The colloquial way of defining what it means for a statement to be true is that it corresponds to reality: if I say “it is raining” and it’s also the case that it’s raining, then what I said is true; if I say “it is raining” and it’s not the case that it’s raining, then what I said is false. This is an extensional truth condition – the extension of the proposition must be the case in reality for the statement to be true. But is this really how truth works? In what follows, I am riffing on some ideas floating around in my head, so feel free to point out any problems so as to help me clarify my thoughts.

One possible way that this view of things might get muddled is when it comes to fiction. Is it a true statement that Frodo Baggins is the Ring bearer? I think most people are inclined to say yes, since the author made this stipulation, but don’t the subject “Frodo Baggins” and the Ring from the predicate not actually exist in the real world? So how can it be true given the extensional truth condition stated above (that true things correspond to reality)? We might then want to revise our notion of true to allow for propositional statements made about fictional ideas to be evaluated as truth.

However, if we allow for fictional ideas to be evaluated as truth, then how do we determine which fictional ideas are true? In other words, if I say that it’s actually Treebeard who has the ring, am I telling the truth? No such characters as Frodo or Treebeard actually exist in reality, and there does not exist anyone who is the Ring bearer since the Ring does not exist in reality, so how does one determine the truth of statements made about fictional characters? Should we defer to what is believed by the most people? If that were the case, it would be possible for Treebeard to become the Ring bearer if, for whatever reason, everyone began to believe this was the case. For all we know, it was the case that Treebeard was the real Ring bearer and for some reason everyone started to believe that Frodo is. It seems that in fiction, metaphysical claims about truth and the actual state of affairs boil down to epistemology: what is true or false about the statement “Treebeard is the Ring bearer.”

So what about presuppositional failures in statements made about actual reality? For instance, if I say “the current King of France is floating above me” is false for two reasons: the obvious one being that there is not anybody floating above me, but also because there is no such person as the “current King of France.” But what about something like “the current King of France has never shaken my hand”? It’s true that nobody who is known as the “current King of France” has ever shaken my hand, but it’s still the case that there is no such person as the “current King of France” which makes the statement false in some way: the statement “the current King of France has never shaken my hand” contains a subject, “the current King of France,” who does not exist, making it a false statement when using the extensional truth condition (a statement is true if it corresponds to reality).

Does this same failure of extensionality as a truth condition apply to abstractions? For instance, if I make the statement “America is the land of freedom” what is it I am actually talking about (forgetting whether or not you feel like freedom in America is eroding, we’ll assume the statement is true if taken in colloquial terms)? Is there something that the subject “America” extensionally refers to in reality? Does “freedom” have an extensional counterpart in the real world?

Or, what about the statement “this woman has two hands”? What, out there in the real world, does “two” refer to? We can name plenty of other things of which there are ‘two’, but we’ll be hard pressed to find “two” by itself out there in the real world.

And so, extensionality as a truth condition seems like it doesn’t work – it may be sufficient, but it is not necessary. This extensionality truth condition is often applied to what are called synthetic a posteori propositions: we discover the proposition is true by reference to the real world. Is there another sort of proposition that would help us with our problem? There is, and it’s called an analytic a priori proposition, which is true by virtue of its definition. The popular example is this: “all unmarried men are bachelors”. We know this is true because of the definition of “bachelors” – we don’t have to go looking at every unmarried man in the world and verify that they are a bachelor, we know they are because that is how bachelor is defined.

Does this solve our problem? What of the statement “America is the land of freedom”? Perhaps if we analyze this statement we can conclude that this statement is true by virtue of its definitions: we analyze what America is (maybe come up with things like “the country that has the bill of rights”) and what freedom is (maybe come up with things like “an environment that is proper for the exercise of one’s volition without infringing on the same for others”) and then analyze these definitions further, eventually coming to a point where we can say that “America” and “land of freedom” are synonymous with each other.

In the case of “this woman has two hands” we might be able to evaluate the truth of the subject (“this woman”) and predicate (“arms”) by the extensional truth condition, but what about the quantifier “two”? We might use the Fregean idea that “two” is extensionally equinumerous with all other concepts that also contain “two”, which is just a way of applying extensionality to define “two” in terms of all of the concepts that contain “two” of something, which both isn’t analytical a priori and is circular.

There is a further problem with analyticity, which was first brought up by Willard Van Orman Quine in his 1951 paper Two Dogmas of Empiricism: you can’t define analyticity without reference to synonymy, but you can’t define synonymy without reference to analyticity. This means that analyticity isn’t a coherent concept.

So, how might we say that something is true if it doesn’t satisfy extensional truth conditions and cannot be determined analytically? I would propose that statements are true if and only if:

1) the modality, quantifier, subject, and predicate all refer to mental concepts (what I will call phenomenological intensional nominalism, or PhenomIntensioNominalism, or PIN for short) that

2) are understood by all parties in a way that is significantly similar (what I will call semantic intensionality),

3) are internally coherent (no contradictions or paradoxes) with all other concepts held to be true (law of non-contradiction), and

4) can be used to make correct predictions and retrodictions (pragmatism)

To clarify, with 1) I am not suggesting a Humean sort of idealism, but more of a neo-Kantian version: PhenomIntensioNominalism (PIN) is the notion that, irrespective of whether our senses give us a faithful representation of the world, they still give us only a representation, and therefore it is only to the PIN of something that we can refer when evaluating the truth of a statement. I would also add that there is a sort of nominalism involved as well, in that when it comes to abstract and general ideas, we can only be certain that these exist as mental concepts. Whether something like “America” or “freedom” exists, we can only refer to our PIN since there is no way to actually measure these things in the real world. Hence, there is an antirealist underpinning to this notion of PhenomIntensioNominalism: it is agnostic, at best, about the reality of abstract or general ideas existing in the world.

What PIN does have, though, is that even if something like “America” or “freedom” or “two” do not have any extensionality – there is not anything in reality that corresponds to them – they do satisfy 2), 3), and 4) from above: we all understand them in significantly similar ways (or, at least, we could understand why someone uses certain words in a particular way even if we have our own preferred definition), none of them contain contradictions, and we can use them to make predictions.

Of course, as I qualified the satisfaction of condition 2) with, it is not always the case that we all share a significantly similar understanding. When I use the word “freedom”, for instance, that can mean any number of different things to different people, or even to the same person in different contexts. To me, though, this is why I think 1) from above is correct: when I use “freedom” in a sentence, I am referring to the idea of freedom I have. This is why communication can be difficult, because different people have different mental concepts for the same word. That’s a practical problem when it comes to political discourse, but to me it’s all the more evidence of the theory I am proposing here.