Ordinary Language Conditionals - 2005

Ordinary Language Conditionals Gilberto Gomes Associate Professor, PGCL, UENF, Brazil 2005 1. Introduction First, this paper proposes a new classification of ordinary language conditionals and discusses some of their properties. My approach is fundamentally based on the classical view that a conditional involves a sufficient condition (the antecedent) and a necessary condition (the consequent). Since the truth of the consequent is necessary for the truth of the antecedent, it is also an integral property of a typical conditional that the falsity of the consequent is sufficient for the falsity of the antecedent. Then the paper goes into the much- discussed question of the truth conditions of a conditional. Some authors maintain that conditionals are not propositions and are not bearers of a truth-value.1 Contrary to these claims, I consider ordinary language conditionals as statements that are considered true or false by the speaker and the addressee and express propositions that may be true or false. Since it involves sufficiency and necessity, a conditional is seen here as a complex sort of modal statement. ‘If’ is considered as an ordinary language operator that establishes a triple modal relation between two propositions. The paradoxes of the material conditional are avoided, as well as some problems of the alternative theories of the conditional. On the other hand, as any theory, the present one has its own problems, which, for lack of space, I will not explore in this article. 1 For accounts of different theories about conditionals, see Dorothy Edgington, “On Conditionals,” Mind 104 (1995): 235-329; Jonathan Bennett, A Philosophical Guide to Conditionals (Oxford: Clarendon Press, 2003).  2 2. Ordinary language conditionals Ordinary language conditionals are propositions of the form If A, B, or of some other related forms, where A and B are themselves propositions. Typical conditionals are used to express that the truth of A is sufficient for the truth of B and, consequently, that the truth of B is necessary for the truth of A. Logically, ‘If A, B’ is equivalent to ‘A only if B’. It also implies that the falsity of B is sufficient for the falsity of A and that the falsity of A is necessary for the falsity of B: If not-B, not-A (the contrapositive of ‘If A, B’); not-B only if not-A.2 ‘A if and only if B’ or ‘A iff B’ is the biconditional: if A, B and if B, A. Ordinary language conditionals are assertions of a compound modal relation between A and B (to be defined later). They may be true or false. Consider: (1) If Peter and Kate have brown eyes, their child will have brown eyes. (2) If Peter and Kate have blue eyes, their child will have blue eyes. Conditional (1) is false, as any biology textbook teaches us. The truth of A does not guarantee the truth of B. By contrast, conditional (2) is true: the truth of A is sufficient for inferring the truth of B. 3. The context-sensitivity of conditionals A conditional is usually asserted in a certain context. This context is often implicit. The truth or falsity of a conditional may depend on this context. A conditional is sometimes ambiguous, since it may be interpreted in different ways, by assuming different contexts. The truth of A may be sufficient for the truth of B only in the context of many other conditions that are necessary for the truth of B. When I say, for example, ‘If she comes, I’ll call you’, this does not exclude that if my telephone is broken, I will not call you, even if she comes. Her 2 Logically, a contrapositive is always possible in typical conditionals, but linguistically it may sometimes be somewhat difficult to shape. Some changes in verb tenses or other, or the use of ‘it is (not) true that’, may be necessary to avoid ambiguity or a different sense. For example, ‘If he comes, I’ll leave’. The contrapositive must not be ‘If I don’t leave, he won’t come’, which has a different meaning, but: ‘If I don’t leave, he hasn’t come’, or ‘If it’s not true that I’ll leave, it is not true that he has come’, or else ‘If I don’t leave, this shows that he hasn’t come’ (see Author’s article).  3 coming may be a sufficient condition for my calling you only in the context of a series of unstated conditions, which includes my telephone being in good order. 4. Typical conditionals In typical conditionals, A and B are contingent. That is, A may be true and B may be true, but it is not necessary that A be true or that B be true. For example, (3) If Paul is French, he is European. Paul is French, but he could have some other nationality. He is European, but he might also be non-European. However, the truth that he is French guarantees the truth that he is European. This conditional may also be interpreted in a different way. I do not know whether Paul is French. He may be French, but he may also have some other nationality. It is also uncertain whether he is European or not. However, in case it is true that he is French, it is true that he is European. In the first interpretation, A and B are true but contingent. In the second, they are possible. A second condition for a conditional to be typical is that contraposition must be valid. That is, if a conditional ‘If A, B’ is typical, it implies ‘If not-B, not-A’. If Paul is not European, he is not French. I view conditionals in which contraposition is invalid as derivative linguistic formations that originate in typical conditionals. Three examples of these will be analyzed in section 10. Typical conditionals may be causal or non-causal. Non-causal conditionals may be conceptual or non-conceptual. In conceptual conditionals, A implies B because of the concepts involved. In (3), for example, the concept of French implies that a person who is French is European, since France is in Europe. In non-conceptual non-causal conditionals, A implies B because of real life facts. For example: (4) If Jim didn’t steal the money, Bill did. The facts that the money was stolen and that only Jim and Bill had access to it justify the conditional.  4 In causal conditionals, A causes B or B causes A. Thus, they may be of two types. In sufficient-cause conditionals, A precedes B and in some way produces B. Occurrence of A (the causal factor) is sufficient to bring about B and is consequently sufficient to infer the subsequent occurrence of B (the effect). This is not to say that other factors are not necessary to bring about B. As noted above, conditionals are context-sensitive. They select an antecedent in a context where many other factors may be taken for granted. A sufficient- cause conditional presupposes that all the necessary accessory causes of B are already present or will be present before the occurrence of B. For example: (5) If the weather is good tomorrow, I’ll go to the beach. This conditional presupposes, among other things, that tomorrow I will not have changed my mind about going to the beach and it states that a good weather is the only missing condition to cause me to go to the beach tomorrow. Of course, if I wake up seriously ill tomorrow, I will not go to the beach. Thus, my being in good health is an implicit necessary condition for me to go to the beach. In a sufficient-cause conditional, B is the necessary effect of A. The second type of causal conditional is the necessary-cause conditional. In this case, B is precedes A and brings about A. B is a necessary but not a sufficient cause of A. According to the conditional, the occurrence of A (the effect) is sufficient to infer the occurrence of B (the causal factor). Thus, A is sufficient evidence of B. For example: (6) If the streets are wet, it has rained. The rain caused the streets to be wet, but the inference goes from the streets being wet to the rain. Even if it has rained, the streets may be dry due to the hot weather. Thus, the fact that it rained some hours ago is not sufficient for the streets being wet. However, it is considered necessary. According to this conditional, only the rain can make the streets wet in this town. Therefore, the condition of the streets being wet is sufficient to infer that it has rained. It is sufficient evidence for this fact.  5 5. Factual, counterfactual and uncertain-fact conditionals Counterfactual conditionals have the form ‘If A, would-B’. They are conditionals involving untrue conditions that are possible or that may be imagined to be possible. In English, counterfactual conditionals have the subjunctive in the antecedent (the if-clause) and ‘would’ in the consequent (the main clause). (7) If Mary had money, she would go to the movies. (8) If the streets were wet, it would have rained. Some authors have argued that a counterfactual may have a true antecedent and a true consequent. An interesting example was given by Alan Anderson:3 (9) If he had taken arsenic, he would have shown just these symptoms [those which he in fact shows]. It seems that this conditional would only be used in very special situations. For example, the doctor could be thinking: “It would be unsympathetic to suggest that he has probably taken arsenic. So I’ll make the default assumption that he hasn’t. Consequently, I’ll have to assume that his symptoms are due to some other cause. Still, his relatives will have to know that, if this is the case, it is also the case that, if he had taken arsenic, he would have shown symptoms that are just like the ones he is showing. Then they may perhaps consider the possibility that he has in fact taken arsenic, since the symptoms are identical.”4 Thus, the antecedent and the consequent may be true but, by using the counterfactual, the doctor is euphemistically pretending they are false. As ‘counterfactual’ is the well-established name for conditionals involving untrue conditions, I have coined the terms ‘factual conditionals’ and ‘uncertain-fact conditionals’ for the other two 3 Quoted in Dorothy Edgington, “On Conditionals,” Mind 104 (1995): 240. 4 A more precise rendering of (9) would be: ‘If he had taken arsenic, he would have shown the symptoms caused by arsenic, the appearance of which is identical to that of the symptoms he is showing.’ The appropriate factual contrapositive would be: ‘If he doesn’t have the symptoms caused by arsenic, the appearance of which is identical to that of the symptoms he is showing, he hasn’t taken arsenic.’ This would consistent with the contextual assumption intended by the doctor to avoid shocking the family.  6 types. Factual conditionals involve true conditions. They may be causal or non-causal. An example is (6), in a context in which one has already seen the wet streets. In factual conditionals, the ‘if’ is equivalent to ‘since’: ‘Since the streets are wet, it has rained.’ Uncertain-fact conditionals involve conditions that may become true or that one may discover to be true. For example, (4) and (5). Another example is (6), in a context in which one does not know yet whether the streets are wet or not. Another is (3), when the speaker does not know whether Paul is French. The contrapositive of a sufficient-cause uncertain-fact conditional (like (5)) is a necessary- cause uncertain-fact conditional. (10) If I don’t go to the beach tomorrow, [you may conclude that] the weather is not good. If (5) is true, the weather not being good is the only possible cause5 of my not going to the beach (in the context of a certain set of assumptions). Therefore, my not going to the beach tomorrow is sufficient evidence that the weather is not good. The contrapositive of a necessary-cause uncertain-fact conditional is a sufficient-cause uncertain-fact conditional. For example, in a context in which one does not know yet whether the streets are wet or not, the contrapositive of (6) is: (11) If it hasn’t rained, the streets aren’t wet. It not having rained is a sufficient cause of the streets being dry (assuming that nothing but the rain could make them wet). That is to say that the fact that the streets are dry is a necessary effect of the absence of rain. As regards a necessary-cause factual conditional, its contrapositive is a sufficient-cause counterfactual conditional. Thus, in a context in which one has already seen the wet streets, the contrapositive of (6) is: (12) If it hadn’t rained, the streets wouldn’t be wet. 5 What we call the “only possible” cause is not in fact merely possible, it is necessary.  7 Another example: (13) If she has solved this problem, she has studied algebra. (14) If she hadn’t studied algebra, she wouldn’t have solved this problem. Having solved the problem is sufficient evidence that she has studied algebra, so not having studied algebra would be a sufficient cause of not solving the problem. A sufficient-cause factual conditional has its contrapositive in a necessary-cause counterfactual conditional. For example, the contrapositive of (2) is: (15) If their child didn’t have blue eyes, Peter and Kate would not both have blue eyes. The condition in which Peter or Kate has non-blue eyes would be a necessary cause of their child’s having non-blue eyes (in the context of the absence of a relevant mutation). The contrapositive of a sufficient-cause counterfactual conditional is a necessary-cause factual conditional. For example, the contrapositive of (7) is: (16) If Mary didn’t go to the movies, [that’s because] she didn’t have money. The contrapositive of a necessary-cause counterfactual conditional is a sufficient-cause factual conditional. For example, the contrapositive of (8) is: (17) If it hasn’t rained, the streets aren’t wet. (Meaning, unlike (11): ‘Since it hasn’t rained, the streets aren’t wet.’) We thus get the following table of causal conditionals, in which new examples are given:  8 Causal Uncertain-fact Factual Counterfactual conditionals If you ate too much, you If she is a child, she Sufficient- If I pass, I’ll stay. would be fat. likes candy. If the temperature is not cause If you hadn’t studied, If she doesn’t have above 0º C, the snow you wouldn’t have HIV infection, she won’t melt. passed. doesn’t have AIDS. If the snow melts, the If she had AIDS, she Necessary- If you passed, you temperature is above 0º would have HIV have studied. C. infection. cause If you aren’t fat, you If I don’t stay, I haven’t If she didn’t like candy, don’t eat too much. passed. she wouldn’t be a child. The complete classification of conditionals would be as follows: ì Conceptual ü ì Non-causal í ï ì Uncertain-fact ï î Non-conceptual ï ï ì Typical í ý í Counterfactual ï ï ì Sufficient-cause ï ï Conditionals í î Causal í ï î Factual ï î Necessary-cause þ î Atypical 6. The truth condition of uncertain-fact conditionals A typical conditional ‘If A, B’ is certainly false when A is true and B is false. It has been much discussed whether the truth-value of a conditional can be derived from the truth-values of A and B in all cases. In propositional logic this may well be so, but not in ordinary language conditionals. I will argue that the case just mentioned is the only one in which the truth-value of a typical ordinary language conditional (false) can be derived from a conjunction of truth- values of A and B (A true and B false). The falsity of a conditional can be established in this case. However, a typical ordinary language conditional is false in other cases too. By contrast, the truth of a typical ordinary language conditional can never be established by the truth-value of its constituents. We need modal thinking to establish its truth. The following formula defines the truth condition of uncertain-fact typical conditionals. An uncertain-fact  9 typical conditional is true when, conjointly, it is possible that both A and B are true, it is possible that both A and B are false, and it is impossible that A is true and B is false, in a given context. ‘If A, B’ iff àC (A & B) & àC (~A & ~B) & □C ~ (A & ~B) (where àC: it is possible, in context C, that; □C: it is necessary, in context C, that) Consider: (18) If butter is heated, it melts. In a given context (involving initial temperature, degree of heating, etc), it is possible that butter is heated and melts, it is possible that butter is not heated and does not melt, and it is impossible that butter is heated and does not melt. That is what the conditional asserts.6 In (5), in normal conditions, it is possible that the weather is good and I go to the beach tomorrow, it is possible that the weather is not good and I do not go to the beach, and it is impossible that the weather is good and I do not go to the beach. When I state (5), that is what I want to say. Of course, I may be wrong. In cases like this, it may be easier to establish that someone believes the conditional to be true, than to prove that the conditional is true. Anyway, it is important to establish what it is for a conditional to be true. I argue that when one believes an uncertain-fact conditional ‘If A, B’ to be true, one believes that, in a certain context of assumptions, it is possible that A and B are both true, that it is possible that A and B are both false and that it is impossible that A is true and B is false. The possibility and impossibility involved in this definition are not necessarily metaphysical. Of course, we can imagine a possible world in which the weather is good tomorrow and I do not go to the beach. Thus, the possibility involved in a conditional may be merely epistemic. I 6 Note that, while the truth-value of a conjunction is determined by the truth value of the conjuncts, its possibility-value is not determined by the possibility-value of the conjuncts. (This is a theorem of modal logic.) For example: Possibly, (A) I’ll go to the movies tomorrow from 2 to 4 PM. Possibly, (B) I’ll go shopping tomorrow from 4 to 6 PM. Possibly, (C) I’ll go shopping tomorrow from 2 to 4 PM. (A & B) is possible while (A & C) is impossible, though (A), (B) and (C), independently, are all three equally possible.  10 do not know whether the weather will be good or not tomorrow, in our world. For all I know, it may be good or bad. However, for all I know, it may not be that the weather is good tomorrow and I do not go to the beach, ceteris paribus. This impossibility is questionable – one might say, for example, that no one can predict what a person will do of her own free will, not even herself. However, this is what the conditional asserts. 7. The truth condition of factual conditionals A factual typical conditional ‘If A, B’ is true, in a given context, when, conjointly, (A and B) is true but not necessary, (not-A and not-B) is false but possible, and (A and not-B) is false and impossible. (3) may be a factual conceptual conditional, when I know that Paul is really French. He is French, but this is a contingent fact: he might have another nationality. He might also be non-European. However, he might not be French and non-European at the same time. Again, we may keep away from questions of metaphysical possibility. Someone might question whether Paul could really have another nationality. Perhaps he would not be Paul if he were not French… Or one might question whether it would really be impossible for him to be French and non-European. Perhaps this could be true, if France were not in Europe… However, these questions are simply out of the contexts in which this conditional may be stated. What matters is that, according to the stance that the speaker adopts when stating the conditional, Paul could have another nationality but he could not be French and non- European at the same time. Many discussions are possible concerning whether a given true (or false) proposition is necessarily or contingently so. However, I insist that we need not go into such discussions. It is often profitable to replace the question of the truth of conditional statements with the question of one’s reasonable belief in their truth – that is, the question of what the speaker must believe about A and B in order reasonably to believe that ‘If A, B’ is true. She may be wrong, but when she believes that a factual conditional is true, she must conjointly believe that (A and B) is true, but could hypothetically be false, that (not-A and not-B) is false, but  11 could hypothetically be true, and that (A and not-B) is false, and could not possibly be true, in a given context. Sometimes, it is not even the speaker’s real beliefs that matter, but the stance she adopts when making the statement. Even if she has different beliefs, when she states the conditional, she makes as if she had these three beliefs. A conditional can (or could) be considered true by someone if these three conditions can (or could) be considered true by the same person at the same time. If all we know is that (A and not-B) is true, this suffices for establishing that ‘If A, B’ is false, since (A and not-B) being true implies that it is not impossible. So one of the three conditions is contradicted. By contrast, if all we know is that (A and B) is true, this is not sufficient for making ‘If A, B’ true, as far as ordinary language conditionals are concerned. If (A and B) is true, it may be contingently or necessarily so and the first condition is met only when it is contingently true; in addition, we do not know whether the other two conditions are met. Similarly, if (not-A and not-B) is all we know. Again, if all we know is that (not-A and B) is true, we do not know if any of the three conditions is met. A conditional says nothing about the possibility that A is false and B is true. In (3) this is possible: Paul may be non-French (for example, German) and European. In some other cases, it is impossible. (19) If this animal is a mammal, breast-feeding is the natural way of feeding its young. In (19), it is impossible that A is false and B is true. This means that the converse conditional ‘If B, A’ is also true. 8. The truth condition of counterfactual conditionals A counterfactual typical conditional is true when, conjointly, (A and B) is false but possible, (not-A and not-B) is true but not necessary, and (A and not-B) is false and impossible, in a given context. For example, in (7), Mary does not have money and will not go to the movies, but this conjunction is a contingent fact. It would be possible that she had money and went to  12 the movies. However, according to the conditional, it would be impossible that she had money and did not go to the movies. 9. The conjoint-possibility/truth table of typical conditionals Analyzing all combinations of possibility-values of the four possible conjunctions of the two truth-values of A and B, we arrive at the following table showing the truth-values of typical conditionals as a function of the possibility-values of these conjunctions.  13 If A, B If A, ~B If ~A, B If ~A, ~ B A&B A&~B ~A&B ~A&~B If ~B, ~A If B, ~A If ~B, A If B, A P P P P F F F F àA&àB P I P P T F F F àA&àB P P I P F F F T àA&àB P P P I F F T F àA&àB I P P P F T F F àA&àB P I I P T F F T àA&àB A iff B I P P I F T T F àA&àB A iff ~B P P I I □A&àB I I P P □ ~A & à B P I P I □B&àA I P I P □ ~B & à A (Atypical) N I I I □A&□B I N I I □ A & □ ~B I I N I □ ~A & □ B I I I N □ ~A & □ ~B Conjoint-possibility/truth table of typical conditionals (P: possible; I: impossible; N: necessary; à : It is possible that; □ : It is necessary that; □ ~: It is impossible that.) I claim that an ordinary language conditional is equivalent to a compound modal statement. Its truth-value is a function of three modal statements. This is of course a partial answer to the question of what makes a conditional true, since, for a complete answer, one must know how to establish the truth of these three modal statements.  14 10. Atypical conditionals Atypical conditionals are conditionals in which A, not-A, B and not-B are not all possible and those in which contraposition is invalid. For example, consider an example given by David Lewis7: (20) If Reagan was in the pay of the KGB, we’ll never find out. First of all, it is questionable whether this is really a conditional, since it may be considered an inversion of ‘We’ll never find out if [whether] Reagan was in the pay of the KGB.’ However, if we say, ‘If Reagan was in the pay of the KGB, we’ll never find out that he was’, we unquestionably have a conditional. This is an atypical conditional because it does not imply its contrapositive: ‘If we find out that Reagan was in the pay of the KGB, he wasn’t.’ Yet, we can admit that this atypical conditional involves an implicit typical conditional that justifies it: ‘If Reagan was in the pay of the KGB, somebody knows or knew it, but we’ll never find it out.’ Of course, if he was in the pay of the KGB, at least he himself and the people at the KGB knew it. What we are presented with as the consequent in the atypical conditional (‘we’ll never find it out’) appears as an adversative commentary on the consequent of the implicit typical conditional. (The contraposition of the implicit conditional is valid: ‘If nobody knows or knew that Reagan was in the pay of the KGB, he wasn’t’.) (20) has the form If A, not-f(A), where f(A) denotes a function of the truth of A. Its contrapositive would be If f(A), not-A, which is invalid because the truth of a function of A that does not deny A implies A. By contrast, the implicit conditional suggested in the previous paragraph has the form If A, f(A). Its contrapositive is If not-f(A), not-A, which is valid because the falsity of a function of A does not imply the truth of A. The same structure is present in an example given by Dorothy Edgington:8 (21) If he took arsenic, he’s showing no signs [of arsenic poisoning]. 7 David Lewis, Philosophical Papers, Volume 2 (Oxford: Oxford University Press, 1986), 155. 8 “On Conditionals,” Mind 104 (1995): 240.  15 The underlying typical conditional and the commentary on its consequent would be: ‘If he took arsenic, signs of arsenic intoxication are expected – but he is showing no such signs.’ Contraposition is also invalid in the following example (also from Lewis):9 (22) If Boris had gone to the party, Olga would still have gone. This counterfactual implies that Boris has not gone to the party, but Olga has. It would have a different meaning without the word ‘still’. What does this ‘still’ mean? It suggests that Olga would be displeased to meet Boris at the party, so that one could even think that she would give up going for this reason, although in fact she would not. So again, we can see an implicit typical conditional at the deep semantic structure of the atypical conditional: ‘If Boris had gone to the party, Olga would be displeased.’ Its contrapositive would be: ‘If Olga was not displeased, [we can infer that] Boris has not gone to the party’. From (22), we can also derive the semantically equivalent conditional: ‘If Boris had gone to the party, this fact wouldn’t have made Olga be absent.’ This is a typical conditional, for it allows deriving a valid contrapositive: ‘If it isn’t true that Boris’s having gone to the party didn’t make Olga be absent, that’s because Boris hasn’t gone to the party’ (since if he had, that would be true).10 (23) If 2+2=4, Beijing is the capital of China. This factual conditional is atypical because A is necessary. Its counterfactual contrapositive would not be valid, because China could have a different capital but 2+2 could not fail to be 4. Many people would consider (23) false, while propositional logic considers it true, but I will not make any claim about the truth or falsity of atypical ordinary language conditionals.11 9 D. K. Lewis, Counterfactuals (Cambridge, MA: Harvard University Press, 1973), 35. 10 Of course, a second, invalid, contrapositive would also be possible in this case: ‘If Boris’s having gone to the party made Olga be absent, that’s because Boris hasn’t gone to the party.’ 11 If (23) is at all meaningful in ordinary language, I would say it is an emphatic way of saying ‘If you have to agree that 2+2=4, you have to agree that Beijing is the capital of China’, meaning ‘If you have to agree that things are as they are, you have to agree that Beijing is the capital of China’. The contrapositive of this typical factual conditional would be the counterfactual ‘If you didn’t have to agree that Beijing is the capital of China, you wouldn’t have to agree that things are as they are’.  16 This atypical conditional may be contrasted with: (24) If Rome is the capital of Italy, Beijing is the capital of China. According to propositional logic, (24) is true. According to my theory, this is a typical conditional and, in ordinary language, it is simply false, because China could change its capital without Italy doing the same. 11. Possible world semantics I have proposed that a typical counterfactual conditional ‘If A, would-B’ is true when, conjointly, (A and B) is false but possible, (not-A and not-B) is true but contingent and (A and not-B) is false and impossible, in a given context. This may also be expressed using the semantics of possible worlds. We may see the context as a set of assumptions that defines a set of possible worlds in which these assumptions are true. In other words, these assumptions represent a restriction that defines a set of accessible possible worlds. A typical counterfactual will then be true when A and B are false in our world but true in some world of this set, and in no world of this set is A true and B false. Consider my definition of the truth condition of a typical factual conditional ‘If A, B’. It may be seen as equivalent to saying that this conditional is true when the set of possible worlds in which the contextual assumptions are true includes our world, in which A and B are true, some world in which not-A and not-B are true and no world in which A and not-B are true. Consider now my definition of the truth condition of typical uncertain-fact conditionals ‘If A, B’. In these, we do not know whether A and B are or will become true. Their truth condition may then be seen as equivalent to saying that the set of possible worlds in which the contextual assumptions are true includes some world in which A and B are or will become true, some world in which not-A and not-B are or will become true, and no world in which A and not-B are or will become true. In this case, we do not know whether our world belongs to the A-and-B subset or to the not-A-and-not-B subset.  17 The contextual assumptions of an uncertain-fact conditional are usually true in our present world, but they may also be false at present but expected to be true when A or not-A and B or not-B become or reveal themselves to be true. Suppose that I am exhausted today and so I will not go to the beach, although the weather is good. I then say ‘If the weather is good tomorrow, I’ll go to the beach’. I expect (among other things) that tomorrow I will be no longer exhausted. My not being exhausted is a contextual assumption that is not true in the present world, but is expected to be true tomorrow. My stating this conditional implies that, in the set of possible worlds to which my contextual assumptions apply, there is one or more than one in which the weather is good and I go to the beach tomorrow, one or more than one in which the weather is not good and I do not go to the beach tomorrow and none in which the weather is good and I do not go to the beach tomorrow. Let us say that the context of a typical conditional is a set of assumptions that defines a set W of accessible possible worlds. Let ‘v(X, w)’ stand for the valuation of X in world w, ‘T’ for true and ‘F’ for false. A typical ordinary language conditional ‘If A, B’ will then be true iff for some world w’ in W, v(A&B, w’)=T & for some world w’’ in W, v(~A&~B, w’’)=T & for every world w in W, v(A&~B, w)=F. 12. Conclusion Conditionals do not assert the truth of B, even when B is true or is considered true by the person who asserts them. Typical conditionals assert the possibility of B being true, accompanied by the truth of A; the possibility of B being false, accompanied by the falsity of A; and the impossibility of B being false, accompanied by the truth of A – all within a given context. When these two possibilities and one impossibility obtain in an independently definable context, a conditional is true in that context. This truth condition applies to the class of typical conditionals, a class that was independently defined. Within this class, different types of conditionals were distinguished, along two dimensions. These distinctions are important to avoid confusions due to different properties of the subclasses; and to reveal relations between pairs of subclasses, when it comes to contraposition.  18 For lack of space, I do not consider here the case of conditionals in which the consequent is the expression of a possibility or of a probability. I will also postpone to a future work the discussion of the question of the probability of conditionals.