​Chapter 3

Take a prior state A and a later state B. The determinist's account of the joint between them runs on two questions: why does B follow from A rather than something else, and how does A bring B about? It answers the first. Ask why the stone fell and the determinist says it was thrown; ask why the water boiled and he gives the temperature and the pressure. The stone was thrown and then it fell. Stones thrown always fall, and the falling has been named and made expectable.

A by itself does not explain why B follows — a description of the state at noon contains no mention of what happens at one o'clock. The determinist supplies a law: if A, then B. Now B follows necessarily, and the account is complete.

To count as a determinate state, A must be closed: whatever is not A lies outside it. A state that shaded into its successor would no longer be a state. Either B lies within A; then whatever will be true at one o'clock was true at noon under another description, nothing arrives, and the demand for production lapses along with the production. Or B lies outside A, and no operation extracts from A what A does not contain.

The law was introduced to bridge precisely that distance. But to do so it must connect with A and with B. Each connection is another joint of the same kind: why does this law apply to this state, and how does its application yield that outcome? The original distance has been divided into two, not crossed. The interpolated term makes its own joints no easier than the joint into which it was inserted.

Take the law as a real structure in the world, a necessity binding the states rather than summarizing what has been observed. The same question returns: what binds this necessity to this pair so that B actually occurs? Necessity settles what must happen; the happening remains untouched.

A holds. If A, then B. From these two, B follows. The passage looks immediate, but it can be questioned: why do these two premises yield B? Because a rule of inference is at work: "From A and if A, then B, infer B." Call that rule L₁.

L₁ answers the question but raises another​^[1]. L₁ is a statement, and the argument now has three premises: A holds, if A then B, and L₁. Why do these three yield B? A further rule is needed to bind A, the law, and L₁ together into B. Call it L₂. L₂ is a statement too; the argument now has four premises, and why these four yield B requires L₃.

The pattern repeats without limit. Each rule, meant to close the gap between premises and conclusion, becomes a premise and reopens the gap at the next level. For any Lₙ there is an Lₙ₊₁, and the conclusion is never any closer than it was at the start. Frank concluded that deriving new knowledge from given knowledge would require an infinite chain of such rules, and no infinite chain completes.

Nature performs no inference, however. A stone consults no premises and falls; a river checks no rule before running downhill. Applying a rule to a case is what someone reasoning does, and the demand for a metalaw making each law take effect — with a further metalaw — is the regress transplanted into physics, where it has no business. The regress belongs to argument.

Which locates the necessity a law carries. Between A and B no rule was consulted, applied, or used to subsume a case: two states occurred, and that was the whole of the occurrence. A law may be a real relation holding between universals rather than a summary of what has been seen, and the concession costs nothing — a relation that holds performs no inference, and inferential necessity is what the regress was about. Derivation keeps everything it had: prediction, control, the power to be shown wrong. What binds the relation to this pair so that B occurs remains untouched.

A alone is too poor — it has nothing of B in it. A-with-B is too rich — B is already there, and nothing was produced. Frank places between them a ground that carries the seed of B without carrying B. Mark it Ab — in it, b is the potential beginning of B, present as a direction, absent as a result. The stone has been thrown, and in the throw sits a tendency toward the fall, a beginning of descent, that is not yet the descent. The passage from Ab to B is a development: the seed unfolds into what it was a seed of, and a development does not leap across a gap because there is no gap to leap across.

A seed of B and of nothing else says why this transition yields this outcome rather than another — the directedness belongs to the seed's nature and does not need importing. A seed that falls short of B keeps the consequence from being given in advance. Disposition, power, mechanism — any later account of this problem repeats the move: a middle term not yet the outcome and already pointed at it.

If Ab contains B in compressed form then the ground contains its consequence, one o'clock adds nothing to noon, and the first horn has returned under the name of potential. If b falls short of B, the seed must still get to B, and the getting is the original transition given a softer name. Development is a transition whose joints have been placed too close together to see.

Why does the seed unfold this way rather than another? Because such is its nature — a residue signed as a source. Frank presents Ab as self-evident in the nature of mediation. But it is declared as a solution, and the transition it was to remove is inside it.

Regularity is the rule, and none of this is in dispute. Most transitions in the world follow stable pairings; prediction is what laws are for, and a law is doing its work whether or not it explains how nature gets from one state to the next.

But the primitive has not been removed. The determinist rejects a free act because nothing lies under it — no ground beneath, no derivation behind — and calls that a fatal defect. His own account rests on a transition he cannot derive. He has a law that says "B follows" and no explanation of the following. Pressed for an account, he offers a further law; pressed again, a power; pressed once more, he stops. Determinism moves the ungrounded joint out of the event and into the law, where nobody thinks to ask for credentials.