How to Be Able to Do Things without Really Trying

How to Be Able to Do Things without Really TryingAuthor(s): William F. EhrckeSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 23, No. 4 (Jun., 1972), pp. 286-291Published by: SpringerStable URL: http://www.jstor.org/stable/4318730 .

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WILLIAM F. EHRCKE

HOW TO BE ABLE TO DO THINGS

WITHOUT REALLY TRYING

(Received 8 June, 1971)

Since the publication of Georg Henrik von Wright's book Nornm andAction in 1963, there has been a fair amount of discussion of the logic of action which he develops there.' There is, however, one interesting aspect of his logic of action which has not yet been pointed out. It is this: If von Wright's logic of action were correct, then it would follow from the fact that a person forbore doing something that he could thereby do a great many other things - even some things which are logically impossible. I shall call this result the 'indolent man paradox', and it will be the purpose of this note to show how this result follows from what von Wright says about his logic of action. First, however, let me give a very brief description of his logic of action and explain some of the terminology which we shall employ later on.

Von Wright's logic of action is called the 'df-calculus', and it is based on a logic of change called the 'T-calculus'. Expressions of the T-calculus are formed by putting well-formed-formulae of the propositional calculus to the left and right of the connective T. Molecular compounds of such expressions are also T-expressions. An elementary T-expression is an expression which consists of a single occurrence of T preceded by a single atomic (propositional) variable or its negation and followed by the same atomic variable or its negation. pTp and -pTp are thus examples of elementary T-expressions. A change-description is "a conjunction-sentence of some n elementary T-expressions of n different atomic variables."2 (pTp) & (qT. q) is a change-description. The connective T is read 'and next'. pT-p may thus be read, 'The world is now such that p is the case, and next it will be such that -p is the case.' If we let p represent the sentence 'The window is open', then we could read pT-p as 'The window is closing'.

Expressions of the df-calculus are formed by prefixing T-expressions with the letters d or f. Molecular compounds of such expressions are

Philosophical Studies 23 (1972) 286-291. All Rights Reserved Copyright C 1972 by D. Reidel Publishing Company, Dordrecht-Holland



TO DO THINGS WITHOUT REALLY TRYING 287

also df-expressions. d is the symbol for doing or acting, andf is the symbol for forbearing. Once again, if p represents 'The window is open', then d (pT-p) may be read, 'Some (unspecified) agent closes the window', and f (pTp) may be read 'Some (unspecified) agent forbears to keep the window open'.

The indolent man paradox arises out of von Wright's explication of 'forbearance' and two of his distribution principles for the d- and f-operators. The first of these principles, which we shall label 'Principle I', is that "the f-operator is disjunctively distributive in front of change- descriptions."3 The example which von Wright gives is that f((pT-p) & (qT-q)) equalsf(pT-p) vf(qT-q). We can generalize this by saying that if ir and af stand for any two elementary T-expressions of different atomic variables, then fQr & a) is equivalent to f(7r) vf(o). The second distribution principle, Principle II, is that "the d-operator is conjunctively distributive in front of change-descriptions".4 The example given is that d((pT-p) & (qT-q)) means the same as d(pT-p) & d(qT-q). We can generalize this by saying that if X and a are any two elementary T-expressions of different atomic variables, then d(7r & a) is equivalent to d(r) & d(o).

We come now to von Wright's definition of 'forbearance'. "An agent, on a given occasion, forbears the doing of a certain thing if, and only if, he can do this thing, but does in fact not do it."6 The 'can' in this definition must be taken in a very strong sense. It does not simply mean that the agent in question has a general ability to do the thing. That this is so is clear from several passages in Norm and Action; in particular, "At the very moment when another agent opens a window, which I have up to this moment forborne to open, the opportunity for (continued) forbearing gets lost... I can no longer forbear to open the window."6 Obviously, when someone else opens a window, I do not thereby lose my window-opening-ability. The reason I can no longer forbear opening the window is that I no longer have the opportunity to open the window. Clearly then, the sense of 'can' intended by von Wright in his definition is that the agent has both the ability and the opportunity to do the thing in question. If we let 0 stand for any T-expression, we can reformulate von Wright's definition of 'forbearance' more explicitly: An agent, on a given occasion, forbears bringing about the change described by 0, i.e. he performs the action described byf(0), just in case he has both the



288 WILLIAM F. EHRCKE

ability and the opportunity to bring about the change described by 0, i.e. to perform the act described by d(0), but does in fact not bring about that change, i.e. does not perform the act described by d(O).

Now consider the following argument. Let 7t and a represent any two elementary T-expressions of different atomic variables, and let M be an operator which represents the sort of 'can' we discussed above, i.e. M[4] will mean that the agent in question has the ability and the opportunity to perform the action 0. Now, assume that a certain agent forbears to bring about some elementary change, 7r:

(1) f(7t)

By simple propositional logic it follows that:

(2) f(7t) vf(a)

By Principle I, (2) is equivalent to,

(3) f(it & a)

By the definition of 'forbearance' discussed above, (3) entails,

(4) M[d( & a)]

By Principle IL, d(7r & a) is equivalent to d(c) & d(a). Thus,

(5) M[d(n) & d(a)]

By distributing M through the conjunction, we get,

(6) M[d(n)] & M[d(a)]

Finally, by propositional logic we derive,

(7) M[d(a)]

Steps (5) and (6) perhaps call for a little explanation. They can, of course, not be justified by an appeal to any of the standard systems of alethic modal logic, since the M-operator we are using here does not represent mere logical possibility. Someone might try to argue that (5) does not follow from (4), since we have no guarantee that substitution of equivalents preserves truth with our M-operator. However, I think that on examination this worry will be shown to be unfounded. If we accept the equivalence of d(r & a) and d(7X) & d(a), then how could the proposi-




tion expressed by (4) be true while the proposition expressed by (5) be false? It could not be because the agent had an opportunity to perform the act described by d(7r & a) but did not have an opportunity to do the act described by d(7r) & d(a), for the conditions under which these acts are possible are the same. It would have to be, then, because the agent had the ability to perform the act described by d(7r & a) but lacked the ability to perform the act described by d(rc) & d(a). Now if these action- descriptions were merely materially equivalent, then one might argue that an agent could have the ability to perform the one but not the other. It could be argued, for example, that a person might have the ability to roll dice and not have the ability to throw snake eyes, even though on a certain occasioln, his rolling the dice and his throwing snake eyes could be described as the same act. But the kind of equivalence we are talking about is stronger than this. Von Wright says in stating his distribution principle that what he is doing is to "make the intended meaning of our symbolic expressions quite clear."7 The claim is, then, that d(7r & a) and d(7r) & d(a) mean the same thing. And if we accept this claim, I do not see how one could argue that still a person might have the ability to perform the act described by the first, but fail to have the ability to perform the act described by the second.

The move from (5) to (6) and (7) is even less problematic. Surely, if a person has both the ability and opportunity to perform each of two acts, he also has the ability and opportunity to perform the first, and the ability and opportunity to perform the second. The only sort of objection to this inference which I can imagine is something like the following: Suppose that d(r) represents flicking the switch, and d(a) represents turning on the light. Suppose also that a certain person can (in von Wright's sense of 'can') flick the switch and turn on the light. It does not follow that this person can turn on the light simpliciter, for it may be that he does not on this occasion flick the switch, and flicking the switch may be the only way in which he can turn on the light. So (7), M[d(a)], does not follow from (5), M[d(7t) & d(a)]. But this conclusion does not follow. All that this argument shows is that (7'), M[ -d(7r) & d(a)], does not follow from (5). But the fact that (7') does not follow from (5) is by no means sufficient to show that (7) does not follow from (5).8

What this argument shows is that it is implicit in the way von Wright has interpreted the df-calculus that if an agent forbears to bring about



290 WILLIAM F. EHRCKE

some elementary change, then he can bring about any other elementary change whatsoever. Von Wright can hardly deny that agents often forbear to bring about elementary changes. And so, he is committed to the consequence that a given agent can do any elementary act. This is a very embarrassing consequence indeed. What this means is not simply that any given agent is virtually omnipotent, although this too is a consequence. It means as well that the agent has the opportunity to perform any elementary act. Thus, since I am at this moment forbearing to open the door, I now have both the ability and opportunity to close my window, even though it is already shut!

The conclusion to be drawn from all this is that von Wright's inter- pretation of the f-operator is not compatible with his distribution principles, for our argument in (1) through (7) can be stopped if we give up either of the distribution principles involved or change the definition of 'forbearance'. Von Wright makes the mistake of thinking that, having defined 'forbearance', he is then at liberty to accept whatever distribution principles he pleases. Notice what he says in defense of Principle II:

Now consider for example the meaning of d((pT-p) & (qT-q)). An agent, on some occasion, through his action makes both of two states vanish. Does this not mean that he makes the one and makes the other state vanish, i.e. does the above expression not mean the same as d(pT-p) & d(qT-q)?

I shall answer in the affirmative and accept the identity of the expressions. I also think this answer accords best with ordinary usage. Be it observed, however, that ordinary usage is not perfectly unambiguous in cases of this type. To say that somebody through his action has become 'responsible' for two changes in the world could be taken to mean that he effected one of the two changes, whereas the other took place independently of his action. But to say that he effected or produced the two changes would not seem quite accurate, unless he actually produced the one and also produced the other. We must not, however, be pedantic about actual usage. But we must make the intended meaning of our symbolic expressions quite clear. Therefore we rule that the d-operator is conjunctively distributive in front of change-descriptions.9

The point, of course, is that von Wright is not free to 'rule' in the way he does. The decisions a philosopher comes to about the meaning of certain action terms, like 'forbearance', will restrict what he can con- sistently say about the logical behavior of those and other related terms. It is one of the benefits of trying to construct an action logic that it helps us to make clear such interrelations, which might otherwise remain obscure.

University of Calgary




NOTES

1 Georg Henrik von Wright, Norm and Action, Humanities Press, New York; 1963. 2 Ibid., p. 33. 8 Ibid., p. 60. 4 Ibid., p. 59. 5 Ibid., p. 45. 6 Ibid., p. 47. 7 Ibid., p. 59. 8 An argument similar in form to the one given here, but in a different context, is given by R. N. McLaughlin in his article, 'Further Problems of Derived Obligation', Mind 64 (1955) 400-2. A reply, similar to mine, is given by von Wright in 'A Note on Deontic Logic and Derived Obligation', Mind 65 (1956) 507-9. 9 Von Wright, Norm and Action, p. 59.



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