If we have an object x in front of us, we can ask many questions about it such as "is x red?", "does x have a mass of more than 5kg?", "is x warmer than 300K?".

Of course, you could argue these questions aren't well-defined. For example, how much of x must be red? All of it? More than half of it? Any portion of it? And what do we mean by red? When does red become orange or pink or violet? And, since color depends on reflected light, what lighting conditions are we using? Sunlight? "Black" (ultraviolet) light? Orange fluorescent light from mercury lamps? Total darkness? (in which case we'd be looking at emitted, not reflected, light).

However, we generally accept that we could find a reasonable definition of "red", and decide whether a given object is red or not.

However, we can't ask the question "does x exist"? Why not? Because the fact you can refer to x means that x must exist in some sense. For example, if we ask "do flying horses exist", we've already created the concept of flying horses. In contrast, if we ask "do sl6eyun7el exist?", we have no idea what sl6eyun7el means, so it doesn't exist even in our minds.

In our first paragraph example above, we would need to have flying horses standing in front of us to ask "do flying horses exist", in which case it's fairly obvious they do.

There is a mathematically precise way to address this issue. Although mathematicians often say "there exists x such that P(x)" or "for all x, P(x)", where P(x) is some property, they are actually being a little sloppy.

Formally, any existential ("there exists") or universal quantification ("for all") must have a "universe of discussion", or more formally, a set.

The correct forms of the earlier statements are "there exists x in set S such that P(x)" or "for all x in set S, P(x)".

How does this help? It now means we can regard the existence of x as a property of the set S, instead of as a property of x itself.

In other words, we can ask "does S have the property that one or more of its elements is a flying horse?".

This makes the answer simple: if S is the world of fiction, it is true that one or more of its elements is a flying horse; if S is the world of reality it is not true (as far as we know) that one or more of its elements is a flying horse.

And, just to be nitpicky, I realize you could put a horse on an airplane or that flying horses may exist in reality but we haven't seen them yet, but you get the idea.

Numbers are contextual too, 1: int is different from 1:real... – Mozibur Ullah – 2017-10-02T15:37:01.660

Modal logic is the logical language that deals with fictional and counterfactual situations. Possible world semantics is key in how logic deals with counterfactuals. In terms of specific difficulties in trying to formulate a logical language for this topic, quantification in modal logic is one of the most contentious topics in the subject. People like Quine said that it is nonsensical to ever allow quantification to take place in modal logic.

– Not_Here – 2017-10-02T16:07:36.823People like Ruth Barcan Marcus took the opposite view, and she specifically laid a majority of the groundwork for the actual logical language, in the same way that Kripke did a lot of the groundwork for giving modal logic its first complete semantics with possible world semantics. Quine's main attack as to why it is nonsensical to quantify modal logic is in his paper Quantifiers and Propositional Attitudes, Kripke gives a great (contemporary) response here.

– Not_Here – 2017-10-02T16:11:11.887On the standard interpretation of quantifiers in first order languages all statements that existentially quantify over fictional entities are false. Those that do not quantify but name, like “Pegasus does not exist,” can be paraphrased a la Russell by converting fictional names into predicates, "there is not a thing which is Pegasus" is plainly true. See here for other ways of dealing with even inconsistent fictions. I am not quite sure why context dependence would be a problem.

– Conifold – 2017-10-02T19:59:45.300@Conifold classical logic is context-independent, right? So … this means it's truth-preserving even in the weirdest combinations of assertions? But if one formalizes nat-lang statements like “My uncle is a plumber”, “my uncle” appears as variable

uand refers context-independent to (say) “Bob J. Miller sr.”? So there doesn't seem any work involved here. Question: is “Pegasus is a flying horse” (=TRUEin some sense!) more problematic for formalization? Because the context (if that's the right term) ‘we're just talking about Greek mythology’ applies to thewholestatement? – viuser – 2017-10-02T20:59:50.507Pragmatics deals with context not by altering the logic, rather by supplementing it by speech act theory. But I am not sure what would be special about fictional discourse in this regard. “Pegasus is a flying horse” can be paraphrased into "for every x if x is Pegasus then x is a flying horse", or have a fictionalization operator attached "according to (Greek mythology), Pegasus is a flying horse", either makes it true. – Conifold – 2017-10-02T23:26:32.833

It occured to me that "according to the fiction" operator is exactly what you mean by context. It alters the universe of discourse to whatever the named fiction posits, where flying horses, and Pegasus in particular, may well occur. Under the scope of fictionalization we can then retain classical logic with standard semantics. Formalizations of this were developed by Rosen as modal fictionalism.

– Conifold – 2017-10-03T20:00:32.557