Saturday, July 31, 2004

More on the Status of Logical Laws

Message text written by Richard Carrier
>>Hello, Victor!

On Wednesday, July 28, 2004, at 01:16 PM, Victor Reppert wrote:

Bill: Thanks for weighing in. Carrier's comments about the laws of physics and the laws of logic seem odd. I take it if you argue that the resurrection of Jesus contravenes the laws of physics, this is not especially a devastating refutation; God could cause Jesus to rise from the grave. But we are not inclined to think it is within the powers of omnipotence to create a round square. So, doesn't that mean the laws of physics are less fundamental than the laws of logic?<<

RC: By definition, the "laws" of logic are the procedures by which one can arrive at true conclusions from true premises. Those procedures are fixed by the nature of the universe--just as all physical laws are.

BV: This obviously begs the question against Reppert. Reppert is arguing that since we can conceive of God contravening laws of physics but not the laws of logic, this gives us a reason for distinguishing the two sorts of law. One cannot respond to this by simply asserting that the laws of logic are laws of physics. That is precisely the issue. The laws of physics are logically contingent: they hold in some but not all logically possible worlds. The laws of logic, however, obviously hold in every logically possible world -- for the simple reason that they define what it is to be logically possible. Maybe one can argue against this distinction -- but then we need to see the argument.

Note that to say that a proposition is logically necessary is to say that it is true just in virtue of its logical form. But does anyone really want to assert that laws of nature are true in virtue of their logical form? Perhaps one will say that the laws of nature are metaphysically necessary -- where metaphysical necessity is distinguished from logical necessity -- but then argument is needed since most philosophers will hold that nomologically possible worlds are a proper subset of both logically possible and metaphysically possible worlds.

RC: God could only violate the laws of physics by changing the geometry of the relevant system (indeed, we might even be able to do that ourselves someday). But the necessity still holds: for any given geometry, a certain set of physical laws holds. God could never change that any more than he could, as you say, make a round square.

BV: This is confused. Suppose it is logically necessary that for any given geometry, a set of physical laws holds. Then that would be something God could not change. But that doesn't show that he couldn't change which geometry holds. From Nec(G --> L) one cannot infer Nec G or Nec L. Given that God could not alter the fact that Nec(G -->L), it does not follow that God could not alter the fact that G.

The necessity of the consequence does not entail the necessity of the consequent, or the necessity of the antecedent. It is a simple point of modal logic that a conditional statement can be necessarily true even if antecedent and consequent are contingently true. For example, it is necessarily true that if every book in my library bears my stamp, then the books on the topmost shelf of my library bear my stamp; but 'every book in my library bears my stamp' and
'the books on the topmost shelf of my library bear my stamp' both express contingent propositions, propositions which, though true, might well have been false.

RC: So physics and logic are in the same boat--they simply refer to different aspects of physical existence (one is about the way the world behaves, the other is about the way a certain goal can be accomplished within that world and all worlds relevantly similar).

BV: Non sequitur -- for the reason just given.

RC: Deductive logic is the same as physical law in this respect, because to violate the Law of Non-Contradiction, for example, God would, as withany other violation of physical law,...

BV: Note that RC is again begging the question. It needs to be argued that logical laws are physical laws, not assumed.

RC: ... have to change the relevant
geometry--but the Law of Non-Contradiction describes every geometry
that contains any physical distinctions, which is pretty much every
interesting universe. In that sense, deductive logic can be regarded as more fundamental in the same way the Laws of Thermodynamics are more fundamental than Boyle's Law, because the former apply to far more regions of the universe than the latter, and underly the latter.

The point is: the only way God could violate the Law of
Non-Contradiction is to change the geometry of existence in such a way that no distinctions would exist there--which of course would mean he could not accomplish anything useful, since he could only violate the Law of Non-Contradiction within a space where no distinctions exist,not in any other space. And what use would there be in having things happen in a universe where no distinctions exist? That is just like violating the inverse square law: God could not violate this unless he changed the geometry of space-time accordingly, but that would have numerous other unavoidable consequences as well.

BV: I have no idea what is going on now, or in the rest of Carrier's comments, which are too vague to merit response. Carrier seems to be missing the point that Reppert maintained (or at least suggested) that God could NOT violate LNC.