|140px|Adequate determinism focuses on [[quantum mechanics|the fact that]], even without a full understanding of microscopic physics, we can predict the distribution of 1000 coin tosses]]

** Often synonymous with Logical Determinism are the ideas behind Spatio-temporal Determinism or [[Eternalism (philosophy of time)|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 a fourth dimension (like the three spatial dimensions). In other words, all the other parts of time are real, like the city blocks up and down a street, although the order in which they appear depends on the driver (see [[Rietdijk–Putnam argument]]).

* Adequate determinism is the idea that [[quantum indeterminacy]] can be ignored for most macroscopic events. This is because of [[quantum decoherence]]. Random quantum events "average out" in the [[Expected value|limit of large numbers]] of particles (where the laws of quantum mechanics asymptotically approach the laws of classical mechanics).<ref>[http://www.informationphilosopher.com/freedom/adequate_determinism.html The Information Philosopher website], "Adequate Determinism", from the site: "''We are happy to agree with scientists and philosophers who feel that quantum effects are for the most part negligible in the macroscopic world. We particularly agree that they are negligible when considering the causally determined will and the causally determined actions set in motion by decisions of that will.''"</ref> [[Stephen Hawking]] explains a similar idea: he says that the microscopic world of [[quantum mechanics]] is one of determined probabilities. That is, quantum effects rarely alter the predictions of [[classical mechanics]], which are quite accurate (albeit still [[Uncertainty principle|not perfectly certain]]) at larger scales.<ref>[[The Grand Design (book)|Grand Design]] (2010), page 32: "the molecular basis of biology shows that biological processes are governed by the laws of physics and chemistry and therefore are as determined as the orbits of the planets.", and page 72: ''"Quantum physics might seem to undermine the idea that nature is governed by laws, but that is not the case. Instead it leads us to accept a new form of determinism: Given the state of a system at some time, the laws of nature determine the probabilities of various futures and pasts rather than determining the future and past with certainty."'' (emphasis in original, discussing a [[Many worlds interpretation]])</ref> Something as large as an [[cell (biology)|animal cell]], then, would be "adequately determined" (even in light of quantum indeterminacy).

==Philosophical connections==

===With nature/nurture controversy===
[[File:JuliusOttoGrimm-Sculpture.jpg|thumb|140px|Nature and nurture interact in humans. A scientist looking at a sculpture after some time does not ask whether we are seeing the effects of the starting materials or of environmental influences.]]
Although some of the above forms of determinism concern human behaviors and [[cognition]], others frame themselves as an answer to the debate on [[nature and nurture]]. They will suggest that one factor will entirely determine behavior. As scientific understanding has grown, however, the strongest versions of these theories have been widely rejected as a [[single cause fallacy]].<ref name="melo-martin">{{cite journal |author=de Melo-Martín I|title=Firing up the nature/nurture controversy: bioethics and genetic determinism |journal=J Med Ethics|volume=31 |issue=9|pages=526–30 |year=2005 |month=|pmid=16131554 |pmc=1734214|doi=10.1136/jme.2004.008417|url=}}</ref>

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.

[[Behaviorism]] is the idea that all behavior can be traced to specific causes—either environmental or reflexive. This Nurture-focused determinism was developed by [[John B. Watson]] and [[B. F. Skinner]].

[[Cultural determinism]] or [[social determinism]] is the nurture-focused theory that it is 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 [[Behaviorism|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.<ref>{{cite journal
|last = Andrew
|first = Sluyter
|authorlink =
|coauthors =
|title=Neo-Environmental Determinism, Intellectual Damage Control, and Nature/Society Science
|journal = Antipode
|volume = 4
|issue = 35}}</ref>

===With particular factors===
[[File:Using Mobile Phone 0251.JPG|thumb|right|150px|A technological determinist might suggest that technology like the mobile phone 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]].

===With free will===
{{Main|Free will}}
[[File:DeterminismXFreeWill.svg|thumb|right|300px|A table showing the different positions related to free will and determinism]]
Philosophers have debated both the truth of determinism, and the truth of free will. This creates the four possible positions in the figure. [[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. The [[hard incompatibilism|hard incompatibilists]] hold that both determinism and free will do not exist, the [[Libertarianism (metaphysics)|libertarianists]] that determinism does not hold, and free will might exist, and the [[hard determinism|hard determinists]] that determinism does hold and free will does not exist.

The [[standard argument against free will]], according to philosopher [[J. J. C. Smart]] focuses on the implications of determinism for 'free will'.<ref>J. J. C. Smart, "Free-Will, Praise and Blame,"''Mind'', July 1961, p.293-4.</ref> However, he suggests free will is denied whether determinism is true or not. On one hand, if determinism is true, all our actions are predicted and we are assumed not to be free; on the other hand, if determinism is false, our actions are presumed to be random and as such we do not seem free because we had no part in controlling what happened.

In his book, ''[[The Moral Landscape]]'', author and neuroscientist [[Sam Harris (author)|Sam Harris]] also argues against incompatibilist free will. He offers one thought experiment where a mad scientist represents determinism. In Harris' example, the mad scientist uses a machine to control all the desires, and thus all the behavior, of a particular human. Harris believes that it is no longer as tempting, in this case, to say the victim has "free will". Harris says nothing changes if the machine controls desires at random - the victim still seems to lack free will. Harris then argues that we are also the victims of such unpredictable desires (but due to the unconscious machinations of our brain, rather than those of a mad scientist). Based on this introspection, he writes "This discloses the real mystery of free will: if our experience is compatible with its utter absence, how can we say that we see any evidence for it in the first place?"<ref>Sam Harris, The Moral Landscape (2010), pg.216, note102</ref> adding that "Whether they are predictable or not, we do not cause our causes."<ref>Sam Harris, The Moral Landscape (2010), pg.217, note109</ref> That is, he believes there is compelling [[evidence of absence]] of free will. Harris' viewpoint implicitly assumes a philosophy of [[materialism]], that is, that mental events are reducible to neurological occurrences.

Some research (founded by the [[John Templeton Foundation]]) suggested that reducing a person's belief in free will is dangerous, making them less helpful and more aggressive.<ref>Baumeister RF, Masicampo EJ, Dewall CN. (2009). Prosocial benefits of feeling free: disbelief in free will increases aggression and reduces helpfulness. Pers Soc Psychol Bull. 35(2):260-8. PMID 19141628 {{DOI|10.1177/0146167208327217}}</ref> This could occur because the individual's sense of [[self-efficacy]] suffers.

===With the "soul" ===
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 [[mind]]s or [[Soul (spirit)|soul]]s of conscious beings.

A number of positions can be delineated:

# Immaterial souls are all that exist ([[Idealism]]).
# Immaterial souls exist and exert a non-deterministic causal influence on bodies. (Traditional free-will, [[interactionist dualism]]).<ref>By 'soul' in the context of (1) is meant an [[Wiktionary:autonomy|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 [[dualism|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</ref><ref>[http://plato.stanford.edu/entries/freewill/ Free Will (Stanford Encyclopedia of Philosophy)]</ref>
# Immaterial souls exist, but are part of deterministic framework.
# Immaterial souls exist, but exert no causal influence, free or determined ([[epiphenomenalism]], [[occasionalism]])
# Immaterial souls do not exist — there is no [[mind-body problem|mind-body]] [[dichotomy]], and there is a [[Materialism|Materialistic]] explanation for intuitions to the contrary.

===With ethics and morality===
Another topic of debate is the implication that Determinism has on [[Ethics|morality]]. [[Hard determinism]] (a belief in determinism, and not free will) is particularly criticized for seeming to make traditional moral judgments impossible. Some philosophers, however, find this an acceptable conclusion.

Philosopher and incompatibilist Peter van Inwagen introduces this thesis as such:

Argument that Free Will is Required for Moral Judgments
# The moral judgment that you shouldn't have done X implies that you should have done something else instead
# That you should have done something else instead implies that there was something else for you to do
# That there was something else for you to do implies that you could have done something else
# That you could have done something else implies that you have free will
# If you don't have free will to have done other than X we cannot make the moral judgment that you shouldn't have done X.<ref>{{cite book|last=van Inwagen|first=Peter|title=The Powers of Rational Beings: Freedom of the Will|year=2009|publisher=Oxford}}</ref>

However, a compatibilist might have an issue with Inwagen's process because one can not change the past like his arguments center around. A compatibilist who centers around plans for the future might posit:
# The moral judgment that you shouldn't have done X implies that you can do something else instead
# That you can do something else instead implies that there is something else for you to do
# That there is something else for you to do implies that you can do something else
# That you can do something else implies that you have free will for planning future recourse
# If you have free will to do other than X we can make the moral judgment that you should do other than X, and punishing you as a responsible party for having done X that you know you should not have done can help you remember to not do X in the future.

== 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]], [[Ralph Waldo Emerson]] and, more recently, [[John Searle]], [[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 [[Mechanism (philosophy)|mechanistic]] at all. Mechanistic determinism assumes that every event has an unbroken chain of prior occurrences, but a selectionistic or probabilistic model does not.<ref>Chiesa, Mecca (2004) ''Radical Behaviorism: The Philosophy & The Science''.</ref><ref>Ringen, J. D. (1993). Adaptation, teleology, and selection by consequences. ''Journal of Applied Behavior Analysis. 60,''3–15. [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1322142]</ref>

=== Eastern tradition ===
{{Section OR|date=December 2010}}
The idea that the entire universe is a [[deterministic system (philosophy)|deterministic system]] has been articulated in both Eastern and non-Eastern religion, philosophy, and literature.

In ''[[I Ching]]'' and [[Philosophical Taoism]], the ebb and flow of favorable and unfavorable conditions suggests the path of least resistance is effortless (see [[wu wei]]).

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, and in combination with the decisions (free will) of living beings, accumulates to determine futuristic situations that the living being encounters. See [[Karma in Hinduism]].{{Citation needed|date=December 2010}}

===Western tradition===
In the West, some elements of determinism seem to have been expressed by the Presocratics Heraclitus<ref>Stobaeus ''Eclogae'' I 5 ([[Heraclitus]])</ref> and Leucippus.<ref>Stobaeus ''Eclogae'' I 4 ([[Leucippus]])</ref> The first full-fledged notion of determinism appears to originate with the [[Stoics]], as part of their theory of universal causal determinism.<ref>[[Susanne Bobzien]] ''Determinism and Freedom in Stoic Philosophy'' (Oxford 1998) chapter 1.</ref> The resulting philosophical debates, which involved the confluence of elements of Aristotelian Ethics with Stoic psychology, led in the 1st-3rd centuries CE in the works of [[Alexander of Aphrodisias]] to the first recorded Western debate over determinism and freedom,<ref>Susanne Bobzien ''The Inadvertent Conception and Late Birth of the Free-Will Problem'' (Phronesis 43, 1998).</ref> an issue that is known in theology as the [[Argument from free will|paradox of free will]]. The writings of [[Epictetus]] as well as [[Middle Platonist]] and early Christian thought were instrumental in this development.<ref>[[Michael Frede]] ''A Free Will: Origins of the Notion in Ancient Thought'' (Berkeley 2011).</ref> The Jewish philosopher [[Moses Maimonides]] said of the deterministic implications of an omniscient god:<ref>Though Moses Maimonides was not arguing against the existence of God, but rather for the incompatibility between the full '''exercise''' by God of his [[omniscience]] and genuine human [[free will]], his argument is considered by some as affected by Modal Fallacy. See, in particular, the article by Prof. Norman Swartz for ''Internet Encyclopedia of Philosophy'', [http://www.iep.utm.edu/f/foreknow.htm Foreknowledge and Free Will] and specifically [http://www.iep.utm.edu/f/foreknow.htm#section6 Section 6: The Modal Fallacy]</ref> "Does God know or does He not know that a certain individual will be good or bad? If thou sayest 'He knows', then it necessarily follows that [that] man is compelled to act as God knew beforehand he would act, otherwise God's knowledge would be imperfect.…"<ref name=maimonides>''The Eight Chapters of Maimonides on Ethics (Semonah Perakhim)'', edited, annotated, and translated with an Introduction by Joseph I. Gorfinkle, pp. 99–100. (New York: AMS Press), 1966.</ref>

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 [[Introduction to quantum mechanics|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,<ref>Swartz, Norman (2003) The Concept of Physical Law / Chapter 10: Free Will and Determinism ( http://www.sfu.ca/philosophy/physical-law/)</ref> as well as the related theological views of [[Classical Pantheism]].

== Modern scientific perspective ==
=== Generative processes ===
{{Main|Emergence}}
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 indication that [[nervous system]]s are influenced by quantum indeterminism due to [[chaos theory]]. It is unclear what implications this has for [[free will]] given various possible reactions to the [[Standard argument against free will|standard problem]] in the first place.<ref>{{cite journal | doi=10.1142/S0219635206001112 | last=Lewis | first=E.R. |coauthors=MacGregor, R.J. | year=2006 | title=On Indeterminism, Chaos, and Small Number Particle Systems in the Brain | journal=[[Journal of Integrative Neuroscience]] | volume=5 | issue=2 | pages=223–247 |url=http://www.eecs.berkeley.edu/~lewis/LewisMacGregor.pdf }}</ref> Not all biologists grant determinism: Christof Koch argues against it, and in favour of [[Libertarianism (metaphysics)|libertarian free will]], by making arguments based on generative processes ([[emergence]]).<ref name=Koch>{{cite book |last1=Koch |first1=Christof |authorlink1=Christof Koch |editor1-first=Nancy|editor1-last=Murphy |editor2-first=George |editor2-last=Ellis |editor3-first=Timothy|editor3-last=O'Connor |title=Downward Causation and the Neurobiology of Free Will |url= |date=September 2009 |publisher=[[Springer Science+Business Media|Springer]] |location=New York, USA|isbn=978-3-642-03204-2 |pages= |trans_chapter= |chapter=Free Will, Physics, Biology and the Brain}}</ref> Other proponents of emergentist or [[emergence|generative philosophy]], [[cognitive science]]s and [[evolutionary psychology]], argue that determinism is true.<ref name= "Kenrick">Kenrick, D. T., Li, N. P., & Butner, J. (2003) "Dynamical evolutionary psychology: Individual decision rules and emergent social norms," Psychological Review 110: 3–28.</ref><ref name= "Nowak">Nowak A., Vallacher R.R., Tesser A., Borkowski W., (2000) "Society of Self: The emergence of collective properties in self-structure," Psychological Review 107.</ref><ref name= "Axtell">Epstein J.M. and Axtell R. (1996) Growing Artificial Societies - Social Science from the Bottom. Cambridge MA, MIT Press.</ref><ref name= "Epstein">Epstein J.M. (1999) Agent Based Models and Generative Social Science. Complexity, IV (5)</ref> 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 [[:wikt:rule|rule]]s and [[parameter]]s. Thus the unpredictability of the emerging behaviour from deterministic processes leads to a perception of free will, even though free will as an [[Ontology|ontological]] entity does not exist.<ref name= "Kenrick"/><ref name= "Nowak"/><ref name= "Axtell"/><ref name= "Epstein"/> Certain experiments looking at the [[neuroscience of free will]] can be said to support this possibility.{{citation needed|date=August 2012}}

[[File:Gospers glider gun.gif|thumb|right|120px|In [[Conway's Game of Life]], the interaction of just four simple rules creates patterns that seem somehow "alive".]]

As an illustration, the strategy board-games [[chess]] and [[Go (board game)|Go]] have rigorous rules in which no information (such as cards' face-values) is hidden from either player and no [[randomness|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 nearly infinite and practically unpredictable behaviourial responses. In theory, if all these events could be accounted for, and there were a known way to evaluate these events, the seemingly unpredictable behaviour would become predictable.<ref name= "Kenrick"/><ref name= "Nowak"/><ref name= "Axtell"/><ref name= "Epstein"/> Another hands-on example of generative processes is [[John Horton Conway]]'s playable [[Conway's Game of Life|Game of Life]].<ref>[http://www.bitstorm.org/gameoflife/ John Conway's Game of Life]</ref> [[Nassim Nicholas Taleb|Nassim Taleb]] is wary of such models, and coined the term "[[ludic fallacy]]".

=== 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 [[accuracy and precision|precision]] in measurement. Such considerations can motivate the consideration of a stochastic model even though the underlying system is governed by deterministic equations.<ref>Werndl, Charlotte (2009). ''[http://dx.doi.org/10.1016/j.shpsb.2009.06.004 Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?]''. Studies in History and Philosophy of Modern Physics 40, 232-242.</ref><ref>Werndl, Charlotte (2009). ''[http://philsci-archive.pitt.edu/archive/00004775/ 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.</ref><ref>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).</ref>

=== Quantum mechanics and classical physics ===

====Day-to-day physics====
{{further|Macroscopic quantum phenomena}}
Since the beginning of the 20th century, [[quantum mechanics]]—the physics of the extremely small—has revealed previously concealed aspects of [[Phenomenon|event]]s. Before that, [[classical mechanics|Newtonian physics]]—the physics of everyday life—dominated. Taken in isolation (rather than as an [[approximation]] to quantum mechanics), Newtonian physics depicts a universe in which objects move in perfectly determined ways. At the scale where humans exist and interact with the universe, Newtonian mechanics remain useful, and make relatively accurate predictions (e.g. calculating the trajectory of a bullet). But whereas in theory, [[Universality (philosophy)|absolute knowledge]] of the forces accelerating a bullet would produce an absolutely accurate prediction of its path, modern quantum mechanics casts reasonable doubt on this main thesis of determinism.

Relevant is the fact that [[certainty]] is never absolute in practice (and not just because of David Hume's [[problem of induction]]). The equations of Newtonian mechanics can exhibit sensitive dependence on initial conditions. This is an example of the [[butterfly effect]], which is one of the subjects of [[chaos theory]]. The idea is that something even as small as a butterfly could cause a chain reaction leading to a hurricane years later. Consequently, even a very small error in knowledge of initial conditions can result in arbitrarily large deviations from predicted behavior. Chaos theory thus explains why it may be practically impossible to [[predict]] real life, whether determinism is true or false. On the other hand, the issue may not be so much about human abilities to ''predict'' or attain ''certainty'' as much as it is the nature of reality itself. For that, a closer, scientific look at nature is necessary.

====Quantum realm====
Quantum physics works differently in many ways from Newtonian physics. Physicist [[Aaron D. O'Connell]] explains that understanding our universe, at such small scales as atoms, requires a different logic than day to day life does. O'Connell does not deny that it is all interconnected: the scale of human existence ultimately does emerge from the quantum scale. O'Connell argues that we must simply use different models and constructs when dealing with the quantum world.<ref>[http://blog.ted.com/2011/06/02/struggling-with-quantum-logic-qa-with-aaron-oconnell/?utm_content=awesm-bookmarklet&utm_medium=on.ted.com-static&utm_source=facebook.com "Struggling with quantum logic: Q&A with Aaron O'Connell]</ref> Quantum mechanics is the product of a careful application of the [[scientific method]], [[logic]] and [[empiricism]]. The [[Heisenberg uncertainty principle]] is frequently confused with the [[observer effect (physics)|observer effect]]. The uncertainty principle actually describes how precisely we may measure the position and momentum of a particle at the same time — if we increase the accuracy in measuring one quantity, we are forced to lose accuracy in measuring the other. "These uncertainty relations give us that measure of freedom from the limitations of classical concepts which is necessary for a consistent description of atomic processes."<ref name="Heisenberg1930">{{cite book |first=Werner |last=Heisenberg |year=1930 (1949) |title=Physikalische Prinzipien der Quantentheorie |trans_title=Physical Principles of Quantum Theory |location=Leipzig |publisher=Hirzel/University of Chicago Press |page=4 |url=http://books.google.com/books?id=NzMBh4ZxKJsC&pg=PA4}}</ref>

[[File:Double-slit experiment results Tanamura 2.jpg|thumb|right|Although it is not possible to predict the trajectory of any one particle, they all obey determined probabilities which do permit some prediction.]]
This is where [[statistical mechanics]] come into play, and where physicists begin to require rather unintuitive mental models: A particle's path simply cannot be exactly specified in its full quantum description. "Path" is a classical, practical attribute in our every day life, but one which quantum particles do not meaningfully possess. The probabilities discovered in quantum mechanics do nevertheless arise from measurement (of the perceived path of the particle). As [[Stephen Hawking]] explains, the result is not traditional determinism, but rather determined probabilities.<ref name=GDesign>[[The Grand Design (book)|Grand Design]] (2010), page 32: ''"the molecular basis of biology shows that biological processes are governed by the laws of physics and chemistry and therefore are as determined as the orbits of the planets...so it seems that we are no more than biological machines and that free will is just an illusion"'', and page 72: ''"Quantum physics might seem to undermine the idea that nature is governed by laws, but that is not the case. Instead it leads us to accept a new form of determinism: Given the state of a system at some time, the laws of nature determine the probabilities of various futures and pasts rather than determining the future and past with certainty."'' (discussing a [[Many worlds interpretation]])</ref> In some cases, a quantum particle may indeed trace an exact path, and the probability of finding the particles in that path is one (certain).{{Clarify|date=July 2011}} In fact, as far as prediction goes, the quantum development is at least as predictable as the classical motion, but the key is that it describes [[wave function]]s that cannot be easily expressed in ordinary language. As far as the thesis of determinism is concerned, these probabilities, at least, are quite determined. These findings from quantum mechanics have found many [[Quantum mechanics#Applications|applications]], and allow us to build [[transistors]] and [[lasers]]. Put another way: personal computers, Blu-ray players and the internet all work because humankind discovered the determined probabilities of the quantum world.<ref name=WhatIsItGoodFor?>[http://www.scientificamerican.com/article.cfm?id=everyday-quantum-physics Scientific American, "What is Quantum Mechanics Good For?"]</ref> None of that should be taken to imply that other aspects of [[quantum mechanics]] are not still [[Interpretations of quantum mechanics|up for debate]].

On the topic of predictable probabilities, the [[double-slit experiment]]s are a popular example. [[Photon]]s are fired one-by-one through a double-slit apparatus at a distant screen. Curiously, they do not arrive at any single point, nor even the two points lined up with the slits (the way you might expect of 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 (wave propagation)|interference]] pattern any individual [[photon]] will make its contribution (although, there may be ways to use [[weak measurement]] to acquire more information without violating the [[Uncertainty principle]]).

Some (including [[Albert Einstein]]) argue that our inability to predict any more than probabilities is simply due to ignorance.<ref>[[Albert Einstein]] insisted that, "I am convinced God does not play dice" in a private letter to [[Max Born]], 4 December 1926, [http://www.alberteinstein.info/db/ViewDetails.do?DocumentID=38009 Albert Einstein Archives] reel 8, item 180</ref> The idea is that, beyond the conditions and laws we can observe or deduce, there are also hidden factors or "[[Hidden variable theory|hidden variable]]s" 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. These matters continue to be subject to some dispute. A critical finding was that quantum mechanics can make statistical predictions which would be violated if local hidden variables really existed. There have been a number of experiments to verify such predictions, and so far they do not appear to be violated. This would suggest there are no hidden variables, although many physicists believe better experiments are needed to conclusively settle the issue (see also [[Bell test experiments]]). Furthermore, it is possible 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.
This debate is relevant because it is easy to imagine specific situations in which the arrival of an electron at a screen at a certain point and time would trigger one event, whereas its arrival at another point would trigger an entirely different event (e.g. see [[Schrödinger's cat]] - a thought experiment used as part of a deeper debate).

Thus, quantum physics casts reasonable doubt on the traditional determinism of classical, Newtonian physics in so far as reality does not seem to be absolutely determined. This was the subject of the famous [[Bohr–Einstein debates]] between Einstein and [[Niels Bohr]] and there is [[Interpretations of quantum mechanics|still no consensus]].<ref>{{cite book |last1=Bishop |first1=Robert C. |editor1-first=Robert |editor1-last=Kane |title=The Oxford Handbook of Free Wil |edition=Second |year=2011 |publisher=Oxford University Press |location=Oxford, New York |isbn=978-0-19-539969-1 |page=90 |chapter=Chaos, Indeterminism, and Free Will |chapterurl=http://books.google.com/books?id=kzcFDsWg0GEC&pg=PA90 |quote=The key question is whether to understand the nature of this probability as epistemic or ontic. Along epistemic lines, one possibility is that there is some additional factor (i.e., a hidden mechanism) such that once we discover and understand this factor, we would be able to predict the observed behavior of the quantum stoplight with certainty (physicists call this approach a "hidden variable theory"; see, e.g., Bell 1987, 1-13, 29-39; Bohm 1952a, 1952b; Bohm and Hiley 1993; Bub 1997, 40-114, Holland 1993; see also the preceding essay in this volume by Hodgson). Or perhaps there is an interaction with the broader environment (e.g., neighboring buildings, trees) that we have not taken into account in our observations that explains how these probabilities arise (physicists call this approach decoherence or consistent histories15). Under either of these approaches, we would interpret the observed indeterminism in the behavior of stoplights as an expression of our ignorance about the actual workings. Under an ignorance interpretation, indeterminism would not be a fundamental feature of quantum stoplights, but merely epistemic in nature due to our lack of knowledge about the system. Quantum stoplights would turn to be deterministic after all.}}</ref><ref>{{cite book|last1=Baggott|first1=Jim E.|title=Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory|accessdate=2013-02-04|year=2004|publisher=Oxford University Press|location=Oxford, New York|isbn=0-19-852536-2|page=203|chapter=Complementarity and Entanglement|chapterurl=http://books.google.nl/books?id=uVdjwsqrgz8C&pg=PA203&dq=scientific+consensus+determinism+bell+theorem&hl=nl&sa=X&ei=4v8PUaL5MarK0QWk8oCwBw&ved=0CFgQ6AEwBw#v=onepage&q=scientific%20consensus%20determinism%20bell%20theorem&f=false|quote=So, was Einstein wrong? In the sense that the EPR paper argued in favour of an objective reality for each quantum particle in an entangled pair independent of the other and of the measuring device, the answer must be yes. But if we take a wider view and ask instead if Einstein was wrong to hold to the realist's belief that the physics of the universe should be objective and deterministic, we must acknowledge that we cannot answer such a question. It is in the nature of theoretical science that there can be no such thing as certainty. A theory is only 'true' for as long as the majority of the scientific community maintain a consensus view that the theory is the one best able to explain the observations. And the story of quantum theory is not over yet.}}</ref>

Adequate determinism (see [[Determinism#Varieties|Varieties]], above) is the reason that Stephen Hawking calls [[Libertarianism (metaphysics)|Libertarian free will]] "just an illusion".<ref name="GDesign"/> [[Compatibilistic]] free will (which is deterministic) may be the only kind of "free will" that can exist. However, Daniel Dennett, in his book [[Elbow Room (book)|Elbow Room]], says that this means we have the only kind of free will "worth wanting". For even more discussion, see [[Free will]].

====Other matters of quantum determinism====
[[File:HEUraniumC.jpg|thumb|150px|left|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. At best scientists can discover determined probabilities in the form of the element's [[half life]].

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.
::<math>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</math>
So if the wave function itself is reality (rather than probability of classical coordinates), quantum mechanics can be said to be deterministic.

According to some,{{Citation needed|date=December 2009}} quantum mechanics is more strongly ordered than Classical Mechanics, because while Classical Mechanics is [[Chaos theory|chaotic]], quantum mechanics is not. For example, the [[Three-body problem|classical problem of three bodies]] under a force such as [[gravity]] is not [[Integrability conditions for differential systems|integrable]], while the quantum mechanical three body problem is tractable and integrable, using the [[Faddeev Equations]].{{Clarify|date=July 2011}} 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 [[Universal wavefunction|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 [[galaxy|galaxies]] are believed by many cosmologists to have originated in quantum fluctuations during the big bang. (''See'' [[cosmic inflation]], [[primordial fluctuations]] and [[large-scale structure of the cosmos]].)

== See also ==
{{col-begin}}
{{col-break}}
* [[Amor fati]]
* [[Block time]]
* [[Calvinism]]
* [[Causality]]
* [[Chaos theory]]
* [[Digital physics]]
* [[False necessity]]
* [[Fatalism]]
* [[Fractal]]
* [[Game theory]]
* [[Ilya Prigogine]]
* [[Interpretation of quantum mechanics]]
* [[Neuroscience of free will]]
* [[Open theism]]
* [[Predestination]]
* [[Philosophical interpretation of classical physics]]
* [[Radical behaviorism]]
* [[Voluntarism (metaphysics)|Voluntarism]]
* [[Wheeler-Feynman absorber theory]]
{{col-break}}
===Types of determinism===
* [[Genetic determinism]]
* [[Biological determinism]]
* [[Social determinism]]
* [[Cultural determinism]]
* [[Economic determinism]]
* [[Geographic determinism]]
* [[Technological determinism]]
* [[Environmental determinism]]
* [[Theological determinism]]

{{col-end}}
==References==

===Notes===
{{Reflist|2}}

===Bibliography===
* [[Daniel Dennett]] (2003) ''Freedom Evolves''. Viking Penguin.
* [[John Earman]] (2007) "Aspects of Determinism in Modern Physics" in Butterfield, J., and Earman, J., eds., ''Philosophy of Physics, Part B''. North Holland: 1369-1434.
* [[George Francis Rayner Ellis|George Ellis]] (2005) "Physics and the Real World," ''Physics Today''.
* Epstein J.M. (1999) "Agent Based Models and Generative Social Science," ''Complexity'' IV (5).
* -------- and Axtell R. (1996) ''Growing Artificial Societies — Social Science from the Bottom''. MIT Press.
* Kenrick, D. T., Li, N. P., & Butner, J. (2003) "Dynamical evolutionary psychology: Individual decision rules and emergent social norms," ''Psychological Review'' 110: 3–28.
* [[Albert Messiah]], ''Quantum Mechanics'', English translation by G. M. Temmer of ''Mécanique Quantique'', 1966, John Wiley and Sons, vol. I, chapter IV, section III.
* {{cite journal |author=Ernest Nagel |title=Determinism in history
|journal=Philosophy and Phenomenological Research,
|volume=20
|number=8
|date=March 3, 1960
|pages=291-317
|publisher=International Phenomenological Society
|url=http://www.jstor.org/stable/2105051 }} (Online version [http://www.drabruzzi.com/NAGEL_Determinism%20In%20History.pdf found here])
* {{cite book |title=The Philosophy of Science: A-M |editor=Sahotra Sarkar, Jessica Pfeifer, eds |author=John T Roberts |chapter=Determinism |url=http://books.google.com/books?id=UchIDBrAQEMC&pg=PA197 |pages=pp. 197 ''ff'' |isbn=0415977096 |publisher=Taylor & Francis |year=2006}}
* Nowak A., Vallacher R.R., Tesser A., Borkowski W., (2000) "Society of Self: The emergence of collective properties in self-structure," ''Psychological Review'' 107.
* {{Literatur|Autor=Schimbera, Jürgen / Schimbera, Peter|Titel=Determination des Indeterminierten. Kritische Anmerkungen zur Determinismus- und Freiheitskontroverse|Verlag=Verlag Dr. Kovac|Ort=Hamburg|Jahr=2010|ISBN=978-3-8300-5099-5}}
* [[Reinhold Zippelius]], ''Das Problem der Willensfreiheit'', in: ''Rechtsphilosophie, § 25'', 6th ed. 2011, C.H. Beck, Munich, ISBN 978-3-406-61191-9

== External links ==
* [http://plato.stanford.edu/entries/determinism-causal/ Stanford Encyclopedia of Philosophy entry on Causal Determinism]
* [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv2-02 Determinism in History] from the ''Dictionary of the History of Ideas''
* [http://www.ucl.ac.uk/~uctytho/dfwIntroIndex.htm Philosopher Ted Honderich's Determinism web resource]
* [http://www.informationphilosopher.com/freedom/determinism.html Determinism on Information Philosopher]
* [http://www.galilean-library.org/int13.html An Introduction to Free Will and Determinism] by Paul Newall, aimed at beginners.
* [http://www.determinism.com The Society of Natural Science]
* [http://www.chabad.org/article.asp?AID=3017 Determinism and Free Will in Judaism]
* [http://www.jottings.ca/john/cogitations.html Snooker, Pool, and Determinism]

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