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material_spiritual - Material and Spiritual Conditionals...

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1 Material and Spiritual Conditionals Richard Johns Department of Philosophy UBC January 28, 2010 1. What’s Up With That? One would think that logic, as a subject, would be logical. It should make sense. Unfortunately this is not the experience of many students of logic. They find certain logical claims hard to swallow. There are two main such claims. One is the logical principle ex falso quodlibet , or “from a contradiction, anything follows”. (I won’t say anything more about that principle here.) The other is the way that conditionals are analysed in sentential logic. In short, “If A then B” is understood to mean “either A is false, B is true, or both”, which is symbolised as ¬ A B, or equivalently A B. This analysis of the (plain, indicative) conditional “If P then Q” just seems plain wrong. After all, its assertion doesn’t require that there be any logical connection between A and B. It has nothing to do with (for example) being able to infer B from A. Whereas “If A then B” seems to express that A leads logically to B, or something like that. This fact that no connection between A and B needs to exist, for the conditional A B to hold, means that some surprising inferences are valid. For example: B ---------- A B And even worse: ¬ A ----------- A B (These are easily verified, using a truth table, to be TT consequences.) How is one to deal with this (unfortunate) fact, that students don’t like the way logicians analyse the conditional? There are three main approaches.
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2 (I) Blame the conditional Barwise and Etchemendy, for example, dismiss non-truth functional connectives (such as conditionals) by saying that “their meanings tend to be vague and subject to conflicting interpretations” ( Language Proof and Logic , p. 177). I see. The poor conditional is such a wretched mess that we simply can’t have it in our (nice, clean) language! We have to put something more presentable there in instead. I must say that this seems awfully procrustean. The fact is that our semantics, based on the idea that the meaning of a sentence is its truth conditions, is inadequate to handle conditionals. So like Procrustes, rather than get a bigger bed we instead hack the legs off the conditional. (II) Blame the student A second approach is to suggest that students who see something inadequate in the standard analysis just don’t get it, and are perhaps unsuited to the study of logic. They are unable to ascend to the required level of abstraction, perhaps. Unfortunately I was myself one of these students, and apparently I still am. So this approach, though attractive, is unavailable to me. (III) Blame the system As mentioned in approach (I), FOL is based on the idea that the meaning of a sentence is its truth conditions. Perhaps this idea is not only false (which it surely is) but also inadequate for the understanding of conditionals? In that case, any “conditional” that appeared in FOL could, at best, be a shadow of the real thing. This is the approach I take.
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