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by Corry Shores
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[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]
Summary of
Graham Priest
An Introduction to Non-Classical Logic: From If to Is
Part I:
Propositional Logic
1.
Classical Logic and the Material Conditional
1.8
Subjunctive and Counterfactual Conditionals
Brief summary:
(1.8.1) A strong objection to the semantics of the material conditional and its application to natural language conditionals are sentences with similar antecedents and consequents but on account of subtle grammatical differences have opposite truth values. Priest’s examples are: {1} If Oswald didn’t shoot Kennedy someone else did. (which is true), and {2} If Oswald hadn’t shot Kennedy someone else would have. (which is false). (1.8.2) One common way to deal with the apparent inconsistency in the above examples is to distinguish them in terms of grammatical properties and say that one type is not a material conditional. When a conditional sentence is indicative, it could be material, but when it is subjunctive or counterfactual, often using “would,” it is not material. (1.8.3) The English conditional is probably not ambiguous between subjunctive and indicative moods, on account of explicit syntactical differences that maintain a clear distinction. (1.8.4) Conditionals are subjunctive when they articulate a temporal perspective located before the stated event or fact, and they are indicative if they articulate a temporal perspective where that event or fact is established.
[Grammar and the Material Conditional]
[Subjunctive or Counter-Factual Sorts of Conditional Formulations]
[The English Conditional as Not Ambiguous Between Subjunctive and Indicative Moods]
[Temporal Perspective and Conditional Mood]
Summary
[Grammar and the Material Conditional]
[A strong objection to the semantics of the material conditional and its application to natural language conditionals are sentences with similar antecedents and consequents but on account of subtle grammatical differences have opposite truth values. Priest’s examples are: {1} If Oswald didn’t shoot Kennedy someone else did. (which is true), and {2} If Oswald hadn’t shot Kennedy someone else would have. (which is false).]
[Previously in section 1.7 we examined the material conditional and objections to its semantic evaluation. In section 1.7.1 we noted the paradoxes of material implication, namely, B ⊨ A ⊃ B and ¬A ⊨ A ⊃ B. And in section 1.7.2 we noted certain English sentences using the conditional that are true according to the semantic evaluation of the material conditional but are intuitively false on account of relevance or breaking the rule of asserting the strongest, as for example, “If New York is in New Zealand then 2 + 2 = 4.” We now will consider two examples with slightly different grammatical sorts of formations which otherwise would seem, formally speaking, to have nearly identical antecedents and consequents.]
A harder objection to the correctness of the material conditional is to the effect that there are pairs of conditionals which appear to have the same antecedent and consequent, but which clearly have different truth values. They cannot both, therefore, be material conditionals. Consider the examples:
(1) If Oswald didn’t shoot Kennedy someone else did. (True)
(2) If Oswald hadn’t shot Kennedy someone else would have. (False)
(13)
[Subjunctive or Counter-Factual Sorts of Conditional Formulations]
[One common way to deal with the apparent inconsistency in the above examples is to distinguish them in terms of grammatical properties and say that one type is not a material conditional. When a conditional sentence is indicative, it could be material, but when it is subjunctive or counterfactual, often using “would,” it is not material.]
[Priest notes a common way to distinguish the two conditionals in section 1.8.1. Ones that are indicative, like:
(1) If Oswald didn’t shoot Kennedy someone else did. (True)
are candidates for the normal semantic evaluation of the material conditional. Ones that are subjunctive or counterfactual, often using the term would, like:
(2) If Oswald hadn’t shot Kennedy someone else would have. (False)
are not instances of the material conditional. Hence, even though its antecedent is false, that does not make the whole conditional true.]
In response to this kind of example, it is not uncommon for philosophers to distinguish between two sorts of conditionals: conditionals in which the consequent is expressed using the word ‘would’ (called ‘subjunctive’ or ‘counterfactual’), and others (called ‘indicative’). Subjunctive conditionals, like (2), cannot be material: after all, (2) is false, though its | antecedent is false (assuming the results of the Warren Commission!). But indicative conditionals may still be material.
(13-14)
[The English Conditional as Not Ambiguous Between Subjunctive and Indicative Moods]
[The English conditional is probably not ambiguous between subjunctive and indicative moods, on account of explicit syntactical differences that maintain a clear distinction.]
[I may not follow this next point. He writes, “The claim that the English conditional is ambiguous between subjunctive and indicative is somewhat dubious, though.” I would think that this is not the claim made above. My guess is that there are people who make a different claim, namely, that there is no way in English to clearly determine whether or not a conditional formation is either indicative or subjunctive. I am not sure what the purpose is for that claim, if even that is the claim. At any rate, if I myself think about English, I have trouble making that distinction. “If” formations to me seem like they could all be subjunctive, as if were are saying “were such to happen, then this other thing can be expected.” And then if for example the things were known in fact, then it is like filling out that supposition with actual fact, which would be like affirming the antecedent. So even if we say, “If Oswald shot Kennedy, then ...” then we in that mode of supposition say that something else would have to be so. And then the affirmation of it would not be a conditional, and thus more clearly indicative in English: “Oswald did in fact shoot Kennedy, and so ...”. At any rate, Priest’s point is that we can still distinguish them by means of the tenses or moods of the verbs involved.]
The claim that the English conditional is ambiguous between subjunctive and indicative is somewhat dubious, though. There appears to be no grammatical justification for it, for a start. In (1) and (2) the ‘if’s are grammatically identical; it is the tenses and/or moods of the verbs involved which make the difference.
(14)
[Temporal Perspective and Conditional Mood]
[Conditionals are subjunctive when they articulate a temporal perspective located before the stated event or fact, and they are indicative if they articulate a temporal perspective where that event or fact is established.]
[Priest now explains the role of time perspective in evaluating such conditionals. In the first case:
(1) If Oswald didn’t shoot Kennedy someone else did. (True)
we evaluate it from the perspective of the present moment, which happens after the fact. And since, from our temporal perspective after the fact Oswald did in fact shoot Kennedy, we would evaluate it as true. (And for that reason it is indicative. For, from the temporal perspective it involves, it is factual. I think that is what Priest is saying.) But in the second one
(2) If Oswald hadn’t shot Kennedy someone else would have. (False)
we are asked to think of the situation from before the moment when Oswald shot Kennedy was shot. (And for that reason it is subjunctive, because from that temporal perspective, it is hypothetical rather than factual that Oswald kills Kennedy. Again, I am guessing.) Priest then notes that this is the past tense of the conditional. (I guess the idea is that the conditional when referring to a past temporal perspective would be past tense.) Priest lastly explains that were both instances present tense conditional, there would no longer be this important distinction. He gives the example comparison: “‘If I shoot you, you will die’ and ‘If I were to shoot you, you would die’” (13). (I am not certain, but I am guessing the idea is the following. Both sentences hold a present temporal perspective, but the first one takes an indicative mood and the second the subjunctive.
If I shoot you, you will die. (True)
If I were to shoot you, you would die. (True)
But were we to use the past tense of the conditional for the second one, it might not be true. So:
Had I shot you yesterday, you would have died. (Maybe True, Maybe False)
But I do not see how there would be such a difference. Would you not have died then for the same reason that you would die now? As I said above, I have difficulty making this distinction so far. At this moment, I am only able to see every “if” clause as subjunctive, with the distinction being a matter of some having all true components and others not. This is just my naïve and probably mistaken sense for the English language, but I have never, phenomenologically speaking, experienced an “if” clause as having the sense of an indicative mood. Or let me be more precise. The conditional on the whole is always in the indicative mood. It is stating a fact about the conditional relation between the antecedent and the consequent. But the “if” clause for me is always, without any exception I can think of at this moment, in the subjunctive mood. Let me make my distinction more clear.
Indicative Conditional with Subjunctive Clause:
If I shoot you, you will die.
Indicative Conditional with Another Indicative Conditional Used within a Subjunctive Clause:
Were it the case that ‘if I shoot you, you will die,’ then I would not shoot you.
or
If, ‘if I shoot you, you will die,’ then I would not shoot you.
So I guess my sense is rather that the conditional as a whole is always indicative, it being the indication and factual declaration of a conditional relation between two other facts, but within that indicatively mooded compound sentence is a subjunctive clause starting with “if”, meaning something like: suppose it were the case that.... And the fact that it happens to be the case ((either now or at some other time)) would not affect the grammatical mood, which is formed or conceived independently of factual information to confirm or deny it. So I am still working on understanding this. Let me quote:)]
What these differences seem to do is to get us to evaluate the truth values of conditionals from different points in time. Thus, we evaluate (1) as true from the present, where Kennedy has, in fact, been shot. The difference of tense and mood of (2) asks us to evaluate the conditional ‘If Oswald doesn’t shoot Kennedy, someone else will’ from the perspective of a time just before Kennedy was shot. It is, in a certain sense, the past tense of that conditional. Notice that no difference of the kind between (1) and (2) arises in the case of present-tense conditionals. There is no major difference between ‘If I shoot you, you will die’ and ‘If I were to shoot you, you would die.’
(14)
From:
Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.
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