Arn't mathematical statements true in all possible worlds? — Banno

Some are, for example "1+1=2" (I hope). Some are not, for example "Sum of interior angles of a triangle is always 180°."

That's the very definition of a property in first-order logic. First order logic is extensional by design.

So you using a non-standard interpretation? — Banno

As far as I know, property in first-order logic is regarded as something that can be had or satisfied by an individual and it is not necessary to interpret property as a collection.

SO for any proposition P you have:

P is true IFF it is consistent and identical with itself

Consistent with what? "Lightwave wrote this post" is consistent, but not true - I wrote this post. — Banno

This proposition describes me (Litewave) inconsistently by referring to me, a person who doesn't have the property of "having written this post", and affirming that I have the property of "having written this post". It is as if you wrote that "Someone who didn't write this post wrote this post", or "A circle is not a circle". By affirming that I have and don't have the same property, the proposition is inconsistent and therefore does not correspond to reality. It defines me as a thing that is not identical to itself and such a thing cannot exist.

Hmm. Think we might leave this here. Treating first order logic as extensional is so far as I know the only way to show that it is complete. But you treat it exclusively as intensional. Hence there is a fundamental divide.

And a few of the things you have said seem clearly incorrect.

But all this is a side issue for the main thread, and I'm no logic tutor, so let it pass.

If you think that properties are collections then reality consists only of collections, which are concrete things, because properties as abstract things that have instances don't exist. — litewave

https://youtu.be/RUzbmIKVAHo?t=47 :wink:

The nominalist cancels out the property and treats the predicate as bearing a one-many relation directly to the several things it applies to or denotes. — Goodman, p49

What I find interesting about the corresponding theory of truth is that it corresponds (for want of a better word) to the way we use the word "truth" in the legal system (at least in the USA).

When a witness in a trial swears to tell the truth, whole truth, and nothing but the truth? Basically this means that the statements (spoken, written, sign language, etc) describe events in the real world as accurately as the witness is capable of doing.