21 The Consequence Argument
We presented Lewis’ contextualism as a principled account of ability: whether an agent can \(\varphi\) depends on which facts we hold fixed at a given context. This provided us with resources to explain how Tim can both kill and not kill Grandfather and to resist fatalism more generally. But the time has come to present contextualism with what may well be its most serious challenge.
The challenge is van Inwagen’s Consequence Argument. Unlike the fatalist argument, it appeals directly to the causal structure of a determinism worlds, and it is designed to show that if determinism is true, then no one has ever had genuine choices open to them. The crucial question for us is whether the contextualist resources we have developed are sufficient to meet the challenge.
(Inwagen 1975) sets out to argue that free will is incompatible with determinism. He understands determinism as the conjunction of two theses:
- For every instant of time, there is a proposition \(P\), which expresses the state of the world at that instant of time.
- If \(P\) and \(Q\) are propositions that express the intrinsic state of the world at two instants of time, then the conjunction of one with the proposition \(L\) that describes the laws of nature entails the other.
Determinism is the thought that the laws of nature, in combination with a description of the past necessarily implies the future. That is, if \(H\) is a true historical proposition that describes the universe at some past time, \(L\) is a proposition describing the laws of nature, and \(P\) is a proposition describing the state of the world after the time of \(H\), then it is a necessary truth that if \(L\), then if \(H\) then \(P\).
21.1 The Informal Argument
Here is now the informal argument that if determinism is true, we have no genuine control over our actions. Suppose \(A\) is an act over which I take myself to have control, e.g., to raise my hand as opposed to put it down on my desk at a later time. (Inwagen 1975) argues that I have no control over \(A\).
If determinism is true, then the \(H\) and \(L\) entails \(P\), which entails \(A\).
If I had control over \(A\), then I would have control over \(P\), since \(P\) entails \(A\).
If determinism is true, then if I had control over \(P\), then I would have control over \(H\) and \(L\), since, according to determinism, \(H\) and \(L\) entail \(P\).
If I had control over \(L\) and \(H\), then I would have control over \(H\) or I would have control over \(L\).
I have no control over \(H\).
I have no control over \(L\).
I have no control over \(H\) and \(L\).
If determinism is true, then I have no control over \(P\).
Therefore, if determinism is true, then I have no control over \(A\).
The core idea is a transfer of powerlessness. I have no control over the laws of nature and no control over the state of the world before I was born. If determinism is true, those two will entail every proposition that describes a future state of the world, including my act \(A\). So my powerlessness over the past and the laws of nature transfers to powerlessness over \(A\).
21.2 The Formal Argument: Rules of Inference.
This informal version captures the intuitive force of the argument, but van Inwagen provides a more rigorous formulation using two explicit rules of inference, which we turn to now.
For a more compact formulation of the argument, we will write that a proposition \(P\) is beyond control if no one has or ever had any choice about whether \(P\).
\[ \begin{array}{lll} NP & : & P, \ \text{and no one has or ever had any choice about whether} \ P\\ \end{array} \]
The relevant rules of inference for this concept are:
Necessary truths are beyond control.
The motivation is simple. If a proposition is necessarily true or true in every possible world, then there is nothing anyone can do to make it otherwise. Control requires the possibility of a different outcome, which is foreclosed by the necessity of the proposition.
If \(P\) is beyond control, and if the conditional proposition that if \(P\), then \(Q\) is beyond control, then the consequent \(Q\) is beyond control as well.
If you have no control over a proposition or over the fact that that propositions entails another, then your powerlessness with respect to the intput transfers into your powerlessness over the output. This is the principle that does the main work of transmitting unavoidability from the past and the laws to the present act.
With these rules in place, we are in a position to present the formal argument.
If is necessary that if \(H\) and \(L\), then \(P\).
From determinism.
If is necessary that if \(H\), then if \(L\), then \(P\).
This is logically equivalent to 1.
It is beyond control that if \(H\), then if \(L\), then \(P\).
From 2 by the \(\alpha\)-rule.
\(H\) is beyond control.
It is beyond control that if \(L\), then \(P\).
From 3 and 4 by the \(\beta\)-rule.
\(L\) is beyond control.
Therefore, \(P\) is beyond control.
From 5 and 6 by the \(\beta\)-rule.
The conclusion of the argument is that we have no control over the state of the world at the later time. The \(\alpha\)-rule moves from the necessity of the conditional that if \(H\) and \(L\), then \(P\) to the lack of control over it, and the \(\beta\)-rule exploits this to spread the lack of control over either \(H\) and \(L\) to lack of control over \(P\). So, it is clear how the argument turns on these two rules.
(Inwagen 2000) has later acknowledged that there is a problem with rule \(\beta\) as it stands, since it appears to validate a rule we might not want to accept:
If \(P\) and \(Q\) are both beyond control, then the conjunction \(P\) and \(Q\) is beyond control as well.
Suppose that \(P\) and \(Q\) are each beyond control, and notice that the conditional that if \(Q\), then if \(P\), then \(P\) and \(Q\) is a logical truth and thus beyond control. By the \(\alpha\)-rule, the conditional is beyond control. But since \(Q\) is beyond control, by the \(\beta\)-rule, the conditional that if \(P\), then \(P\) and \(Q\) is now beyond control. By another application of the \(\beta\)-rule, it follows that the conjunction \(P\) and \(Q\) is beyond control.
But this is a problematic conclusion. Suppose I had an opportunity to flip a coin yesterday. I did not flip it, but if I had the coin might have land heads or tails. Because I did not flip it, it landed neither heads nor tails.
- It is beyond control that the coin did not land heads.
- It is beyond control that the coin did not land tails.
- Therefore, it is beyond control that the coin landed neither heads nor tails.
The premises seem true, since I had no control over how the fair coin would have landed even if I had tossed it. However, the conclusion is false. It is not beyond control that the coin landed neither heads nor tails, because the coin would have invariably land one way or another if I had tossed it. Since the \(\beta\)-rule validates agglomeration, this means that it must be flawed.
There are, however, alternative rules of inference one may use instead of rule \(\beta\):
If \(P\) is beyond control and it is necessary that if \(P\), then \(Q\), then \(Q\) is beyond control.
The difference is subtle but important. The original \(\beta\)-rule required merely that the conditional if \(P\), then \(Q\) be beyond control, but the new rule requires the conditional to be necessary. That is sufficient to block the derivation of agglomeration, because one of the conditionals involved in the derivation is not necessary: it is not necessary that if \(P\), then \(P\) and \(Q\).
With this replacement, the argument may be reformulated:
If is necessary that if \(H\) and \(L\), then \(P\).
From determinism.
It is beyond control that \(H\) and \(L\).
Therefore, \(P\) is beyond control.
From 1 and 2 by the necessary conditional rule.
The argument is now more compact and avoids the problem with the \(\beta\)-rule. It now appeals instead to the necessary conditional rule to move from 1 and 2 to 3, which is still the conclusion that we have no control over \(P\).
There is a residual concern. The repair relies on the conjunction of \(H\) and \(L\) being beyond control, which is strictly stronger than that each \(H\) and \(L\) being beyond control. One way to move from the individual claims to the joint claim is agglomeration, which is invalid. However, the premise seems independently motivated in this case.
The main question now is that the force of the argument ultimately depends on how we understand ‘beyond control’ and what it would be to have control over a proposition. This is where Lewis will intervene again. His response will not deny that the past and the laws are strictly beyond control, but it will contest whether the sort of control the argument rules out is the one of that matters for free will. In particular, he will argue that the \(\beta\)-rule and its replacement rely on an unreasonable interpretation of control: one that no compatibilist should accept unexamined.