The Consequence Argument

If determinism is true, then what you do now is a consequence of the laws of nature and the state of the world before you were born, and neither of those is up to you.

That is the whole argument in one sentence, and it is the reason incompatibilism is not a superstition. The previous lesson dismantled two arguments that reach the same conclusion by a scope error, and isolated the shape that survives: fixity, connection, transfer. Peter van Inwagen assembled exactly that shape from purely secular materials in a 1975 paper and at length in An Essay on Free Will in 1983, and named it the Consequence Argument. Almost everything written since has been a response to it.

The argument in words

Van Inwagen's own statement is worth having in front of you. If determinism is true, our acts are the consequences of the laws of nature and events in the remote past. It is not up to us what went on before we were born, and it is not up to us what the laws of nature are. Therefore the consequences of these things, including our present acts, are not up to us.

Read it slowly and notice what it does not do. It does not say the laws compel anybody. It does not say the future is fixed regardless of what we do. It does not confuse a necessary connection with a necessary conclusion. It grants that your deliberation is a real cause of your action, and simply observes that your deliberation is itself a consequence of things you had no say in.

The plausibility comes from the two fixity claims, each of which is close to undeniable on its face. Nobody can now make it the case that the universe was other than it was a billion years ago. Nobody can now make it the case that the laws of nature are other than they are. Whatever freedom is, it does not include those two abilities.

The argument in symbols

To see whether it is valid, write it out. Following van Inwagen, introduce an operator: $N p$ means that $p$ is true and no one has, or ever had, any choice about whether $p$ .

Two rules govern it. The first, usually called alpha, says that if $p$ is a logical or metaphysical necessity then $N p$ : nobody has a choice about the truths of arithmetic. The second, beta, is the transfer principle, and it is where all the trouble lives:

N p, N (p \to q) ⊢ N q

In words: if nobody has a choice about $p$ , and nobody has a choice about the fact that $p$ leads to $q$ , then nobody has a choice about $q$ .

Now let $P_{0}$ be a complete description of the state of the world at some moment in the remote past, $L$ the conjunction of all the laws of nature, and $A$ the proposition that you raised your hand at nine o'clock this morning. Determinism, as stated two lessons ago, gives $Box ((P_{0} \land L) \to A)$ : the past state together with the laws entails the act.

The derivation runs in four steps. From determinism and rule alpha, $N ((P_{0} \land L) \to A)$ , since a logical consequence of the deterministic thesis is not something anyone has a choice about. From the fixity of the past and of the laws, $N (P_{0} \land L)$ . Apply beta to those two lines and $N A$ follows: nobody has, or ever had, any choice about whether you raised your hand. Since the argument used nothing specific about the act, the conclusion generalises to every act anyone has ever performed.

The argument is valid if beta is. Its premises are the determinist thesis and the two fixity claims. So a compatibilist has exactly three options: deny the fixity of the past, deny the fixity of the laws, or deny the transfer principle. Every serious compatibilist response since 1983 takes one of those three routes, which is a rare and welcome tidiness in philosophy.

Example. Someone objects that the argument proves too much, since by the same reasoning nobody has a choice about anything at all, including trivial matters like whether a kettle boils. Is that an objection?

No, it is a correct reading of the conclusion. Van Inwagen's argument is meant to show that if determinism is true, then nothing that happens is up to anyone, and the kettle is not a special case. An objection would have to show that the conclusion is false in some instance, not merely that it is sweeping. What the observation does usefully highlight is that the argument targets one specific thing, the ability to do otherwise, and says nothing directly about whether people are the sources of their actions or whether they can be responsible for them. A compatibilist who has given up the leeway condition, in the manner of a later lesson, can accept the entire argument and deny that it touches moral responsibility.

Now you. Rewrite the argument's target so that it concerns a near-deterministic world, in which the past and the laws fix only the chances of your raising your hand. Does the argument survive?

Answer

Largely, yes. Replace $A$ with the proposition that the objective chance of your raising your hand at nine o'clock was 0.7. That proposition is entailed by $P_{0}$ and $L$ , so the same three steps give $N$ applied to it: nobody had any choice about what the chances were. The libertarian then has to locate free will in the gap between a fixed chance and an actual outcome, and the outcome, given the chance, is settled by nothing at all rather than by the agent. That is why the physics lesson concluded that the question of strict determinism is close to irrelevant: the argument mutates to fit, and the mutation is if anything harder to answer.

Attacking the laws: Lewis on breaking them

David Lewis published a four-page reply in 1981 titled "Are We Free to Break the Laws?", and it is the most discussed compatibilist response to the argument.

Lewis distinguishes two things the compatibilist might be committed to. The strong thesis: I am able to break a law of nature, that is, able to perform an act which would itself be, or cause, a law-breaking event. The weak thesis: I am able to do something such that, if I did it, a law would have been broken at some point beforehand.

He accepts the weak thesis and rejects the strong one. The point turns on how we evaluate the counterfactual "if I had raised my hand". On Lewis's own account of counterfactuals, we go to the nearest possible world in which I raise it. Since the actual laws plus the actual past entail that I do not, that world must differ either in its laws or in its past, and the nearest such world contains a tiny divergence miracle shortly before the moment of choice, after which the ordinary laws resume. In that world I raise my hand, and a law is broken. But I do not break it: the miracle happens before my act and is no part of it. My raising my hand is a perfectly law-abiding event in a world whose history diverged slightly from ours.

The compatibilist claim is therefore only that had I acted otherwise, the past or the laws would have been slightly different, and that is not an outrageous ability to attribute to anyone. What is outrageous is the strong thesis, and nobody needs it.

The reply has not gone unchallenged. Critics, including Helen Beebee, argue that Lewis's account smuggles in a picture of laws as mere summaries of what happens, so that a divergence costs nothing metaphysically, and that on a stronger view of laws as genuine governors of events the weak thesis is no more available than the strong. Which side you find convincing depends on your view of laws of nature, which is a question in metaphysics with no connection to agency, and that dependence is itself interesting: the free will problem keeps turning out to be entangled with other unfinished business.

Attacking the fixity of the laws

Lewis's reply concedes that the laws are fixed and argues about what an agent's abilities amount to given that. A bolder line denies the fixity itself, and it turns on what a law of nature is.

On a Humean view, associated with Lewis's own metaphysics, laws are not governors of events but summaries of them: the laws are whatever axioms give the best combination of simplicity and strength in describing the total history of the world. Notice what follows. If the laws are a summary of everything that ever happens, and your raising your hand is part of everything that ever happens, then what the laws are depends in part on what you do. Helen Beebee and Alfred Mele called the resulting position Humean compatibilism in 2002: the fixity premise is false, not because anyone can break a law, but because the laws were never independent of the total pattern that includes our actions.

The reply is unsettling in a specific way. It does not give you a power to do otherwise in any dramatic sense; it says that in the nearest world where you act otherwise, the best summary of history is slightly different, and no fact about that world is being violated by anybody. Whether that counts as denying the premise or as a very careful restatement of Lewis's position is itself argued about.

The cost is that the whole reply is hostage to a view about laws. If laws are genuine necessitation relations, as many philosophers of science hold, the move is unavailable, and the fixity of the laws is as secure as the fixity of the past.

Example. Which premise does each of these deny: (a) a Humean who says the laws supervene on the total history; (b) someone who says that had you acted otherwise, a small miracle would have occurred before you acted; (c) someone who says that having no choice about $p$ and no choice about $p \to q$ leaves it open whether you have a choice about $q$ ?

(a) denies the fixity of the laws, by making what the laws are partly depend on what happens, including what agents do. (b) denies the fixity of the past, in the specific and modest form Lewis defends: the divergence lies before the act, so nothing is broken by the agent, but the past of the nearest world in which she acts otherwise is not quite this one. (c) denies the transfer principle. These are the three doors out of the argument, and there is no fourth, which is what makes the Consequence Argument such a good organiser of the debate.

Now you. A determinist objects that Humean compatibilism gets things backwards, since the laws explain the events rather than being constituted by them. Is this an objection to the position or a disagreement about something else?

Answer

It is a disagreement about the metaphysics of laws, and the objector is right that it settles the matter if they are right. Humean compatibilism is not a free-standing thesis about agency: it is a corollary of a view in the philosophy of science, and it inherits every objection to that view, of which the explanatory circularity charge is the standard one. This is a general and slightly deflating feature of the area worth noticing early: several of the best moves in the free will debate are downstream of unfinished business elsewhere, in the metaphysics of laws, of causation and of modality, and a reader who wants a self-contained answer will not find one.

Attacking the transfer principle

The other line of attack goes for beta directly, and it succeeded.

In 1996 Thomas McKay and David Johnson showed that beta entails a principle of agglomeration: from $N p$ and $N q$ , infer $N (p \land q)$ . And agglomeration has a counterexample. Suppose I did not toss a coin this morning, though I could have. Let $p$ be that the coin does not land heads and $q$ be that the coin does not land tails. Both are true. I had no choice about either taken singly, since nothing I could have done would have guaranteed heads, and nothing would have guaranteed tails. But their conjunction says the coin lands neither way, which is true only because it was never tossed, and I certainly had a choice about that. So $N p$ and $N q$ hold while $N (p \land q)$ fails, agglomeration is invalid, and beta with it.

This is a genuine result and it killed the original formulation. It did not kill the argument. Alicia Finch and Ted Warfield pointed out in 1998 that the derivation never needs the full strength of beta, because determinism supplies a strict entailment rather than a mere conditional. So replace the rule with

N p, Box (p \to q) ⊢ N q

which says that whatever is entailed by something nobody has a choice about is itself something nobody has a choice about. That version is not touched by the coin, since it never licenses agglomeration, and the four steps go through as before.

Whether the repaired rule is true is now the question, and the honest answer is that it is very plausible and not provable. It has the same status as the fixity premises: something almost everyone accepts on reflection, which a determined compatibilist can reject at a cost.

Example. Where does each of these replies attack the argument? (a) "Had I acted otherwise, the past would have been very slightly different." (b) "It is only in an irrelevant sense that I could not have done otherwise, since I certainly could have if I had chosen to." (c) "The coin case shows that the rule licensing the argument is invalid."

Reply (a) attacks the fixity of the past, in Lewis's manner, by allowing that my acting otherwise is compatible with the past having been different, and it must then explain why this does not amount to an absurd power over history. Reply (b) attacks neither premise directly but the interpretation of "up to us", proposing that the ability the argument denies is not the ability freedom requires; that is the conditional analysis of the next lesson, and it has its own problems. Reply (c) attacks the transfer principle, and it is correct against the original version and answered by the repaired one. Only (c) is a technical objection; (a) and (b) are substantive philosophical positions.

Now you. A compatibilist says the argument equivocates, because "up to us" in the premises means "within our power to alter", whereas in the conclusion it must mean "within our power to determine". Is this a good objection?

Answer

It is a natural thought and it does not survive contact with the operator. $N$ was defined once, and the same definition is used in every line: $p$ is true and no one ever had a choice about whether $p$ . There is no second sense floating in the conclusion. What the objector is groping towards is better put as a challenge to the transfer rule itself: perhaps having no choice about the antecedent and the entailment is compatible with having some relevant kind of choice about the consequent. Making that precise is exactly what a semi-compatibilist does by giving up leeway and defending sourcehood instead. Stated as an equivocation, though, the objection is answerable in one line, and this is a good illustration of why the argument is stated formally in the first place.

Where this leaves the dispute

The Consequence Argument does not prove that we lack free will, and van Inwagen never claimed it did. He is a libertarian: he accepts the argument and rejects determinism, while candidly writing that free will remains a mystery, since he cannot explain how an undetermined choice would be his.

What the argument does is fix the burden. Before 1983 a compatibilist could treat incompatibilism as a confusion, a hangover from the puppet picture that a little clear thinking would remove. That is no longer available. There is now a valid argument, from premises most people accept on reflection, to the conclusion that determinism removes the ability to do otherwise. Anyone who wants to keep both determinism and free will must say precisely which premise is false, and pay for it.

The next lesson is the answer that has convinced the majority of philosophers: that the ability the argument targets is the wrong ability, because freedom was never about how many futures were open. It has a distinguished history, a devastating counterexample in its simplest form, and two modern successors that survive.