[revised & reposted October 15, 1998]

  I think that van Inwagen's argument is invalid because it equivocates on the modal auxiliaries. To give a quick idea of what I think has gone wrong, consider for comparison two arguments which are transparently invalid, though they superficially resemble Modus Tollens arguments:

(a) If Lincoln was honest, he couldn't have pocketed the penny (such taking being dishonest).
(b) But it is false that Lincoln could not have pocketed the penny: after all, he was not paralyzed and did not fail to realize that the penny was (slightly) valuable and would be his for the taking.
(c) Therefore, Lincoln was not honest.

(a') If determinism is correct, then if various past events had occurred earlier, the judge could not have raised his hand at the time of the execution (since doing so would be inconsistent with the behavior issuing from and predictable from those earlier events).
(b') But it is false that the judge could not have raised his hand at the time of the execution: for he was not paralyzed or unconscious-- he certainly possessed the power to move his hand.
(c') Therefore, since the various past events did occur earlier, determinism is not correct.

  We will begin by looking at (4)-(6) of van Inwagen's argument. You will notice that 5 ends with "J could have rendered L false" rather than ending with "J could have rendered P₀ false." A glance at the explanation at the bottom of page 53 shows that this is a rhetorical choice; to make the argument more transparent, I will rewrite (5) and (6) to remove what seems to be a red herring.^[1] Next we need to look at the move from (2) to (3); I take it that (1) and (2) are unproblematic.

1. If determinism is true, then the conjunction of P₀ and L entails P.

2. If J had raised his hand at T, then P would be false.

3. If (2), then if J could have raised his hand at T, J could have rendered P false.

  Premise 2 is correct since P states that J does not raise his hand. Now what does 3 mean by "if J could have raised his hand"? It presumably means "if J had the ability at T to raise his hand;" evidently, if J had the ability at T to raise his hand, then J had the ability at T to render P false, since P states that J does not raise his hand. J's having the ability at T to raise his hand is consistent with P; but this ability is the ability to render P false. Revising (3) to talk explicitly about abilities, and similarly revising later steps, we have:

3*. If (2), then if J had the ability at T to raise his hand, then J had the ability at T to (do something which would) render P false.

4*. If J had the ability at T to (do something which would) render P false, and if the conjunction of P₀ and L entails P, then J had the ability at T to (do something which would) render the conjunction of P₀ and L false.

5*. If J had the ability at T to (do something which would) render the conjunction of P₀ and L false, then J had the ability at T to (do something which would) render P₀ false (since J could not have rendered a law of nature false).

  We have a difficulty already: to say that J cannot render a law of nature false is not to say that he lacks the ability to do something which, given certain assumptions, would render a law of nature false. For the conjunction of P₀ and L implies that J does not raise his hand; it does not imply that he lacks the ability or power to raise his hand. One possible explanation for J's not raising his hand is that he has become paralyzed or otherwise incapacitated; but this is not the only possible explanation for his not raising his hand. Thus, the verb of (6*) does not match up with the verb of (5*): van Inwagen is equivocating on the modal auxiliaries. Anyway, why is it that one cannot render a law of nature false? At the end of ß I on page 49, van Inwagen suggests that one cannot render a law of nature false because anything qualifying as a "law of nature" must, in van Inwagen's words, "come out true;" thus, nothing would count as "rendering a law of nature false."^[2] So, the modal auxiliary is no longer being used to talk about one's abilities and powers, but is used to signal that "J renders a law of nature false" is contradictory.

6*. J could not at T have (done something which would have)
rendered P₀ false (since that state of affairs already existed prior to T).

  Now, the difficulty we have at this point is that 6* does not talk about J's abilities but talks about what he "could not" do. We must then ask ourselves whether it is because of a limitation of J's abilities that he could not render P₀ false or for some other reason. It would seem that if P₀ entails P, then if J had the ability at T to render P false, he had the ability at T to render P₀ false. The only ground for saying that J cannot at T render P₀ false is that P₀ is already given as being true. But this isn't a matter of the limitations of J's abilities; the limitation of his abilities may explain why he can't fly, but it is not a fact about his abilities but a fact about logic which explains why he cannot make false something which was true before he was born.^[3] To see this, suppose that P₀ includes, contrary to van Inwagen's instructions, the fact that J will not raise his hand at T: in other words, we will temporarily suppose that it is true at T₀ that J will not raise his hand at T. Then once again it follows that J could not have raised his hand at T; but this isn't surprising or worrisome since we can easily see how J's raising his hand is inconsistent with (the special future-tensed clause of) P₀. The fact that he cannot at T render false the true statement of T₀ that he will not raise his hand is explained by the statement's being true, not by his lacking the ability to move his limbs in such a way to render false a description of a state of affairs prior to J's birth.)

7. If determinism is true, then J could not have raised his hand at T.

  Surely, this doesn't follow at all when "could not" is understood as a denial of the claim that J had the ability to raise his hand at T. (When van Inwagen writes of "can" as "has it within [one's] power" in commenting on premise (5) (6* in my revision),^[4] he shows that he understands the modal auxiliary to be referring to J's abilities. While 6* allows us to say that because J's moving his hand at T₀ is inconsistent with P₀, J did not move his hand at T, nevertheless, the "could not" in 6* signals that J's moving his hand would contradict what has been given as true. Thus, the "could not" in 6* does not imply that J was paralyzed or incapacitated or otherwise powerless at T; it only points out what the determinist explicitly says --that J's raising his hand is inconsistent with^[5] the truth of P₀. Thus, if we are careful to keep the claims about J's abilities separate from claims about what he "could do" given the truth of statements used to frame the example, we find no terrible difficulty to be revealed about determinism.

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  Let's recast the argument to make it simpler. In what follows, we will assume that determinism is true. Imagine that we have conjectured or proposed P₀ as a description of the state of the world at T₀--but we have not verified that it is an accurate one; we will, though, assume that P is a correct description of the world at T.

1. If J had raised his hand at T, then P would have been false.
2. If J had the ability at T to raise his hand, then J had the ability at T to render P₀ false.

(As we said earlier, P₀ does not entail that J lacks the ability at T to raise his hand; it only entails that he will not exercise that ability. Thus:)

2'. If J had raised his hand at T, then J would have rendered P₀ false.
3. J could not have rendered P₀ false (since P₀ was describing states of affairs existing prior to J's birth).
4. J could not have raised his hand at T.

  We need to focus on 3. We can allow 3 to be true only so long as we suppose that P₀ is a correct description of the world at T₀: if it is given that P₀ is true, then J could not (as a matter of logic) have rendered it false, and therefore could not (logically) have done something (viz., raising his hand) which would have rendered P₀ false. On the other hand, as soon as we recognize that P₀ is merely our conjecture of the state of the world at T₀, we realize that premise 3 is false; for by raising his hand at T, J would have falsified P₀ , and J did have the ability to raise his hand at T. For since P₀ implies that J will not raise his hand at T, then if J does raise his hand at T, P₀ is thereby falsified. (Similarly, if we grant that doing X at T₀ would cause an explosion at T, then the absence of an explosion at T falsifies the claim that X was done at T₀.) What this helps us to see in the original argument is this: it isn't the fact that P₀ describes a state of affairs earlier than the time when J refrains from raising his hand which forces us to say that J "could not have" raised his hand at T; the feature of the example which forces that assertion is the assumption that P₀ is true. If a true description implies that he didn't raise his hand then, of course, it cannot (logically) be true that he did raise it.

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  Finally, compare van Inwagen's argument to the following one:

1. If the description of the eye-witness is true, then Ralph broke the window with a rock.
2. Since Ralph had the ability at T to refrain from throwing a rock, Ralph had the ability to render the eye-witness description false.

(Maybe we should say, more simply: )

2'. If Ralph had refrained, he would have rendered the description false.
3. If the description is true, then Ralph could not have refrained from breaking the window. (N.B.: the "could not have" does not mean that Ralph lacked the ability.)

  This argument does not show that Ralph lacked the ability (or the "power") to refrain from throwing the rock; it only shows that his refraining is inconsistent with the eye-witness' description. Similarly, the earlier argument does not show that J lacked the ability or power to raise his hand; it only shows that his doing so is inconsistent with the causal explanation of his not having done so.

  Uses of "could" are tricky: while sometimes they are used to assert that an individual possessed the ability or power to do something, at other times they are (differently) used to assert that the individual's doing something is consistent with some other description. (You might compare these examples with some of the examples in the document, "Queer Modal Arguments," under Theory of Knowledge on this web page.) Of course there is nothing new or surprising in the claim that J's raising his hand is inconsistent with a description of prior states of affairs which implies that J will not raise his hand. Thus, van Inwagen has failed to show that determinism entails that, at T, J lacked the capacity or power to raise his hand.

--Boardman

 

 

ENDNOTES:

¹ I have merely reversed the order of van Inwagen's premises, so that his (5) corresponds to my (6*) and his (6) corresponds to my (5*)--which, in addition, I have revised by rephrasing "could" by means of the explicit "having the ability." My revision does not disturb the basic logical (Modus Tollens) pattern of the argument: van Inwagen's own (5) has the form, "If J could have rendered the conjunction of p and q false, then J could have rendered q false"--since, if J can't render the first element of the conjunction false, he would have to render the second element false in order to render the conjunction false. And, he argues, at the bottom of page 53, J cannot render p false. Then his (6) has the form that "J cannot render q, the remaining member of the conjunction, false either"--the argument for which being given on page 54. Thus, since the consequent of (4) is false, so is its antecedent, and similarly for (3). Throughout my changes, this remains a Modus Tollens argument; but I consider the rejection of van Inwagen's second member of the conjunction before I consider the rejection of the first. Since van Inwagen rejects both, the order in which we do this cannot affect the soundness of the argument.

² Are we commenting on a person's lack of power when we say that he "cannot" be his own father? He might, for example, marry his mother and even file adoption papers; but that simply wouldn't count as his becoming his own father; nor would any act qualify, since "x is the father of y" is defined as an irreflexive relation.

³ Thus, the crucial phrase here is not "before he was born," but "was true." It is a matter of logic, not a limitation of one's abilities, that one cannot make false what is true.

⁴ Watson (ed.), Free Will (Oxford: 1982), page 54.

⁵ Of course, if there were no inconsistency, the past could scarcely be said by the Determinist to "determine" the future! A "Compatibilist," the target of van Inwagen's argument, affirms that a description of the events of P₀ together with the laws of nature entails the description, P; what the Compatibilist denies (and what van Inwagen needs to show) is that J had no power, as a result of his action's being determined, to do otherwise at T than what he did do. The Compatibilist will say that since J had the power to do otherwise, he was free; what is determined is his failure to make use of this power. Thus, given a complete description of the initial conditions and a statement of the laws of nature, J could not do otherwise than refrain from raising his hand; here the modal auxiliary signals the deductive relation between premises and conclusion. But, from this, it does not follow that J could not do otherwise in the sense that he lacked the power or ability to raise his hand.