Sorry for not having much context but taking Pegasus to be the mythological beast from greek mythology.
"To be Pegasus is to be capable of flying."
Is this definition an necessary truth or a possible (contingent) truth? Thanks
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That sentence is not a definition. A definition is an attempt to fix a meaning to a term. What you have is an attempt to establish a metaphysical necessity between an entity and a property.
The MW definition of the Pegasus:
a winged horse that causes the stream Hippocrene to spring from Mount Helicon with a blow of his hoof
What makes the sentence you list a metaphysical claim is that broadly speaking one simply cannot be Pegasus unless one has the capacity of flight. This is a necessary condition imposed on an ontological claim.
Note, the definition provides the fact that Pegasus is winged, and that having wings generally confers the status of flight. Also notice that your claim may not include other necessary conditions of being Pegasus.
To be Pegasus is to eat an apple.
Notice the truth value of this claim is contingent. It may very well be that at a given moment Pegasus is eating an apple given by Perseus, but the next day the claim would be false.
Firstly, it should be set down that those statements that fall under our concept of definition diverge into a variety of types that are yet to be clearly delineated, quite ironically for the etymology of the word 'definition'; to some extent, due to a lack of a widely accepted general theory of definitions that avail itself formal treatment, though there have been several attempts in this direction.
Therefore, not seldom, we need to refer to the cases we think typical and the function the statement serves within a specific discourse to decide on whether it is a definition or not, and if it is, what type it has.
Only after we have sufficiently clarified definitional status of a statement, we can talk about whether it is truth-apt or not, since some types of definitions are amenable to truth evaluation, some are not. For example, within the discourse of logic, when one defines '→' derivatively and stipulates that P → Q (i.e., definiendum) will be used for ¬P ∨ Q (i.e., definiens), in effect, one introduces an abbreviation that is formally eliminable. Thus, it is meaningless to assign a truth-value to this definition. Notice that our concern is not the grammatical form of the definition in a formal or natural language. The preceding example can be expressed as (P → Q) ↔ (¬P ∨ Q) in the language of propositional logic, but we cannot require that all definitions should take on this form. Probably, the topic of definitions would not be so intricate, if the matter turned only on this form. The issue is well pointed out by Karl Popper in his 1963 paper Creative and Non-Creative Definitions in the Calculus of Probability (p. 174, the emphases are in the original):
Thus our definition C is indeed an abbreviating convention. But is it no more than this? Certainly it is. The fact that it is not merely an abbreviating convention can be easily established. For a number of important theorems in which the sign of complementation does not occur fail to be demonstrable in the absence of our definition C.
I should be content with only recommending this paper, since a discussion of the ideas it involves is quite far-fetching for a single question. But it tells us to be alert that many definitions (actually, many of those useful ones) do not conserve the "balance" between the definiens and the definiendum. However, some kind of correspondence between them has to be observed also. Consider the following examples:
The first sentence is a close paraphrase (to facilitate comparisons) of the definition of even numbers usually set forth in the topic of natural numbers. It is an explicative definition; it improves our comprehension of the concept of evenness/oddness of numbers. From another perspective, it is an operational definition; it offers us what to do to separate the even numbers out of any set of numbers. Is it truth-apt? We may suppose that it is possible to separate even numbers without appealing to divisibility. It may be even said that, apart from its historical evolution (which is a matter of history of mathematics), it is quite conceivable that one who does not know how to divide, even not how to count two by two, could develop a sense of evenness by pairing the stuff around. If this supposition is agreed on, then it can be judged whether the extension of the definiens coincide (perfectly -in the present case) with the extension of the definiendum. If so, then the statement of this definition is assigned true -which, actually, it is.
The second sentence is W. V. O. Quine's criterion of ontological commitment for theories. Sure, not intended as a definition of being in its general philosophical sense, one may take it within in a restricted discourse as an ontological definition as well, just as it is done in the previous example. When we get farther away from well-defined contexts, it gets harder to tell what defines what.
The third example is the OP's sentence. Elliptically, it can be accepted as a definition (as we could do in the second example); that it is a mythological horse, etc. could be added. But let us leave its adequacy to those who are interested in its subject-matter and focus on the philosophically relevant part: What position should we take when a non-existent thing or a thing that could be analysed to incoherence is defined or occurs as a constituent of a definition? Herein, I take into view of the fact that Pegasus is a stock (but unfortunate, for it gives the false impression that the talk of things of fiction is meaningless) example of non-existent things. In other words, what if we do not have an appropriate extension to query whether the statement holds or not (as can be done in the first example)?
In many areas of knowledge, such a question never comes to the fore, for example, the model theory of mathematical logic works with non-empty universe of well-specified objects. Hence, in many respects, that is a purely philosophical question and still much a topical of debate as well a motivation for various logical systems. Two mainstream trends, Russellian and Fregean, stand out in the philosophical discourse as logical analysis. The suggested improvements on and consequences drawn from Russell's and Frege's views do not exhibit uniformity and sometimes become puzzling, but the following considerations reflect viewpoints at least in spirit:
In Russellian analysis, a proper name, like Pegasus, stands for a particular being in the statement (in fact, of the proposition, but this distinction, though important in itself, can be ignored for the present discussion) and brings in certain assertions (as opposed to suppositions) as a constituent, one of which is the existence of Pegasus. Since Pegasus does not exist, one of the assertions fails to hold and the statement does not provide a genuine predication. Hence, the definition is reduced to falsity according to Russellian analysis. There is no truth gap, if it is not possible for a statement to be true, then it is false.
In Fregean analysis, a proper name stands as a constituent by its (Fregean) sense. If the reference of the name is empty, we have still a genuine predication (we speak on the grounds of concepts), but thereby the statement is devoid of its touchstone, the referent, and so not truth-apt. However, this does not present a problem for the statement qua a definition, for a definition does not need to have a truth value.
If we accept only the original characterisation of Pegasus as definitive, which has been completed, and reject later additions or modifications, then, all those that have been said about it will remain necessarily so. Thus, on Russellian view, the statement is necessarily false. On Fregean view, this is entirely out of question.