The Consequence Argument's Unravelling: Rule (β), Agglomeration, and Why the Epistemic Objection Misses — Epoche C2
The rule at issue Rule (β), the transfer principle at the centre of Peter van Inwagen's Consequence Argument, licenses the step from 'no one has any choice about whether $p$' and 'no one has any choice about whether if $p$ then $q$' to 'no one has any choice about whether $q$'. Whether that step is valid is the question of this note. The answer is that it is not, and that the argument does come apart there — but the reason is a fact about how inability behaves under conjunction, not the epistemic limitation the essay offered when it was first published. That earlier diagnosis was wrong and is withdrawn below, with the reasons set out in full, since a right conclusion reached by a wrong route is more dangerous than a wrong conclusion. Two matters of statement come first, because the published version misreported both rules and one of the misreports is what made the epistemic objection look promising. Van Inwagen writes $\mathrm{N}p$ as an abbreviation for '$p$, and no one has, or ever had, any choice about whether $p$'. The operator is factive by stipulation: $\mathrm{N}p$ entails $p$. The two rules of his 1983 presentation are then Rule (α) : from $\Box p$, infer $\mathrm{N}p$ — where $\Box$ is broad logical necessity. No one has any choice about a necessary truth. Rule (β) : from $\mathrm{N}p$ and $\mathrm{N}(p \supset q)$, infer $\mathrm{N}q$ — where $\supset$ is the material conditional. The published essay stated (α) as a closure principle — that if no one has a choice about $p$ and $p$ entails $q$, then no one has a choice about $q$ — which is not (α) but a stronger relative of (β). And it stated (β) with '$p$ entails $q$' where van Inwagen has the material conditional $p \supset q$. That second slip is the load-bearing one: an objection about our grasp of entailments has nothing to bite on once the second premise is a claim about a plain truth-functional conditional. The argument, run out in full Let $P_0$ be a proposition specifying the total state of the world at some instant before any presently living person existed. Let $L$ be the conjunction of the laws of nature. Let $Q$ be any truth about the present — say, that I raised my hand at noon today. Determinism, on van Inwagen's rendering, is the thesis that for every such $Q$, $$\Box\bigl((P_0 \wedge L) \supset Q\bigr).$$ The two premises about choice are $\mathrm{N}P_0$, that no one has any choice about how the world was before they existed, and $\mathrm{N}L$, that no one has any choice about what the laws are. The derivation then goes: From $\Box((P_0 \wedge L) \supset Q)$, propositional logic gives $\Box(P_0 \supset (L \supset Q))$. By (α), $\mathrm{N}(P_0 \supset (L \supset Q))$. By (β) applied to $\mathrm{N}P_0$ and line 2, $\mathrm{N}(L \supset Q)$. By (β) applied to $\mathrm{N}L$ and line 3, $\mathrm{N}Q$. Since $Q$ was an arbitrary present truth, including every truth about anyone's actions, no one has any choice about anything. Note that the whole modal content enters at line 2 through (α): the conditional whose $\mathrm{N}$ the argument needs is a necessary truth, so the premise is not that anyone knows the conditional but that no one can render a necessary truth false. Why the epistemic objection has to be withdrawn The objection offered in the published essay was that claiming 'no one has a choice about ($p$ entails $q$)' outstrips our epistemic capacities, since we do not know $P_0$, do not know $L$, and cannot survey the entailment; and that the argument therefore conflates a metaphysical truth with its epistemic accessibility. There are three reasons this cannot be right, and they are worth separating. First, $\mathrm{N}$ is not an epistemic operator, and nothing in the argument requires it to be. $\mathrm{N}p$ says that $p$ is true and that no one has it in their power to have made it otherwise. It says nothing about whether anyone knows $p$, or knows that no one has a choice about it. The Consequence Argument is perfectly compatible with universal ignorance of what $P_0$ and $L$ actually are. An objection that would require the argument's premises to be known by those to whom the conclusion applies is aimed at a claim the argument never makes. Second, as the derivation shows, the conditional premise is not asserted on its own authority; it is obtained from (α), and (α)'s content is that no one can render a broadly logical necessity false. To resist line 2 one must claim that someone has it in their power to falsify a necessary truth. Whatever the merits of that claim, it has nothing to do with the limits of anyone's information. Third, the objection proves too much. If incomplete knowledge of $p$ blocked assertions of $\mathrm{N}p$, it would block $\mathrm{N}P_0$ as readily as anything else, since nobody knows the total state of the world at any past instant either. An objection that disables every application of a rule identifies no defect in the rule. That is the mark of an objection aimed at the wrong target. So the diagnosis is withdrawn. What survives, and what the rest of this note establishes, is the conclusion the essay drew from it: that (β) is where the argument fails. The reason is different and it is decisive. The real defect: (β) yields agglomeration, and agglomeration fails Fix the reading of $\mathrm{N}$ that the premises require. 'No one has any choice about whether $p$' must at least mean that $p$ is true and no one is able to render $p$ false — no one has it in their power to bring it about that $\neg p$. This is the reading on which $\mathrm{N}P_0$ and $\mathrm{N}L$ are plausible, and it is the reading under which the conclusion says something about freedom. Now observe that (α) and (β) together entail a principle about conjunction that neither states. Suppose $\mathrm{N}p$ and $\mathrm{N}q$. $p \supset (q \supset (p \wedge q))$ is a tautology, hence $\Box\bigl(p \supset (q \supset (p \wedge q))\bigr)$. By (α), $\mathrm{N}\bigl(p \supset (q \supset (p \wedge q))\bigr)$. By (β) with $\mathrm{N}