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Do We Have Freewill? Van Inwagen's and David Lewis on Determinism

Causation in Action


Introduction to freewill and determinism

It seems intuitive to most people that both free will and causation (everything is the result of a cause e.g. I cook dinner because I am hungry because I didn’t eat lunch…) are realities which we can experience. However, when it is studied more closely it does seem as though a comprehensive understanding and acceptance of causation could mean the denial of free will. When everything is the result of a causal chain it seems counter-productive to then make the claim that we have free will to do whatever we want. Surely our wants cannot undermine the causation inherent in the world as we perceive it. Either free will or causation (determinism) it seems must be false if the other is true. Peter Van Inwagen formulates his consequence argument in support of determinism. He presents three arguments in support of his claim of determinism but each of them make a similar point; “these three arguments, or versions of one argument...are intended to support one another. Though they are essentially the same point, they are very different in structure and vocabulary (Van Inwagen 1986, 56). Due to the similarities in each argument this paper will focus on only the first formal argument which uses no symbolic logic so is perhaps a more complicated argument but is simpler in vocabulary and so is easier to debate in plain english. The first formal argument initially seems to be logically sound yet there is an argument from David Lewis which counters Van Inwagen's claim.

Are we free to choose?


Van Inwagen's 4 properties of propositions

Below is Van Inwagens argument in summary. It is very wordy though so a summary of it’s conclusion according to Van Inwagen can be found at the bottom of this paragraph in bold.

Van Inwagen believes that the notion of determinism relies on three subordinate notions: “The notion of proposition...and the notion of the state of the entire physical world at an instant, and the notion of the law of nature” (1986, 58). It is upon these three initial notions that he bases his formal arguments for determinism. Propositions, according to Van Inwagen, have four properties:
1. “to every possible way the world could be, there corresponds at least one propositions, a proposition that is necessarily such that it is true if and only if the world is that way”

  1. “every proposition is either true or false”
  2. “the conjunction of a true proposition and a false proposition is a false proposition”
  3. “Propositions obey the Law of Contraposition with respect to entailment. That is, for every x and every y, if x and y are propositions, and if it is impossible for x to be true and y false, then it is impossible for the denial of y to be true and the denial of x to be false” (Van Ingwagen 1986, 58).

Van Inwagen proposes that we use the idea of possible worlds in order to understand propositions. Sets of possible worlds in this sense would act to identify propositions and a propositions would be true only if it in fact contains the reality of the actual world. The second subordinate notion of the state of the entire physical world at an instant (the state of the world) is defined by two features:
1. “our concept of state must be such that...nothing follows about its state at any other instant: if x and y are any “states”, and some possible world is in x at T1 and y at T2, there is a world that is in x at T1 and not in y at T2” (Van Inwagen 1986, 59).

  1. “If there is some observable change in the way things are...this must entail some change in the state of the world” (Van Inwagen 1986, 60).

A state is one singular moment in time, distinct from events before and after. In other possible worlds the causal effects of a state could be different than in the actual world; dropping a cup at T1 (the first state) may cause it to harden rather than shatter at T2 (a second state) in other possible worlds. Observable changes in the world must be preceded by some change in the state of the world. Together with the notion of propositions this means that a proposition expresses “the state of the world at T provided it is a true proposition that asserts of some state that, at T, the world is in that state” (Van Inwagen 1986, 60). The third subordinate notion is the law of nature which Van Inwagen admits that he cannot actually define. He does though attempt to explain what it is not; “it is not an epistemological term. Ontologically speaking, a law of nature is a proposition” (Van Inwagen 1986, 60). Only some propositions are laws of nature though, which qualify as laws of nature though is beyond our knowledge. What we believe and have discovered through science is inconsequential, the laws of nature remain the same whether we know about them or not. Our scientific progress has no effect on the laws, “the laws of nature would be just as they are even if there had never been any human beings or other rational animals” (Van Inwagen 1986, 61). Laws of nature are something we can do nothing about, it is immune to possible dis-confirmation; we cannot prove a law of nature false for then it would not be a law of nature. The resulting logical consequences of the laws of nature are also laws as they must necessarily happen as a result of the laws. The laws of nature do though impose limits on us, they are able to determine the limits of what it is possible for us to do. On the sets of possible worlds model for propositions “a law of nature is any set of worlds that has a subset the set of all worlds in which the laws of nature are the same as those of the actual world, or...are nomologically congruents with the actual world” (Van Inwagen 1986, 65). Now that all three subordinate notions are defined determinism can be better understood in Van Inwagens sense. He claims that “for every instant of time, there is a proposition that expresses the state of the world at that instant; If p and q are any propositions that express the state of the world at some instants, then the conjunction of p with the laws of nature entails q” (1986, 65). So, if given p, q must necessarily happen as the laws of nature determine that one must entail the other. Given a past state of the world, determinism makes the claim that there is only one possible future which could result from it due to the laws of nature. Determinism thus requires that the world be necessarily on a single course of events, the past determines the present and the future, and the present and future determines that there had been a singular unique past. The causal chain of events determines a single path.

Van Inwagen's formal argument

Van Inwagen's first formal argument follows on from this definition of what determinism requires. Van Inwagen proposes an example of a judge who, upon raising his hand at a certain time, T, can prevent a criminals execution. This judge, J, does not raise his hand at T and so the criminal was put to death. Assuming no force, injury or necessity and assuming that the judge took rational and due deliberation in making his decision etc. then Van Inwagen would still claim that, due to determinism, it would still have been impossible for J to have raised his hand; it was determined; J could not have made any other choice given the past events of the world (the chain of causes that led to T). If we take T0 as an arbitrarily chosen instant of time before J's birth and P0 as a proposition that expresses that state of the world at T0, and P as a proposition that expresses the state of the world at T, and L as the conjunction into a single propositions of all the laws of nature and take all of these symbols to be rigid designators then Van Inwagens first formal arguments runs as follows:

  1. “If determinism is true, then the conjunction of P0 and L entails P”
  2. “It is not possible that J have raised his hand at T and P be true”
  3. “If (2) is true, then if J could have raised his hand at T, J could have rendered P false”
  4. “If J could have rendered P false, and if the conjunction of P0 and L entails P, then J could have rendered the conjunctions of P0 and L false”
  5. “If J could have rendered the conjunction of P0 and L false, then J could have rendered L false”
  6. “J could not have rendered L false”
  7. “If determinism is true, J could not have raised his hand at T.” (Van Inwagen 1986, 70).

Each of the premises is true “in all possible worlds in which the story we have told about J is true” (Van Inwagen 1986, 71). If any act a person 'could have made' is incompatible with the state of the world as it was before that persons birth then, given the laws of nature, the person was incapable of performing that act. As Van Inwagen states “if determinism is true, it never has been within my power to deviate from the actual course of events that has constituted my history” (1986, 75). Van Inwagen's resulting understanding of determinism is that the actual world is deterministic and that “every world distinct from the actual world either differs from it at every instant, or, if it differs from the actual world at only some instants, is governed by a different set of laws of nature” (1986, 86). Free will is an issue as a result of the deterministic view as it would seem that free will requires an act of choice and choice cannot be made if all actions are pre-determined by past states. Van Inwagen talks of a persons possible abilities (possible choices) as having access to these alternatives. Having access to an ability is similar to it being a possibility in normal language. Say Mike had a cup of tea he had the possibility to, he had access to, have a cup of coffee instead; assuming that there was available all the necessary ingredients for both tea and coffee when Mike made the decision. Mike thus had access to a possible world in which he had coffee instead of tea. However, these non-actual worlds are still only unrealised possibilities. Van Inwagen claims “no act I might have performed is such that my having performed it entails the actuality of any particular world... thus it would probably be more realistic to describe my unexercised abilities in terms of access to sets of possible worlds.” (1986, 90). He also states that no one has any access to possible worlds in which the laws of nature are different. Free will it seems is thus incompatible with the notion of determinism as Van Inwagen sees it.

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David Lewis' response

David Lewis makes a response to Van Inwagens consequence argument which relies in the notions of hard and soft determinism. Soft determinism, as Lewis sees it, is the doctrine that “sometimes one freely does what one is predetermined to do; and in that case one is able to act otherwise though past history and the laws of nature determine that one will not act otherwise” (1981, 113). Thus, there is a notion of determinism which still allows for free will. One acted freely despite the fact that they were determined to do so by past events and the causal relations inherent in the nature of the world. From this doctrine of soft determinism compatibilism is formed which is the stance that Lewis takes. Lewis explains his definition of free action by presenting an example of his putting his hand on a desk:

“I have just put my hand down on my desk. That... was a free but predetermined act. I was able to act otherwise... But there is a true historical proposition H about the intrinsic state of the world long ago, and there is a true proposition L specifying the laws of nature that govern our world, such that H and L jointly determine what I did. They jointly imply the proposition that I put my hand down. They jointly contradict the proposition that I raised my hand. Yet I was free; I was able to raise my hand. The way in which I was determined not to was not the sort of way that counts as inability.” (1981, 113)

Thus, for Lewis there is still a sense of freedom in his choices even though they are predetermined to happen by the states of the past and the laws of nature. If he was to raise his hand though then he argues that there are three things, one of which must have been true in that case:

1. “Contradictions would have been true together”;

2. “the historical proposition H would not have been true”;

3. “the law proposition L would not have been true” (1981, 114)

Lewis believes the first of these can be rejected as a possibility, is he were to have raised his hand then there would have been no true contradiction. He also believes that we can reject the second possibility as the state of the world in the past would be no different is he were to raise his hand or not. Therefore, he argues that, of these three possibilities, it must be the case that the law proposition, L, would not have been true. It seems intuitively unlikely that we are able to break the laws of nature though. Lewis goes on to claim there are two ways of looking at this notion of breaking a law: a strong and weak thesis. The strong thesis would claim that we are able to break the laws of nature, while the weak thesis would claim that we are “able to do something such that, if [we] did it, a law would be broken.” (Lewis 1981, 115). Lewis presents an example of throwing a stone to represent the difference between these two theses. If one is able to throw a stone in such a way that the stone would fly faster than the speed of light (contrary to law) then one would be able to break a law; one would be able to do something such that, if they did it, it would cause a law-breaking event (the weak thesis). In opposition, if when throwing the stone, ones hand itself began to move faster than the speed of light then one would be able to do something such that, if they did it, the act would itself be a law-breaking event (the strong thesis). In the case of Lewis raising his hand when he in fact placed it on the table he is able to raise his hand although it is predetermined that he will not; “if I raised my hand some law would be broken. I grant that some law-breaking event would take place” (Lewis 1981, 116). He questions whether it is actually the act of raising his hand which would qualify as the law-breaking event itself though as he claims that if he had raised his hand then a law-breaking even would have happened before-hand and it is at this point of divergence from the actual course that a law-breaking event takes place (a divergence miracle as Lewis terms it). The divergence miracle would not have been caused by his raising his hand, if anything his raising his hand would have been caused by this divergence miracle. Thus, Lewis claims that he was able to raise his hand and that a law would have been broken if he had but yet he still maintains that he is unable to break a law. From this initial stance Lewis claims that there are two premises of Van Inwagen's argument which cannot both be true:

Premise 5,“If J could have rendered the conjunction of P0 and L false, then J could have rendered L false”

Premise 6, “J could not have rendered L false”

He claims that which one of these two premises is true depends on what Van Inwagen means when he states 'could have been rendered false'. Lets agree that in order to falsify a proposition requires that if that events occurs then the proposition is false. Lewis claims: I could have rendered a proposition false in the weak sense iff I was able to do something such that, if I did it, the proposition would have been falsified (though not necessarily by my act, or by any event caused by my act). And... I could have rendered a proposition false in the strong sense iff I was able to do something such that, if I did it, the proposition would have been falsified either by my act itself or by some event caused by my act'(1981, 120). Either way, Lewis does accept that the initial part of Van Inwagens formal argument succeeds whichever sense is taken; 'If I could have raised my hand despite the fact that determinism is true and I did not raise it, then indeed it is true both in the weak sense and in the strong sense that I could have rendered false the conjunction HL of history and law'(Lewis 1981, 120). However, if the weak sense is taken throughout the argument then Lewis would claim that premise 6 should be denied, while, if we take the strong sense then premise 5 should be denied. Lewis claims that Van Inwagen supports both premises by considering analogous cases but Lewis thinks that these argument fail because the cases produced are not analogous: they are cases in which the weak and strong senses do not diverge'(1981, 120). Lewis argues that Van Inwagen wants us to reject the supposition that a physicist could render a law false by building and operating a machine that would accelerate protons to twice the speed of light'(1981, 120). This though only offers us reason to accept premise 6 in the strong sense, it fails to support the claim in the weak sense. For premise 5 however, Van Inwagen offers support for it in the weak sense but not the strong sense when he invites us to reject the supposition that a traveller could render false a conjunction of a historical proposition and a proposition about his future travels otherwise than by rendering false the nonhistorical conjunct'(Lewis 1981, 120). Essentially, Lewis claims that when the notions presented by Van Inwagen are viewed through the lense of strong and weak sense of consequentialism separately, there is one premise which fails to satisfactorily conform to each. Premise 5 fails to conform to the strong sense while premise 6 fails to conform to the weak sense. Thus, for Lewis, Van Inwagen's consequentialist argument fails to be sound as the argument is incoherent by either the strong or the weak reading.


In conclusion, Van Inwagen's consequence argument certainly makes a valid point in that the determinism of past states along with the notion of laws does make present and future events seem inevitable. However, his argument does limit free will greatly and thus counters what most people would believe to be intuitively within our capabilities; that we are able to make a choice to act or not. Lewis's response though reopens the possibility that free will could still persist despite the predetermined nature of the world. This stance being more forgiving and more supporting of our intuitions makes it seem much more attractive, perhaps though only for the sake of our ego. Lewis's points in the sense of the strong and weak notions are in a sense a little shakey, but their existence alone and the validity of them as a possibility does open up questions of how sound Van Inwagen's argument really is. The notions Lewis presents in favour of the notions of determinism and free will working together are a little uncertain and the way in which he makes it theoretically possible to break the laws of nature seem dubious but his claims regarding Van Inwagen's formal argument surely at least leave the case open for necessary improvement if it to be relied upon.


Lewis, D. 1981. “Are We Free to Break the Laws?”. Teoria. 47(3); 113-121.

Van Inwagen, P. 1986. An Essay on Free Will. Oxford: Oxford University Press.

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