Determinism

with Terrance Tomkow

Despite its central role in so many philosophy disputes-- or perhaps because of it-- there is widespread confusion about what ‘determinism’ means.

Certainly the standard textbook definitions are wrong. Wrong in the way that definitions are wrong: they don't capture what anyone really means by the term.

On the standard definitions to say that a world is deterministic is to say that:

"Determinism is quite simply the thesis that the past determines a unique future… it is the thesis that there is at any instant exactly one physically possible future."  Van Inwagen

"…determinism says that, given the state of the world at any particular time, the laws of nature determine all future developments, down to the last detail. Another convenient way of putting the thesis is this: a complete description of the state of the world at any given time and a complete specification of the laws of the nature together entail every truth as to what events happen after that time."  Ginet

Determinism is the thesis that a complete statement of a universe’s natural laws together with a complete description of the condition of the entire universe at any point in time logically entails a complete description of the condition of the entire universe at any other point in time. Mele

…determinism is the thesis that the precise state of the Universe at any moment( a billion years ago, or five seconds ago or whatever, together with the laws of nature, determines the precise state of the Universe at any other time (999 million years ago, in one seconds time or in another 999 million years time). To put it even more precisely, let Pt be a statement that describes the exact state of the whole Universe at a particular time t, and let L be statement that describes all the laws of nature. Then Pt & L logically entail a statement that describes the exact state of the Universe at any other time. Hence if someone knew all the facts about the state of the Universe at a given moment, and they knew all the laws of nature, then they would be able to predict with certainty what the state of the Universe will be in, say, ten seconds’ time. Beebe

…determinism is the thesis that for every instant of time t, there is a proposition that expresses the state of the world at that instant, and if P and Q are any propositions that express the state of the world at some instants… the conjunction of P together with the laws of nature entails Q.  Vihvelin

Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a), the world is deterministic. Logical entailment, in a sense broad enough to encompass mathematical consequence, is the modality behind the determination in 'determinism'.  Hoefer 

And so on.

To see what's wrong with this, consider this simple, logic circuit world

W1

 

Possible world W1 is governed by the simple law:

L1  It is nomologically necessary that: A iff (B v C)

We can describe all the worlds that are nomologically possible given this law with a simple truth table

		A	B	C
	W4	T	T	T
	W3	T	F	T
	W2	T	T	F
	W1	F	F	F

W1 is deterministic according to the standard definitions. It has laws "true at all places and times". It has only one nomologically possible future given its initial condition. Its laws are not probabilistic. Given its laws and given a description of the total state of W1 at t1, we can accurately deduce the total state of the world at t2. Indeed, W1 is, on the standard definition, deterministic in both temporal directions: given the total state W1 at t2, and L1, we can deduce the state of the world at T1.

But W1 isn’t really deterministic in the sense that anyone intends.

Of course, given that A is false at W1 we know given L1 that both B and C must be false. But L1 does not require that A is false. So what would happen if A were true at W1? Would B be true, or C or both?

Notwithstanding W1’s simplicity and the clarity of its laws, there is obviously no determinate answer to these questions.

We can infer the actual future of W1 from its actual past but that we can do so is an accident of what is actually true in it. We could not predict its future if it’s past were different; different in ways its laws permit. Which is why no one would call W1 “deterministic”. Indeed W1 could serve as a poster child for what everyone means by 'indeterminism'.

To capture what we mean we have to amend the definitions. We need to say that a deterministic world is not just one whose laws entail its actual future given its actual past but one in which a unique nomologically possible future is entailed by every nomologically possible past and a unique past by each nomologically possible future.

John Earman gets it right,

Letting W stand for the collection of all physically possible worlds, that is, possible worlds which satisfy the natural laws obtaining in the actual world, we can define the Laplacian variety of determinism as follows. The world W ϵ W is Laplacian deterministic just in case for W’ ϵ W, if W and W ’ agree at any time, then they agree for all times. By assumption, the world-a-a-given-time is an invariantly meaningful notion and agreement of worlds at a time means agreement at that time on all relevant physical properties. This concept to determinism can be broken down into two subconcepts. A world W ϵ W is futuristically (respectively, historically) Laplacian deterministic just in case of any W’ ϵ W, if W and W ’ agree at any time then they agree for all later (respectively, earlier) times. A Primer on Determinism, p.13.

Why do so many get it wrong? We think it not so much a matter of carelessness but as the upshot of a kind of philosophical wishful thinking. The wish is that the “nomological” in nomological determinism would go away. Recall Hoefer’s claim that:

"Logical entailment, in a sense broad enough to encompass mathematical consequence, is the modality behind the determination in 'determinism.'"

Hoefer wants the only kind of necessity involved in determination to be logical. He wants to see the determination of facts as simply a matter of their entailment by the more general truths we call “laws”. But determination means more than that. When we speak about determinism we suppose not just that there are laws of nature that describe general truths about the way world is but that they also, somehow, circumscribe the ways the world can be.

Unsurprisingly, David Lewis gets the definition right:

A deterministic system of laws is one such that, whenever two possible worlds obey the laws perfectly, then either they are exactly alike throughout all of time, or else they are not exactly alike through any stretch of time. They are alike always or never. They do not diverge, matching perfectly in their initial segments but not thereafter; neither do they converge. Let us assume, for the sake of the argument that the laws of nature of our actual world are in this sense deterministic.  Lewis 

By explicitly quantifying over nomologically possible worlds, Lewis captures the modal commitments the standard definitions overlook. His definition makes clear how much we are assuming when we assume for the sake of any philosophical argument that determinism is true.

And yet we contend that even Lewis does not get determinism right. Lewis gets it wrong because he has other metaphysical doctrines that prevent him from properly understanding the implications of determinism.

Counterfactual determinism

Here, across the centuries, two great systematic metaphysicians directly contradict each other.

“… ultimately, because of the connection of things, the whole universe with all its parts would be very different, and would have been a different one from the beginning if the least thing in it went differently from how it does go. On account of this, it is not the case that events are necessary, but it is the case that they are certain, given the choices that God made of this possible universe, whose concept contains this sequence of things.” Leibniz

“Under determinism any divergence… requires some violation of the actual laws. If the laws were held sacred, there would be no way to get rid of e without changing all of the past; and nothing guarantees the change could be kept negligible except in the recent past. That would mean that if the present were ever so slightly different, then all of the past would have been different—which is absurd. Lewis

 

Leibniz is asserting counterfactual determinism.

Counterfactual Determinism
However the world happens to be: If the world had been different in any respect at any time then it would have been different in some respect at every moment in the future and the past.

Lewis accepts that nomological determinism entails counterfactual determinism going forward. That is, he agrees that, in a deterministic world, if things were different at any time they would be different at every time thereafter. And he does not deny that, in a deterministic world, if things were different now then things would typically have to be different in the recent past. What he denies is that the past would have to be different at every moment. This denial is a direct consequence of his account of counterfactuals.

When we evaluate a counterfactual of the form:

If A had been the case at t1 then C would have been the case at t2

We consider whether C is true at worlds like ours at which A is true. But because Lewis does not “hold the laws sacred”, he doesn’t think that we are constrained to consider worlds that obey the laws of the actual world. Indeed, Lewis supposes that, if the actual non-A world is deterministic, then the closest worlds where A happens will always be ones in which A is the upshot of “miracle” -- an event contrary to the laws of the actual world-- which occurs at or shortly before t1. The histories of such worlds—the way things would be if A-- are exactly like ours right up until the moment of the miracle.

For Lewis, “Backtrackers”-- counterfactuals which assert that the remote past would have been different in some non-miraculous respect if the present were otherwise-- are always false.

But Lewis’ theory is not the only one on offer. In past posts we have argued for a different theory: Jonathan Bennett’s Simple Theory of Counterfactuals.

Bennett’s theory does “hold the laws sacred”. It holds that when we evaluate

If A had been the case at t1 then C would have been the case at t2

we must restrict ourselves to considering only nomologically possible worlds at which A is true. If the world is nomologically deterministic, in the modally relevant sense, it must be that every nomologically possible world has a different past and future than every other nomologically possible world. If worlds diverge at any time, they must diverge at every time. If that is so then the closest nomologically possible A world must always be one which differs from the actual world at every moment.

Thus Bennett’s theory vindicates Leibniz: Nomological Determinism entails Counterfactual Determinism. And that, we submit, is yet another argument in favor of Bennett’s Simple Theory.