When using formal logic, what are the referents of a given proposition? If we take a proposition to be of the form X is P where the subject X is some object or concept sublated to a predicate i.e. a more general concept P, what is it that X and P refer to? Logicists like Gottlob Frege would say that X refers to some object in the world while P refers to a concept; Ferdinand de Saussure would deny that X refers to anything in the real world, instead saying that it refers only to the psychological concept of some object.
Even Frege had to concede that there is a psychological aspect to reference in his Sense and Reference paper. It is difficult to bypass the representational aspect of reference. As Saussure pointed out, this is most observable when translating from one language to another: there is not a one-to-one correspondence between words in one language and another. The concept of some object in one language might include or leave out objects that the same (or similar) concept would in another language.
But when we refer to something that is only conceptual, then what we are really referring to is something that can be apprehended phenomenologically. This is most easily understood when it comes to adjectives being predicated of nouns: the house is white; the cat is soft; the tree is tall. Adjectives like white, soft, or tall are phenomenological insofar as the qualia being referred to exist only as subjective experiences within a consciousness. Whiteness is a sensation in consciousness that only arises from the mixing of electromagnetic radiation within a particular range of wavelengths; softness is something that arises through the experience of a consciousness evolved to discriminate between different tactile sensations and imbue them with value for itself; size exists only in relation to the consciousness (a tree is tall for a human, but short compared to the size of the planet).
And so, even though we experience these things, the reference to objects in the world is only true in a nominal sense, since the objects do not contain those sensations in themselves, but only as experienced phenomena.
Of course, more abstract propositions, such as “the United States is a free country” also do not make sense absent some subjective criteria. What does “the United States” actually refer to? What does the predicate “free” refer to? Certainly not tangible objects out there in the world, but concepts inside of human minds. The demarcation of land distinguishing between that which is the United States and that which is not the united states is not some objective state of affairs, but a (useful) fiction created and maintained within human minds – it is nominal, not real. Freedom is also based on the way human minds conceive it and experience it. It would not exist in the absence of conscious beings.
This brings me to why I gave this explication: are valid inferences objective? Does logic tell us something about the world, or just something about how the human mind understands the world? If I give the following syllogism (which is valid, though not necessarily sound):
All stars in the sky are white
Polaris is a star
Therefore Polaris is white
Is this objectively valid? What about if I made sure it was subjective:
All stars visible to humans appear white
Polaris is a star visible to humans
Therefore Polaris appears white
Or, if I try to make it as objective as possible:
All gravitationally self-sustaining hydrogen fusion reactors give off electromagnetic waves in the range of 400-750 nm
Polaris is a gravitationally self-sustaining hydrogen fusion reactor
Therefore, Polaris gives off electromagnetic waves in the range of 400-750 nm
The more subjective one simply adds qualifiers, but I don’t think it substantively alters the syllogism. The objective one attempts to remove anything subjective, such as how things appear, but gives a neutral description of states of affairs. But it is still grounded in rules of inference that are based on human consciousness. Would it ever be possible to determine whether logical inference is objectively valid, or are we stuck in the realm of the subjective?
There also arise issues when we consider ignorance or imprecision. When we say X is P, but have a faulty understanding of P, but by our definition of P it is true that X is P, then what can we say about this proposition or any inferences drawn from it? For instance, if I say “all mammals give live birth” this seems like part of the definition of what makes something a mammal. But what about the platypus? Was the proposition true before the discovery of the platypus? What might we think is true right now that we will find to be incorrect in the future?
Or, if we take imprecision, if I say “my house is white” but it is actually, if we examined it much more closely, a light shade of gray, does this make the proposition “my house is white” untrue? And, if I learn this fact, will that then alter the phenomenological experience I have of the house?
Or, a more topical example, if we say “this paper is an instance of gain-of-function research” what does that mean? The slippery term gain-of-function does not have clear, universally accepted necessary and sufficient criteria that could distinguish between those experiments that are gain-of-function and those experiments that are not gain-of-function, so what does the proposition “this paper is an instance of gain-of-function research” mean if the term gain-of-function does not strictly refer to anything (either concrete or conceptual)?
My own views on the epistemological issue in question have to do with a sort of pragmatist justification. A concept or predicate is true if it can be used to make correct predictions. For instance, the proposition “all stars in the sky are white” is true because, if someone asks me what color is of a star that I have never seen before, I can accurately predict that it will be (that it will appear) white; I can also predict that it will give off electromagnetic waves in the range of 400-750 nm.
Another issue, though one I have only some cursory thoughts on, is the phenomenology of actually making a logical inference. What is the actual mechanism in our consciousness that allows for some inference to “make sense” to us? When we see a syllogism:
All A are B
X is an A
Therefore, X is a B
There is a certain intellectual phenomenology (even a sort of satisfaction) that occurs where the validity of this syllogism is felt, in a way (and for lack of a better word). There is a phenomenological difference between knowing the two premises and the conclusion each independently and understanding that the conclusion follows from the two premises and is grounded in the two premises. Is that phenomenological experience there because we evolved in a world where the objective validity of certain inferences is true of things in themselves?
This could be narrowed down even further. What is the phenomenological experience of comprehension when reading a sentence? Each word has a meaning on its own, but its meaning is also determined by all the other words in a sentence. So, at what point in reading a sentence do we go from simply reading isolated words to having the words come together to form a single (though possibly complex) thought? What is the phenomenological difference between reading and comprehending the meaning of each individual word in isolation and comprehending and understanding the sentence as a whole?