The liar paradox solved!

In metaphysics, I’m what you call a realist.

I don’t mean in the sense of realism vs antirealism, which is a question of the nature of truth and reality.

I mean in the sense of realism vs nominalism. Realism as for universals, abstract objects, etc.

In this sense, a realist is someone who believes in the existence of abstract objects or certain kinds of abstract objects.

(By the way, I spoke about this on today’s episode of The Philosophy Show, which is at the bottom of this post. I elaborate on it more in this written version, though.)

An abstract object is sort of a concept. It can best be explained by examples:

Hockey is an abstract object, a hockey game is a concrete object.
2 is an abstract object, 2 apples is a concrete object.
Redness is an abstract object, a red ball is a concrete object.

One type of abstract object believed in by realists of the past couple hundred years (nobody had thought of it until then) is the proposition.

A proposition is a thing that is capable of being true or false, and it exists apart from any written, spoken, or thought expression of it. It is the bearer of claims about the world.

Propositions can be true or false, and that only. And only propositions can be true or false.

And what does this have to do with the liar paradox?

The liar paradox goes like this:

This sentence is false.

An alternate version goes:

The following sentence is true.
The preceding sentence is false.

You see the problem: if you claim any of these are false, they’re true. If you claim any are true, they’re false. Contradiction.

If we’re going to be formal and proper about this, we need to restate the paradoxes as:

The proposition represented by this sentence is false.

and

The proposition represented by the following sentence is true.
The proposition represented by the preceding sentence is false.

The paradox remains. Unless...

The theory I’m about to propose, I admit, has some consequences that may seem counterintuitive, but not so counterintuitive as to be unreasonable.

I theorize that all propositions refers to things that exist. Something is not a proposition (and thus cannot be true or false) unless it refers to existing things.

An example of how this could be counterintuitive is:

The current Queen of France is 43 years old.

Most people would say this is false, but, according to my theory, it has no truth value, because it isn’t a proposition, since it refers to non-existing entities (I.e., the Queen of France). This may seem counterintuitive, not not enough so to be inconceivable.

When we apply this to

The proposition represented by this sentence is false.

we find that this is not a proposition at all, since it refers to something that doesn’t exist, namely, itself as a proposition.

The same applies to

The proposition represented by the following sentence is true.
The proposition represented by the preceding sentence is false.

The former refers to something that doesn’t exist (i.e., the following sentence as a proposition) and the latter refers to something that doesn’t exist (i.e., the former sentence as a proposition).

None of these sentences are propositions, so there’s no problem in none of them being either true or false.