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Some New Thoughts on Conditionals

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Abstract

The paper describes a new way of thinking about conditionals, in terms of information transfer between worlds. This way of looking at things provides an answer to some of the standard problems concerning conditionals, and undercuts the claim that indicative and subjunctive conditionals are distinct.

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Notes

  1. The verb of X may be in indicative or subjunctive moods; that of Y can be in other moods, such as interrogative or imperative. How this is possible has to be part of a full story of conditionals, but I will ignore these other moods in what follows.

  2. A referee objected that this is a conditional of the “biscuit” variety: ‘if you’d like some, there are biscuits on the sideboard’. But it seems that this just means the same as ‘there are biscuits on the sideboard and you may help yourself to them’, which is clearly not a conditional.

  3. Those who hold that moral judgments are not truth-apt have had to face a similar problem, and have suggested various ways around it. [For a survey of these, see van Roojen (2013).] To discuss how successful they are, and whether they can be applied to conditionals, would take us too far afield in the present essay. So let me just record my view that such strategies are fighting a desperate and implausible rear-guard action—and in the case of conditionals, where perfectly adequate truth conditions can be given, a quite unnecessary one.

  4. Or more generally, when evaluating the conditional \(A>B\) at world w, information is carried over from w.

  5. A referee objected concerning following pair of conditionals, made popular by Quine (1960), p. 222:

    • If Caesar had commanded the US forces in the Korean War, he would have used nuclear weapons.

    • If Caesar had commanded the US forces in the Korean War, he would have used catapults.

    In appropriate contexts, the referee claimed, both of these can be heard as true, but, whatever information is imported from the real world, there are worlds where the antecedents are true and the consequents are false. Now, I do not know enough about Caesar as a military commander or the strategic situation in the Korean War to know whether these conditionals are true. But on the assumption that Caesar was a ruthless commander (ruthless commanders being ones who always choose the most powerful weapons), there is information which imports making the conditionals true in both cases. In the first, we import the information that the North Korean War was fought in the Twentieth Century CE, that Caesar was a ruthless commander, and that the most powerful weapons in the Twentieth Century CE were nuclear. For the second, we import the information that Caesar was alive in the First Century BCE, that Caesar was a ruthless commander, and that the most powerful weapons in the First Century BCE were catapults.

  6. One difference between the two cases (pointed out to me by Franz Berto) is that in the case of fiction, though the information imported is normally true, it may not be. Suppose, for example, that there is some scientific claim, C, that was generally believed to be true in the late Nineteenth Century, but which is actually false, and that in a Doyle story Holmes presupposes this to successfully solve a case. Doyle, however, does not state C explicitly, since he assumes that his readers all know it. Now, there may well be some post-modern interpretations of the story where Holmes just got lucky. However, the natural interpretation of the story is one in which C holds.

  7. A referee cast doubt on the second claim. Surely Graham Priest would (still) have been born in London (even) if Emile Zola had written the Holmes novels? I think not. There are surely worlds where Zola wrote the stories, and the circumstances under which this happened had quite far-reaching consequences.

  8. Indeed, when logically inconsistent antecedents come into the picture (a topic that I will not pursue in this essay), consistency with the antecedent cannot even be a necessary condition.

  9. Goodman (1947), p. 115.

  10. The approach in this paper compares interestingly with that of Gauker (1987), which also evaluates a conditional by adding certain contextually determined information to the antecedent. However, it is different in notable aspects. One of these is that Gauker gives his account in terms of assertability conditions, which he distinguishes sharply from truth conditions. Another is that for him the context just is the imported information. (Whether he also requires this to be true, is not clear to me, though the remarks in his Section 6 suggest not.) A third is that Gauker endorses the difference between indicative and subjunctive conditionals. These differences deliver logics of conditionals different from that provided in this paper.

  11. Bennett (2003), p. 85.

  12. See Priest (2008), ch. 4. For the first-order extension of the semantics, see ch. 19. To handle the semantics of counter-logicals properly, the semantics need to be expanded to include impossible worlds, as in ch. 10 (10.7).

  13. In some sense, as a referee pointed out, this delivers an answer the the million dollar question. The information imported is precisely what holds in all accessed worlds. Of course, the answer is entirely uninformative philosophically.

  14. An interesting question in this context is as follows. Consider a conditional with an embedded conditional, such as \(A>(B>C)\). Is the information imported in evaluating the outer conditional the same as that imported in evaluating the inner conditional? If it is, this will verify the following condition: if \(w_{1}R_{A}w_{2}\) and \(w_{2}R_{B}w_{3}\) then \(w_{1}R_{B}w_{3}\). For if \(R_{A}\) imports the information \(\iota\) and \(R_{B}\) imports the information \(\iota\) (or more), then \(w_{3}\) is a world where B is true and all of \(\iota\) is imported. Hence, \(w_{1}R_{B}w_{3}\). Nothing said in this essay settles this matter.

  15. The main idea in what follows can be found essentially in Whittaker (2016), though it appears in a somewhat different form there.

  16. For the example concerning Antecedent Strengthening, part of the information imported in the premise is that nothing breaks the fall. If the conclusion is evaluated with the same information, it is still true. (The safety harness must have broken.) The example concerning Contraposition is slightly less straightforward. Part of the information imported into the premise is that the car is reliable. If we import that information into the conclusion, then, because of the antecedent, we end up at an impossible world. (If the car breaks down, it was not reliable.) On the present semantics, this makes the conclusion vacuously true. I note that if one deploys a semantics that allows for impossible worlds, Contraposition may fail for quite independent reasons: truth preservation forward does not guarantee falsity preservation backward.

  17. See Priest (2009), 2.4, 2.5.

  18. See, e.g., Priest (2008), 10.7, and also Berto et al. (unpublished paper).

  19. Or with a present subjunctive: ‘If Oswald shoot not Kennedy, someone else will.

  20. A referee suggested that something like the Backshift Thesis is to be found in the work of Dudman, e.g., (1983, 1984, 1989). Now, I have the highest regard for Dudman’s work on the linguistics of conditionals, its erudition and insights—and sense of humour!. However, I must confess that I struggle to combine this with a logician’s perspective on conditionals. I am therefore happy to leave the matter of Dudman’s attitude to the Backshift Thesis to those who can do this better than I can.

  21. The general behaviour and import of tenses and moods in conditionals is a very tricky subject which I am happy to leave to linguists, such as Dudman. (See previous note.)

  22. It might be suggested that the use of a past subjunctive in the antecedent mandates importing the information that it is false. Not so. There has been a burglary. The detective, assuming nothing about the mode of entry, thinks (truly), ‘If the burglar were to have come in through the window, there would be footprints outside’. All that is imported is the information that the earth outside the window is wet. For good measure, they then investigate, find the footprints, and eventually come to the conclusion that the burglar did, in fact, come in through the window. The subjunctive in the antecedent of the conditional simply indicates—as is one of its standard functions—that the detective holds the matter to be moot.

  23. Hartry and I taught a course on Conditionals in New York in the Fall of 2014. Thanks go to him for many enjoyable and insightful conversations.

  24. Edgington (1995), p. 239. I have changed her numbering.

  25. Rott (unpublished paper); quotation reformatted. He takes the pair to distinguish between what he calls epistemic (indicative) and ontological (subjunctive) conditionals. The distinction is from Linström and Rabinowicz (1995), who note that it may not necessarily line up with the grammar.

  26. Thanks to Damian Melamedoff for the point.

  27. It might appear that this strategy cannot be applied when the imported information is not a universally quantified sentence, such as ‘If I were to see Bilbo, I would see a hobbit’, where the information imported is that Bilbo is a hobbit. However, the imported information can be thought of as the universally quantified sentenec: all things identical with Bilbo are hobits.

  28. Thanks go to Monique Whittaker for the example.

  29. Thanks go to Larry Horn here.

  30. The point applies, more generally, to so called ‘Sobel Sequences’ (Sobel 1970), where the addition of successive conjuncts to the antecedent changes the information naturally taken to be imported.

  31. Versions of this paper were read to the Department of Philosophy at the University of Toronto, December 2015, the 20th Amsterdam Colloquium, University of Amsterdam, December 2015, the 4th Colombian Congress on Logic, Epistemology and the Philosophy of Science, Unversidad de los Andes, February 2016, and the conference Logic in Bochum II, June 2016. I am very grateful to those present for helpful questions and observations. I am also grateful to three referees of this journal for their helpful comments.

  32. As in the subjunctives: If I/she be allowed to speak my/her mind, it will be a very interesting occasion.

  33. As in: I loved her. I would that she loved me.

  34. As in: He told me she was married. I wish that it were not so.

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Correspondence to Graham Priest.

Appendix: The English Subjunctive

Appendix: The English Subjunctive

If one is going to discuss indicative and subjunctive conditionals, it is worth getting straight exactly what the English subjunctive is. In this appendix, I lay the matter out. The English subjunctive mood is vestigial, and is also the linguistic analogue of an endangered species. However, to the extent that it is still extant, it works like this.

English has only two tenses: present, I love, and past (imperfect), I loved. Things which are expressed by grammatical tenses in many other languages are expressed in English by using auxiliary verbs, notably have and will. So we have future, I will love, (past) perfect, I have loved, pluperfect, I had loved, future perfect, I will have loved.

Each of the two tenses has an indicative mood and a subjunctive mood. Take the present tense first. For regular verbs, the present subjunctive is the same as the infinitive, (to) love. But so is the indicative in all persons, except the third person singular, where one adds an s. So the only person in which one can tell the difference explicitly is the third person singular: she loves you (indicative); I would that she love me (subjunctive).

The most irregular verb in English is (to) be. Here, none of the persons in the indicative is the same as the infinitive (am/are/is, are/are/are). The subjunctive is, however, as in regular verbs: that is, the same as the infinitive. So the difference between indicative and subjunctive shows up in all persons. I am, I be; she is, she be; they are, they be.Footnote 32

Turning to the past tense: in regular verbs, the past subjunctive is the same as the past indicative (and so the same in all persons).Footnote 33 However, again, the verb (to) be is irregular, and the past indicative conjugates (was/were/was, were/were/were). The subjunctive in all persons is were. So the difference shows up in the first and third persons singular.Footnote 34

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Priest, G. Some New Thoughts on Conditionals. Topoi 37, 369–377 (2018). https://doi.org/10.1007/s11245-016-9438-4

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