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In this comment, I wrote:
You replied:
Actually, they are both true if A itself is false. This is the import of the logical principle ex falso quodlibet.
But I take your point to be that certain logical statements (such as "A => ~~A") are true of any actual physical system.
It is true that things are a certain way. They are not some other way. So, if a territory satisfies A, it follows that it does not satisfy ~A. And this is a fact about the territory. After all, the point of a map is to be something from which you can extract purported facts about the territory.
However, what is not in the territory is the delineation of its properties into axioms, on the one hand, and theorems, on the other. There are just the properties of the territory, all co-equal, none with logical priority. The territory just is the way it is.
For example, consider the statements "A" and "~~A", where A is the application of some particular predicate to the territory. It is not as though there is one property or feature of the territory according to which it satisfies A, while there is some other property of the territory according to which it satisfies ~~A. That feature of the territory in virtue of which it satisfies A is exactly the same feature in virtue of which it satisfies ~~A.
In the logic, "A" and "~~A" are two distinct well-formed formulas, and it can be proven that one entails the other. But in the territory there are no two distinct features corresponding to these two wffs, so it's not really sensible to speak of an entailment relationship in any nontrivial sense. The territory just is the way that the territory is, and this way, being the way that the territory is, is the way that the territory is. There is nothing more to be said with regard to the territory itself, qua logical system.
What about a tautology such as "A => ~~A"? Tautologies do give us true statements about the territory. But, importantly, such a statement is not true in virtue of any feature of the territory. The tautology would have been true no matter what features the territory had. There is nothing in the territory making "A => ~~A" be true of it. In contrast, there is something in the logical system making "A => ~~A" be a theorem in it — namely, certain axioms and rules of inference such that "A => ~~A" is derivable. (Some systems with different axioms or rules of inference would not have this wff as a theorem). This is another reason why the territory ought not to be thought of as a logical system of which the features are axioms or theorems.
Thank you for comment, and I hope this reply isn't too long for you to read. I think your last sentence sums up your comment somewhat:
In support of this, you mention:
... (read more)