# ON THE TRUTH CONDITIONS OF INDICATIVE AND COUNTERFACTUAL CONDITIONALS Wylie Breckenridge

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1 ON THE TRUTH CONDITIONS OF INDICATIVE AND COUNTERFACTUAL CONDITIONALS Wylie Breckenridge In this essay I will survey some theories about the truth conditions of indicative and counterfactual conditionals. My aim is to give a taste of the issues involved, while pushing for no conclusion but this: they are difficult. By an indicative conditional I mean any statement that can be expressed in the form "If A is the case then C is the case", and I will write these as A C. By a counterfactual conditional I mean any statement that can be expressed in the form "If A were the case then C would be the case" and I will write these as A C. Three comments. First, indicative conditionals are written as A C rather than as A C to remove any presumption that they are material conditionals (even though they might turn out to be so). Second, any statement can be expressed in either of these forms if we are prepared to change its meaning, so I mean without changing its meaning or, if that seems problematic, at least in such a way that the person who made the statement agrees does not change its meaning. Third, "is the case" is intended to be tenseless - it should be understood as "is the case now, was the case in the past, and always will be the case in the future". Similarly for "were the case" and "would be the case". Specifications of time, where relevant, should be included in A and C. Although it is usually clear whether or not a given statement is a conditional and, if so, what its antecedent and consequent are, it is by no means always clear whether it is intended to be an indicative or a counterfactual. I will not try to clarify the distinction any further here, but will do so when and only when needed throughout the essay. PART I: INDICATIVE CONDITIONALS A die is about to be rolled. I guess the result and make the following statement: (1) If it's even then it will be a six. Most of us would say that if a 6 is rolled then my statement was true, and that if a 2 or a 4 is rolled then my statement was false. But if a 1, 3 or, 5 is rolled then opinions tend to diverge. Some say that it was neither true nor false. Some say that it was true (recalling, perhaps, something from elementary logic). And some say that they cannot judge its truth or falsity until they know what the result would have been if it had been even. For present purposes we can ignore people in the last case. They seem to be interpreting my statement as the counterfactual conditional: (2) If it were even then it would be a six, and here we are interested in what people say about (1) when it is interpreted as an indicative conditional. The example suggests the following: (i) we are prepared to judge indicative conditionals as true or false, so it makes sense to ask what their truth conditions are; (ii) we are Page 1 of 10

2 prepared to make those judgments solely on the basis of the truth and falsity of the antecedent and consequent, so we should be able to give their truth conditions in terms of them alone; and (iii) indicative conditionals might sometimes lack truth value, even when their antecedents and consequents do not. Mackie [1962] does not accept that indicative conditionals have truth conditions. He claims that they are expressions of condensed arguments rather than assertions of propositions, and explains observation (i) by saying that when we judge them true or false we are really judging whether or not they are acceptable. Suppose there is a cricket match this weekend. I know that the groundkeeper is proud of his pitch and that there is no alternative venue, so I assert the following: (3) If it rains then the match will be cancelled. I am, according to Mackie, expressing an argument which might more fully go something like this: "Suppose that it rains. Then if the match is played the pitch will be badly damaged. But the groundkeeper is proud of his pitch and will demand that the match is moved. But there is no alternative venue ", and so on. I am not asserting a proposition, not even the proposition that this argument exists. Rather, I am expressing the argument itself. If he is right then any search for truth conditions for indicative conditionals is in vain, and should, rather, be a search for acceptability conditions. McDermott [1999, p. 295] asks how, if indicative conditionals are condensed arguments, can we explain their use as the antecedent or consequent of other indicative conditionals? Consider these compound indicative conditionals: (4) If the match is cancelled if it rains, then the groundkeeper is proud of his pitch. (5) If the groundkeeper is proud of his pitch, then if it rains the match will be cancelled. McDermott claims that even though (5) may be thought of (in a somewhat ad hoc manner) as a condensed argument in which a second supposition is made within the scope of the first, no such treatment seems available for (4). My question to Mackie is this: what argument does he think I'm expressing when, in the case of the rolling die, I simply guess that if it's even then it will be a six? I can make the supposition that it's even alright, but I have no rational reason to go on to conclude that it will be a six. So any argument that I do offer ought to be judged unacceptable by any reasonable standard. So Mackie must say that if I make such a guess then it cannot be true. But that doesn't seem right. McDermott agrees with him that at least some indicative conditionals should be thought of as condensed arguments, but not all, and so we are left with the question of what, if any, are the truth conditions for the ones that aren't? Adams [1975] agrees with Mackie that indicative conditionals do not have truth conditions, but for quite a different reason. As well as talking about the truth of statements it is common to talk about their assertability - the (subjective) extent to which speakers are prepared to assert (or assent to) them. It is widely accepted that for a non-conditional statement, A, its assertability, Ass(A), goes by its probability of truth, P(A). That is, a speaker is prepared to assert a non-conditional statement just to the extent that he believes the statement is true. Adams hypothesised (and it seems to now Page 2 of 10

7 that aren't? (He also argues (pp ) that Mackey fails, anyway, to give a noncircular account of their acceptability conditions.) Lewis [1973; 1986, Ch. 17, Postscripts] believes that counterfactuals have truth conditions. He says that A C is vacuously true (at our world, w 0 ) if and only if there is no possible world in which A is true, and non-vacuously true if and only if there is a possible world w 1 at which A and C are both true, and which is more similar to w 0 than any other world w 2 at which A is true and C is false (That is, if and only if every closest A-world is a C-world). He says that our judgments about the similarity of possible worlds seem to be constrained by the following: (L1) It is of the first importance to avoid big, widespread, diverse violations of law. (L2) It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails. (L3) It is of the third importance to avoid even small, localized, simple violations of law. (L4) It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly. (1986, p.48; labeling altered to follow McDermott) His theory seems to assign the correct truth value to (8): Of all the worlds in which the match was struck, the ones most similar to the actual world (according to L1 - L4) are those in which (a) the match was still dry when struck, (b) the match was still wellmade when struck, (c) the match was still in the presence of oxygen when struck, and (d) all dry, well-made matches in the presence of oxygen light when struck, and in all of these the worlds the match lights when struck. Most of us evaluate counterfactuals under the assumption that things could have gone differently, and could have done so without miracles. That is, we evaluate counterfactuals under the assumption that the laws of nature are indeterministic. So truth conditions that give intuitively wrong verdicts when indeterminism is assumed cannot be the ones that we actually use. A good theory of the truth conditions of counterfactuals must work in an indeterministic world. Lewis's theory, it seems, does not. McDermott illustrates this via two examples. The first [1999, p. 304] he attributes to Morgenbesser. An (indeterministic) coin is about to be tossed. I bet on heads, it lands tails, and I lose. Then the following is intuitively true: (11) If I had bet on tails then I would have won. But Lewis's theory says that this is false. Why? Of all the closest worlds (according to L1-L4) in which I bet on tails, L1-L4 cannot distinguish between those in which the coin still lands tails (so that I win) and those in which the coin lands heads (so that I still lose). Why? First, the coin toss is indeterministic so no law is violated whether the coin lands heads or tails. So they cannot be distinguished by L1 or L3. Second, in both types of world the region of spatio-temporal perfect match with the actual world ends at the moment of the bet, so they cannot be distinguished by L2. Third, if it is of no importance to secure approximate similarity of particular fact then we cannot use L4 to distinguish them. If it is of some importance, then those worlds in which the coin lands Page 7 of 10

10 MACKIE, J. L. (1962), "Counterfactuals and Causal Laws", in R. J. Butler (ed.) Analytical Philosophy, Oxford: Blackwell, pp MCDERMOTT, M. (1996), "On the Truth Conditions of Certain 'If'-Sentences", The Philosophical Review, 105, pp (1999), "Counterfactuals and Access Points", Mind, 108, pp Page 10 of 10

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