My previous posts on Sobel's Logic and Theism, have been pretty favorable and made only minor criticisms or qualifications. In this post, my criticism will be much more strenuous for, in his criticism of modern modal ontological arguments, Sobel has made a serious error.
Sobel wants to argue that there is no strong presumption in favor of the possibility of a perfect being, and that, because of contrary evidence (e.g. the problem of evil), if the ontological argument is to benefit the theist (by showing that, necessarily, there is a perfect being), rather than harm the theist (by showing that a perfect being is impossible), we need strong grounds for belief in the possibility of God. My next post will discuss the overall dialectical situation for ontological arguments. Here, I am concerned with just one mistaken objection to ontological arguments. Sobel argues (pp. 92-96) that "a priori self-consistency" - the property a proposition has just in case "[n]o contradiction follows merely by virtue of the meanings of words" (p. 94) - will not create the kind of presumption the theist needs. Following William Rowe, Sobel introduces the concept of a 'magican'. The word 'magican' is to mean, 'magician that exists in the actual world.' According to Sobel (and, evidently, to Rowe), it is a priori self-consistent but nevertheless impossible that there be a magican, a a priori self-consistency is not good evidence of possibility. Sobel is mistaken about this.
To see why, we must first introduce a distinction which Sobel introduces on p. 93, the distinction between rigid and non-rigid uses of the phrase 'the actual world'. Something is a magican just in case it (exists and) is a magician in the actual world. If this is interpreted non-rigidly, then magican is a synonym of magician, for anything that is a magician actually exists and is actually a magician. (Actually, Sobel believes in non-existent objects, but let's ignore that for now.) This is because, on the non-rigid interpretation, to say that, in some world w, an object x is a magician in the actual world, is just to say that, in w, x is a magician in w. However, on the rigid interpretation, no matter what world we are talking about, 'actual world' always refers to our world - call it @. On this reading, magican is not a synonym of magician because to say that something is a magican in w is to say that that thing is a magician in @. As a result, none of the many merely possible magicians (magicians who could exist, but don't) are magicans, on the rigid interpretation.
Now, right after making this distinction, Sobel says that the concept of a magican is a priori self-consistent but impossible. However, he has forgotten the distinction drawn on the very same page (in fact, he doesn't seem to use this distinction at all). A magican is a priori self-consistent only on the non-rigid interpretation, and impossible only on the rigid interpretation, so that Sobel (and possibly also Rowe) is guilty of a fallacy of equivocation.
First, let's consider the non-rigid interpretation, and show that on this interpretation magican is a priori self-consistent and also possible. It's self-consistent, because the concept of a magician is self-consistent, and we've already shown that, on this interpretation, 'magican' is synonymous with 'magician'. But it is also possible, for a world in which there was a magician might have been actual, and then there would be a magician existing in the actual world, and that thing would be a magican.
Now the rigid interpretation. It is impossible, Sobel says, that there be a magican on the rigid interpretation, because @ does not contain a magician, and if nothing is a magician in @, then there is no world in which any object x is such that, in @, x is a magician. Since it is, in ever possible world, false that there is a magican, it is impossible that there be a magican. So far, so good. But, on the rigid interpretation, the concept magican is not a priori self-consistent either - there is a hidden contradiction in the meanings of the words. Sobel says that possible worlds are sui generis abstract objects, that are "more of the nature of propositions than sentences and of universals than paradigmatic particulars" (p. 100). For simplicity, let's suppose that possible worlds are maximal consistent sets of propositions, what Plantinga calls 'books on worlds'. Let M be the proposition that there is a magican, and m be the proposition that there is a magician. M is a priori equivalent to the proposition that possibly m &elementof; @. But sets have their members essentially. So, in fact, if we knew the meaning of @ (knew which set it referred to), we would see that it is a contradiction that that set should contain m, and so that M is self-contradictory. Of course, in real life, we can only fix the referent of @ by saying something like 'the set of all and only the (actually) true propositions', and, as a result, we can't determine a priori that M is inconsistent. However, if we do understand our words - if we understand that @ is a rigid designator of a set, and that it is part of the concept of set that sets have their members essentially - then we will understand what our situation is, and be able to see that M might not be self-consistent.
For comparison, suppose I am thinking of a number, and you are considering the proposition that the number I am thinking of is > 5. Now, on the non-rigid (de dicto) reading, it is a priori self-consistent that the number I am thinking of be > 5, because there is clearly no contradiction involved in the meanings of the words 'Kenny is thinking of a number > 5.' But, without knowing what number I am thinking of, you cannot determine a priori whether it is self-consistent that the number I am thinking of should be > 5 on the rigid (de re) reading, for I might be thinking of 2, and 2 > 5 is not self-consistent.
As a result, if possible worlds are like other abstract objects in existing necessarily and having their properties essentially, then Sobel's argument (attributed to Rowe) that a priori self-consistency is not indicative of possibility fails.Posted by Kenny at August 25, 2010 10:48 PM
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