Metaphysics » Lecture 10
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 those things (including our present acts) are not up to us. (van Inwagen 1983: 56)
van Inwagen (1983: §3.3) recasts the thesis of determinism:
For every instant of time, there is a proposition that expresses the state of the world at that instant;
If \(p\) and \(q\) are any propositions that express the state of the world at some instants, then the conjunction of \(p\) with the laws of nature entails \(q\). (van Inwagen 1983: 65)
State of the world is a temporary, global, description of how everything is at an instant.
We might hesitate about entails; if so, how about: where \(\mathcal{L}\) is a proposition expressing the laws of nature, the propositions \(\mathcal{L}\), \(p\), and \(¬q\) cannot all be true together.
There is a key notion that is important for connecting possible actions with determinism: having the ability to render a proposition false:
to be able to render a proposition false is to be able to arrange or modify the concrete objects that constitute one’s environment – shoes, ships, bits of sealing wax – in a way sufficient for the falsity of that proposition.
More precisely, we may define ‘\(s\) can render \(p\) false’ as follows:
It is within \(s\)’s power to arrange or modify the concrete objects that constitute his environment in some way such that it is not possible in the broadly logical sense that he arrange or modify those objects in that way and the past have been exactly as it in fact was and \(p\) be true. (van Inwagen 1983: 67–68)
This is the most general form of ability ascription; many outcomes I control indirectly, and this notion allows us to talk about all the things under my control, not only my immediate bodily movements.
Let us suppose that there was a judge who had only to raise his right hand at a certain time, \(T\), to prevent the execution of a sentence of death upon a certain criminal,… Let us further suppose that the judge – call him ‘J’ – refrained from raising his hand at \(T\)…
I shall use ‘\(T_{0}\)’ to denote some arbitrarily chosen instant of time earlier than J’s birth, ‘\(P_{0}\)’ to denote a proposition that expresses the state of the world at \(T_{0}\), ‘\(P\)’ to denote a proposition that expresses the state of the world at \(T\), and \(\mathcal{L}\) to denote the conjunction into a single proposition of all the laws of nature. All these symbols are to be regarded as ‘rigid designators’. (van Inwagen 1983: 68–70)
A modal operator like necessarily, or possibly, is a non-truth functional one-place sentential connective.
We can demonstrate this by considering two sentences \(p\) and \(q\) which have the same truth-value, but where \(\mathcal{O}p\) and \(\mathcal{O}q\) differ in truth value.
So let \(p\) be the falsehood \(2+2=5\), and \(q\) be the falsehood Antony is 50 years old. But:
We can’t therefore capture the meaning of a modal operator using a truth table, unlike, e.g., \(¬\). But we can characterise it using inference rules. So, for example, using \(\square\) to represent necessarily, this rule is valid:
Van Inwagen’s third (version of the) argument uses a distinctive modal operator \(N\). The intended interpretation of \(Np\) is this:
\(p\) and no one has, or ever had, any choice about whether \(p\). (van Inwagen 1983: 93)
If \(b\) represents the proposition the universe began with a Big Bang, then presumably \(b\) is true of our universe, and true that no one (God aside) ever had any choice about whether there was a Big Bang – we all came on the scene too late. So \(Nb\) is true.
There are two rules which van Inwagen takes to govern the behaviour of \(N\):
\(\square ((P_{0} \wedge \mathcal{L}) \to P)\) (Follows from definition of determinism, because when \(\phi\) can’t be true together with \(¬\psi\), then if \(\phi\), \(\psi\) is necessary.)
\(\square (P_{0} \to (\mathcal{L} \to P))\) (Elementary logic of the material conditional ‘\(\to\)’, 1)
\(N(P_{0} \to (\mathcal{L} \to P))\) (2, rule \(\alpha\))
\(NP_{0}\) (premise)
\(N(\mathcal{L} \to P)\) (3, 4, rule \(\beta\))
\(N\mathcal{L}\) (premise)
\(NP\) (5, 6, rule \(\beta\))
The conclusion (7) is incompatible with the judge having free choice over whether he raises his hand. Hence his action is unfree. The argument obviously can be generalised to any action, and hence supports incompatibilism.
The options for the compatibilist, who wants to retain the possibility of both determinism and free action, are: reject premise (4); reject premise (6); reject rule (\(\alpha\)); or reject rule (\(\beta\)).
The incompatibilist, like van Inwagen, has an easier response to the argument: accept the conclusion, or reject determinism (and hence premise 1). The latter is van Inwagen’s preferred route.
Rule (\(\alpha\)) is unchallengable:
I do not see how anyone could reject rule (\(\alpha\)). If (\(\alpha\)) is invalid then it could be that someone has a choice about what is necessarily true. (van Inwagen 1983: 96)
I do not see how anyone could reject ‘\(NP_0\)’ or ‘\(NL\)’. My reasons are essentially those I gave in support of … premises [(12)] and [(13)] of the First Formal Argument. The proposition that \(P_{0}\) is a proposition about the remote past. We could, if we like, stipulate that it is a proposition about the distribution and momenta of atoms and other particles in the inchoate, presiderial nebulae. Therefore, surely, no one has any choice about whether \(P_{0}\). The proposition that \(\mathcal{L}\) is a proposition that ‘records’ the laws of nature. If it is a law of nature that angular momentum is conserved, then no one has any choice about whether angular momentum is conserved, and, more generally, since it is a law of nature that \(\mathcal{L}\), no one has any choice about whether \(\mathcal{L}\). (van Inwagen 1983: 96)
Van Inwagen’s defence of (\(\beta\)) is to point out (i) its seeming self-evidence; (ii) its apparent correctness in other cases; and (iii) the reliance on it by others, particularly those who are involved in the biological determinism debate.
Some compatibilists may deny (\(\beta\)); many did (e.g., Gallois 1977). Many such denials seem to beg the question (see van Inwagen 1983: 102–4).
So the charge of ‘begging the question’ must involve something more. The traditional fallacy of begging the question is: to accept the premises because you accept the conclusion. To reject rule (\(\beta\)) only because it leads to a conclusion you reject seems to be an instance of this informal fallacy.
As van Inwagen accepts the premises because of their intuitive plausibility, he avoids the traditional charge.
Some argue – by direct counterexample, not appeal to compatibilism – that (\(\beta\)) is invalid.
For example, (\(\beta\)) entails this rule:
McKay and Johnson (1996) argue this rule has counterexamples; and thus (\(\beta\)) is problematic. Van Inwagen ends up agreeing: ‘Agglomeration is therefore invalid, and the invalidity of (\(\beta\)) follows from the invalidity of Agglomeration’ (van Inwagen 2000: 4).
The following counterexample shows that the principle of agglomeration is invalid:
Suppose that I do not toss a coin, but could have.
\(p\) = the coin does not fall heads.
\(q\) = the coin does not fall tails.Both premises of agglomeration are true, ‘\(Np\)’ and ‘\(Nq\)’; no one can choose to falsify \(p\) (no one can choose to make the coin fall heads) and no one can choose to falsify \(q\) (no one can choose to make the coin fall tails). The conclusion, ‘\(N (p \wedge q)\)’, is false, however. I could have chosen to make ‘\((p \wedge q)\)’ false by choosing to toss the coin, so I had a choice about whether ‘\((p \wedge q)\)’ is true. (McKay and Johnson 1996: 115)
If determinism is true, then the conjunction of \(P_{0}\) and \(\mathcal{L}\) entails [or necessitates] \(P\). (premise, definition of determinism)
It is not possible that: J could have raised his hand at \(T\) and \(P\) be true. (premise, definition of \(P\))
If J could have raised his hand at \(T\), J could have rendered \(P\) false. (From 9, logic)
If J could have rendered \(P\) false, and if the conjunction of \(P_{0}\) and \(\mathcal{L}\) entails \(P\), then J could have rendered the conjunction of \(P_{0}\) and \(\mathcal{L}\) false. (premise)
If J could have rendered the conjunction of \(P_{0}\) and \(\mathcal{L}\) false, then J could have rendered \(\mathcal{L}\) false. (premise)
J could not have rendered \(\mathcal{L}\) false. (premise)
If determinism is true, then if J could have raised his hand at \(T\), J could have rendered \(\mathcal{L}\) false. (8, 10, 11, 12)
If determinism is true, J could not have raised his hand at \(T\). (14, 13)
premise [(11)] is an instance … of the following… principle:
If \(s\) can render \(r\) false, and if \(q\) entails \(r\), then \(s\) can render \(q\) false.…
This principle is a trivial truth. For if \(q\) entails \(r\), the denial of \(r\) entails the denial of \(q\). Thus anything [including any arrangement of objects \(s\) can produce] sufficient in the broadly logical sense for the falsity of \(r\) is also sufficient for the falsity of \(q\). (van Inwagen 1983: 72)
Premise (12) is an instance of:
If \(q\) is a true proposition that concerns only states of affairs that obtained before \(s\)’s birth, and if \(s\) can render the conjunction of \(q\) and \(r\) false, then \(s\) can render \(r\) false. (van Inwagen 1983: 72)
This seems right: if J had raised his hand, then the distant past would (still) have been the same; and so if J had raised his hand, its the laws that would have been different – given that one or the other of them would have to be different.
Van Inwagen supports this by considering a case he regards as analogous: if I am to render false the conjunction of a historical and a non-historical proposition, it must be by rendering false the non-historical proposition.
This seems to follow immediately from whatever a law of nature is: given that the laws of nature are – at the very least – non-accidental exceptionlessly true regularities, I cannot break a law, or through any action of mine, cause a law to be broken:
if human beings can (have it within their power to) conduct an experiment or construct a device that would falsify a certain proposition, then that proposition is not a law of nature. … the laws of nature impose limits on our abilities: they are partly determinative of what it is possible for us to do. (van Inwagen 1983: 62)
Any compatibilist, who thinks that J could have raised their hand, is thereby logically committed to the antecedent of the conditional premise (12) – for J’s raising his hand would ensure that at least one of \(P_{0}\) and \(\mathcal{L}\) is false.
Since this conditional obeys modus ponens, compatibilism appears to entails that J could falsify a law of nature:
[As a compatibilist] who accepts the requisite auxiliary premises and principle of counterfactual logic, I am committed to the consequence that if I had done what I was able to do – raise my hand – then some law would have been broken. (Lewis 1981: 114)
“That is to say,” my opponent paraphrases, “you claim to be able to break the very laws of nature. And with so little effort! A marvellous power indeed! Can you also bend spoons?”
Distinguo. My opponent’s paraphrase is not quite right. He has replaced the weak thesis that I accept with a stronger thesis that I join him in rejecting. The strong thesis is utterly incredible, but it is no part of soft determinism. The weak thesis is controversial, to be sure, but a soft determinist should not mind being committed to it. The two theses are as follows.
- (Weak Thesis)
- I am able to do something such that, if I did it, a law would be broken.
- (Strong Thesis)
- I am able to break a law.
A counterfactual, ‘If it were that \(A\), then it would be that \(C\)’ is (non-vacuously) true iff and only if some (accessible) world where both \(A\) and \(C\) are true is more similar to our actual world, overall, than is any world where \(A\) is true but \(C\) is false. (Lewis 1979: 465)
- (C1)
- It is of the first importance to avoid big, widespread, diverse violations of law.
- (C2)
- It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails.
- (C3)
- It is of the third importance to avoid even small, localized, simple violations of law.
- (C4)
- It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly. (Lewis 1979: 472)
Had I raised my hand, a law would have been broken beforehand. The course of events would have diverged from the actual course of events a little while before I raised my hand, and, at the point of divergence there would have been a law-breaking event—a divergence miracle…. But this divergence miracle would not have been caused by my raising my hand. If anything, the causation would have been the other way around.… To accommodate my hypothetical raising of my hand while holding fixed all that can and should be held fixed, it is necessary to suppose one divergence miracle, gratuitous to suppose any further law-breaking.
Thus I insist that I was able to raise my hand, and I acknowledge that a law would have been broken had I done so, but I deny that I am therefore able to break a law. (Lewis 1981: 116–17)
Lewis argues that to evaluate any conditional of the form If I had raised my hand, then \(p\), we need to consider the closest possible situations in which I raise my hand.
For someone to break a law
Since the laws are at least exceptionless regularities, it is not possible to break a law in this sense; no one can satisfy clause (ii), breaking a law while it remains a law.
The weak thesis doesn’t require clause (ii), but rather, as the discussion of counterfactuals just showed, only this weaker claim:
Van Inwagen’s argument runs as follows, near enough. (I recast it as a reductio against the instance of soft determinism that I feign to uphold.) I did not raise my hand; suppose for reductio that I could have raised my hand, although determinism is true. Then it follows, given four premises that I cannot question, that I could have rendered false the conjunction \(H\mathcal{L}\) of a certain historical proposition \(H\) about the state of the world before my birth and a certain law proposition \(\mathcal{L}\). If so, then I could have rendered \(\mathcal{L}\) false. (Premise [12].) But I could not have rendered \(\mathcal{L}\) false. (Premise [13].) This refutes our supposition. (Lewis 1981: 118–19)
Lewis invites us to consider a counterfactual: had I raised my hand, the conjunction \(H\mathcal{L}\) would have been false.
Accordingly, one of these counterfactuals must be true:
On Lewis’ view, it is more important to keep the past the same than to keep the exact laws; so he rejects Different Past, but accepts:
The Weak Thesis … is the thesis that I could have rendered a law false in the weak sense. The Strong Thesis, which I reject, is the thesis that I could have rendered a law false in the strong sense.
The first part of van Inwagen’s argument succeeds whichever sense we take. If I could have raised my hand despite the fact that determinism is true and I did not raise it, then indeed it is true both in the weak sense and in the strong sense that I could have rendered false the conjunction \(H\mathcal{L}\) of history and law. But I could have rendered false the law proposition \(\mathcal{L}\) in the weak sense, though I could not have rendered \(\mathcal{L}\) false in the strong sense. So if we take the weak sense throughout the argument, then I deny Premise [13]. If instead we take the strong sense, then I deny Premise [12]. (Lewis 1981: 120)
There has been considerable debate over whether Lewis’ criteria really do manage to successfully capture the intuitive truth-conditions of counterfactuals (Fine 1975; Wasserman 2006).
Vihvelin argues that Lewis’ response is actually insensitive to this issue – that Lewis’ conclusion is that we are able to do law-violating things, but these are abilities
which we would exercise only if the past (and/or the laws) had been different in the appropriate ways. And while this may sound odd, it is no more incredible than the claim that the successful exercise of our abilities depends, not only on us, but also on the co-operation of factors outside our control. (Vihvelin 2013: 165–66)
Fatalists – the best of them – are philosophers who take facts we count as irrelevant in saying what someone can do, disguise them somehow as facts of a different sort that we count as relevant, and thereby argue that we can do less than we think – indeed, that there is nothing at all that we don’t do but can. I am not going to vote Republican next fall. The fatalist argues that, strange to say, I not only won’t but can’t: for my voting Republican is not compossible with the fact that it was true already in the year 1548 that I was not going to vote Republican 428 years later. My rejoinder is that this is a fact, sure enough; however, it is an irrelevant fact about the future masquerading as a relevant fact about the past, and so should be left out of account in saying what, in any ordinary sense, I can do. (Lewis 1976: 151)
Incompatibilists who use (IC) to express their view are not trying to make a linguistic claim. But if the standard view is right about can, the sentence (IC) has a subtle context-sensitivity.
To defend (IC), despite the context-sensitivity it involves, would involve arguing that facts about the complete distant past and the laws are always contextually salient – they can never be properly ignored (Lewis 1996: 554).
A sort of compatibilism can be defended if there are contexts in which the proposition expressed by (IC) is false, in which some of the past or the laws can be properly ignored:
Such contexts exist, and … it would certainly be premature to reject compatibilism on the basis that there exist other contexts where (IC) is true. My own view is that compatibilism is the correct attitude in ordinary contexts, largely because ordinary unreflective use is clearly compatibilist, and there is no evidence that uses of can … invariably force the whole past and the laws to be relevant in a context. (Eagle 2011: 286)