The Consequence Argument

The Consequence Argument is the most rigorous and influential argument for incompatibilism — the thesis that free will is incompatible with determinism. Developed independently by Carl Ginet, David Wiggins, and, in its canonical form, by Peter van Inwagen (An Essay on Free Will, 1983), it transformed incompatibilism from a bare intuition into the conclusion of a valid-looking deductive argument. Its central idea is a transfer principle: we have no choice about the remote past, and no choice about the laws of nature, and — if determinism is true — no choice about the fact that these entail everything we ever do; so we have no choice about anything we do.

This page gives the informal argument, its formal regimentation (the $N$-operator and the modal rules $\alpha$ and $\beta$), the standard derivation, the major compatibilist replies, and van Inwagen's own dark companion to it, the Mind argument. It is a leeway argument — it targets the ability to do otherwise — and so its fate is bound up with the Frankfurt cases that question whether free will requires alternatives at all.

The informal argument

Van Inwagen's best-known statement:

If determinism is true, then our acts are the consequences of the laws of nature and events in the remote past. But it is not up to us what went on before we were born, and neither is it up to us what the laws of nature are. Therefore the consequences of these things (including our present acts) are not up to us.

The argument rests on two intuitively compelling fixity premises and one consequence of determinism:

• Fixity of the past. No one has any choice about what happened in the remote past — say, the total state of the world a million years ago. That is simply not up to anyone now.
• Fixity of the laws. No one has any choice about what the laws of nature are. We cannot act so as to make the laws of physics other than they are.
• Entailment (from determinism). Determinism says the past plus the laws entail a unique future. So a complete description of the remote past, conjoined with the laws, logically entails the truth of any proposition describing your present action.

The argument then "transfers" our lack of choice along the entailment: if we have no choice about the past, and no choice about the laws, and no choice about the fact that they entail our acts, then we have no choice about our acts. They were settled before we existed, by things over which we have no power.

The formal core: the $N$-operator and rules $\alpha$, $\beta$

Van Inwagen sharpens this with a sentential operator. For any proposition $p$, define

$$Np:=\text{“}p\text{, and no one has, or ever had, any choice about whether }p\text{.”}$$

The argument uses two inference rules governing $N$:

$$(\alpha )\frac{\square p}{Np}(\beta )\frac{Np,N(p\to q)}{Nq}$$

• Rule $\alpha$ says: if $p$ is broadly logically necessary ($\square p$), then no one has a choice about $p$. (No one gets a say over necessary truths.)
• Rule $\beta$ — the transfer of powerlessness (or "transfer of non-responsibility") principle — is the engine. It says: if no one has a choice about $p$, and no one has a choice about the conditional $p\to q$, then no one has a choice about $q$. Powerlessness flows across known entailments.

The derivation

Let $P_0$ be a proposition giving the complete state of the world at some instant in the remote past (before any agents existed), let $L$ be the conjunction of the laws of nature, and let $P$ be any true proposition about a present action. Determinism is the claim that $P_0\wedge L$ entails $P$, i.e. $\square ((P_0\wedge L)\to P)$. Then:

$$\begin{array}{rlrl}1.& \square ((P_0\wedge L)\to P)& & \text{(determinism)}\\ & & & \\ 2.& \square (P_0\to (L\to P))& & \text{(1, exportation)}\\ & & & \\ & & & \\ 3.& N(P_0\to (L\to P))& & \text{(2, rule }\alpha )\\ 4.& N{P}_0& & \text{(fixity of the past)}\\ 5.& N(L\to P)& & \text{(3, 4, rule }\beta )\\ 6.& NL& & \text{(fixity of the laws)}\\ 7.& NP& & \text{(5, 6, rule }\beta )\end{array}$$

Line 7 says: $P$ is true, and no one has, or ever had, any choice about whether $P$ — no one has a choice about their own present action. Since $P$ was an arbitrary truth about what an agent does, nothing anyone does is up to them. If having free will requires having a choice about what one does, then determinism is incompatible with free will. ∎

The argument's power is that the two substantive premises ($N{P}_0$, $NL$) are extraordinarily plausible, rule $\alpha$ is nearly undeniable, and the logic is otherwise just modal propositional reasoning. The compatibilist must therefore attack rule $\beta$ or one of the fixity premises.

Compatibilist replies

1. Reject Rule $\beta$ — the agglomeration failure (McKay & Johnson)

The most decisive technical result is that rule $\beta$ is invalid. Thomas McKay and David Johnson (1996) proved that $\beta$ entails a principle of agglomeration:

$$\text{from }Np\text{ and }Nq,\text{ infer }N(p\wedge q),$$

and that agglomeration is false. Their counterexample uses a fair coin I never tossed. Let:

• $p$ = "the coin does not land heads,"
• $q$ = "the coin does not land tails."

Since I never tossed the coin, both are true, and (plausibly) I had no choice about either individually: I have no choice-determining power over whether it specifically fails to land heads, nor over whether it specifically fails to land tails. So $Np$ and $Nq$. But I did have a choice about their conjunction $p\wedge q$ = "the coin lands neither heads nor tails," because I could have tossed it, which would (almost surely) have made the conjunction false. So $\neg N(p\wedge q)$. Agglomeration fails — and since $\beta$ implies agglomeration, $\beta$ is invalid.

This does not by itself refute incompatibilism; it refutes one formulation. Van Inwagen accepts the result and the dialectic shifts to repaired transfer principles:

• Finch & Warfield (1998) propose a weaker, valid principle ${\beta }_2$ (using $Np$ together with the premise $\square (p\to q)$ rather than $N(p\to q)$), arguing it still drives the argument while escaping the agglomeration counterexample.
• Critics (e.g. Campbell) then question whether the new premises (especially a strong fixity-of-the-past claim) are as secure as the originals, and whether the repaired argument begs the question. The validity of some transfer principle remains contested.

2. Deny fixity of the laws — Lewis's local-miracle compatibilism

David Lewis ("Are We Free to Break the Laws?", 1981) targets premise $NL$ by distinguishing two things the incompatibilist runs together. Suppose I could have raised my hand when in fact I did not. In a deterministic world, had I done so, the past-plus-laws would not have entailed my actual inaction — so something would have had to be different. Lewis distinguishes:

• The Strong Thesis: I am able to do something such that, if I did it, I myself would break a law — my act would be, or would cause, a law-breaking event. This is indeed incredible; no one can break a law of nature.
• The Weak Thesis: I am able to do something such that, if I did it, a law would have been broken — by some earlier "divergence miracle" — though my act itself breaks no law. This is not incredible.

Lewis argues the compatibilist needs only the Weak Thesis, while the Consequence Argument's intuitive pull comes from the Strong Thesis. Being able to act such that the past or laws would have been slightly different is not the absurd power to break laws or change the past. So $NL$ (read in the strong way needed for the argument) can be rejected without absurdity. The literature on "local miracles," divergence vs. convergence miracles, and whether the Weak Thesis really suffices (Fischer, Ginet) is large and ongoing.

3. Distrust $\beta$ by analogy — Slote's selective necessity

Michael Slote (1982) observes that the $N$-operator behaves like other non-agglomerative modalities — "it is obligatory that," "it is known that," operators carrying a tacit ceteris paribus or selectivity. For such operators, transfer/agglomeration inferences fail in just the way McKay–Johnson exhibit. If "no one has a choice about" is selectively necessary in this sense, $\beta$ is exactly the kind of principle we should expect to fail, so the argument's key rule is independently suspect.

4. Concede the conclusion, save responsibility — semicompatibilism

John Martin Fischer's semicompatibilism grants, for the sake of argument, that the Consequence Argument is sound — that determinism really does remove the power to do otherwise ($NP$). It then denies that this matters for moral responsibility, which (Fischer argues, leaning on the Frankfurt cases) requires only guidance control — acting on one's own moderately reasons-responsive mechanism — not regulative control (genuine access to alternatives). On this view the Consequence Argument may win the battle over leeway while losing the war over responsibility. This is why so much turns on whether free will and responsibility really require alternative possibilities at all.

Van Inwagen's dark companion: the Mind argument

Van Inwagen pairs the Consequence Argument with a second argument — he calls it the Mind argument (after the journal Mind, where versions appeared) — aimed at showing that indeterminism is also incompatible with free will. The reasoning is the luck objection in transfer form: if an action is genuinely undetermined, then whether it occurs is not settled by anything about the agent — the agent's prior states leave it open — so the agent has no more choice about it than about a chance event. Powerlessness transfers here too.

Put together, the two arguments are devastatingly symmetrical:

$$\underset{\text{determinism}\Rightarrow \text{no free will}}{\underbrace{\text{Consequence Argument}}}\underset{\text{indeterminism}\Rightarrow \text{no free will}}{\underbrace{\text{Mind argument}}}$$

Since determinism and indeterminism are exhaustive, the conjunction seems to show free will is impossible — the conclusion the hard incompatibilist embraces. Van Inwagen himself draws a different, famous moral: because he takes it as evident that we do sometimes act freely, while finding both arguments nearly compelling, he concludes that free will remains a genuine mystery — something we know exists but cannot understand how it is possible. (This is the structural mirror of the hard incompatibilist's two-sided case; the two views share the premises and differ only on whether to keep "free will exists" or "free will is intelligible.")

Where the Consequence Argument sits

The Consequence Argument is the rigorous core of leeway incompatibilism: it makes precise the intuition that a future fixed by the pre-natal past and the laws is not open, and that what is not open is not up to us. Its lasting achievement is to have forced the debate into clear alternatives — the compatibilist must either reject the transfer principle (the McKay–Johnson/Slote route, now a debate over which transfer principle is valid), deny the fixity of the laws or past (the Lewisian local-miracle route), or concede leeway but relocate responsibility (semicompatibilism). None of these is obviously correct, which is why, four decades on, the argument is still the fixed point around which the compatibilism debate turns.

Its companion Mind argument is equally important for understanding why indeterminism is no easy refuge: the same transfer intuition that threatens determined freedom threatens undetermined freedom as luck. Anyone attracted to libertarianism must answer the Mind argument exactly as anyone attracted to compatibilism must answer the Consequence Argument — and the hard incompatibilist is the theorist who concludes that neither can be answered.