Are the Christian and Muslim Gods the same? Why not settle this in short order with a nice, crisp, Indiscernibility argument? To wit,
a. If x = y, then x, y share all intrinsic properties. (A version of the Indiscernibility of Identicals)
b. The God of the Christians and that of the Muslims do not share all intrinsic properties: the former is triune while the latter is not.
Therefore
c. The God of the Christians is not identical to that of the Muslims.
Not so fast!
With no breach of formal-logical propriety one could just as easily run the argument in reverse, arguing from the negation of (c) to the negation of (b). They are the same God, so they do share all intrinsic properties!
But then what about triunity? One could claim that triunity is not an intrinsic property. A Muslim might claim that triunity is a relational property, a property that involves a relation to the false beliefs of Christians. In other words, triunity is the relational property of being believed falsely by Christians to be a Trinity.
Clearly, a relational property of this sort cannot be used to show numerical diversity. Otherwise, one could 'show' that the morning and evening 'stars' are not the same because Shlomo of Brooklyn believes of one that it is a planet but of the other than it is a star.
Now consider a 'mind' argument.
a. If x = y, then x, y share all intrinsic properties. (A version of the Indiscernibility of Identicals)
b*. This occurrent thinking of Venus and its associated brain state do not share all intrinsic properties: my mental state is intentional (object-directed) whereas my brain state is not.
Therefore
c*. This occurrent thinking of Venus is not identical to its associated brain state.
Not so fast! A resolute token-token mind-brain identity theorist will run the argument in reverse, arguing from the negation of (c*) to the negation of (b*).
But then what about intentionality? The materialist could claim that intentionality is not an intrinsic property, but a relational one. Taking a page from Daniel Dennett, he might argue that intentionality is a matter of ascription: nothing is intrinsically intentional. We ascribe intentionality to what, in itself, is non-intentional. So in reality all there is is the brain state. The intentionality is our addition.
Now Dennett's ascriptivist theory of intentionality strikes me as absurd: it is either viciously infinitely regressive, or else viciously circular. But maybe I'm wrong. Maybe the infinite regress is benign. Can I show that it is not without begging the question?
Question for the distinguished MavPhil commentariat: Are there good grounds here for solubility-skepticism when it comes to philosophical problems?
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