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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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  • There is not enough information about this scenario. Many things are capable of flying. We can't be sure one of them is Pegasus. Perhaps you should have went the unicorn route. Pegasus is a flying unicorn. Are all unicorns winged & flying creatures? If the answer were yes that all unicorns are winged & fly then this would be a better example by definition. One would need to define unicorns way better that just having the ability of flying. Also I think your terminology is off. Propositions can be analytic or synthetic. You are using necessary & contingent in the same context as those terms
    – Logikal
    Aug 2 at 11:50
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    This is not a definition but an assertion. If the meaning of "Pegasus" is taken to be a certain flying horse then for it to be capable of flying is an analytic consequence of the definition, hence necessarily true (on traditional accounts).
    – Conifold
    Aug 3 at 3:49

3 Answers 3

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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.

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  • I wonder whether necessity can be established "directly". I think, what you are explaining, is fixing a meaning a priori -- what would be close to a definition. Necessity, then follows from a priori.---Isn't necessity what is true in all worlds? How can you establish what is true in all worlds other than logically, semantically or by naming?
    – Mr. White
    Aug 1 at 22:30
  • @Mr.White It depends on the interpretation of possible worlds. I reject modal realism, and interpret it metaphorically as a shorthand for instances of claims. Pegasus is imaginary, after all. Hence to establish what is true in all possible worlds is simply to establish that in all instances of a model something is true. Since there are no literal other possible worlds, to tie necessity to their existence would be meaningless, right?
    – J D
    Aug 2 at 4:41
  • For the record Richard, possible worlds is a widely accepted framework that many people do hold in the same awe as multiple-worlds interpretations of quantum physics. My disdain for it as anti-empirical is my personal prerogative, so Mr. White's interpretation you will see often. Also, Conifold, who is an encyclopedia of facts, is right in calling this analyticity (analytic-synthetic dichotomy). I avoided the term because since Quine's Two Dogmas, it doesn't have the universal appeal that it held after Kant put the idea out there.
    – J D
    Aug 7 at 18:47
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My two cents:

Even if "Pegasus" is rigid, why shouldn't there be a (mythological) world where this thing does not fly? So, it is flying contingently.

Not sure, what you mean by definition, though. I would assume, Pegasus was just there (or rather born by Medusa) and named, much like H2O.

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  • Aren't you conflating Is with Ought? Isn't the question not whether you believe there should be an Ancient Greek myth of Pegasus without wings and flight, but whether there is an ancient Greek myth where it is so? And since there aren't, in no actual mythological world the Greeks told tales of can it be true. Hence, it isn't contingent on the mythological world you refer to, since no possible world has such a wingless Pegasus?
    – J D
    Aug 2 at 5:01
  • @JD No, I think Mr White's point is that if we consider Pegasus to be an inhabitant of a possible world in which the Greek myths are true, then there can be other PWs in which Pegasus, or a counterpart of Pegasus, exists but does not fly. Hence it is not necessarily true that Pegasus flies. Even if we use Pegasus as a rigid designator, not all properties of a thing are essential.
    – Bumble
    Aug 4 at 4:22
  • @Bumble Excellent riposte, and I read it as that even in the case that a rigid designator is part of a model, then since the model itself is restricted only by the desires of the agent who models, and therefore by extension, a vast class of necessary claims must be contingent since both the semantic and logical grounding of the model are preferences. In fact, it seems that there are no compulsions at all to have a model have any specific necessary claims. If one's rationale for necessity is a posteriori, then imagination clearly disregards this since the list of fanciful non-existent...
    – J D
    Aug 7 at 18:58
  • far potentially outstrip any real existences, and as for a priori knowledge used as a restraint, no such justification of a priori knowledge can be used if one accepts even a modicum of logical pluralism (where contradictions of propositions needn't be rejected) and fallibilism (that there is no certainty of truth of introspection and intuition). If the senses, logic, and intuition can't constrain a possible world-as-model, then it seems there's to be hand no necessity at all.
    – J D
    Aug 7 at 19:02
  • Thus, using metaphysical necessity to distinguish fanastic winged-beasts from normal horses, is more than adequate ground from a pragmatic stand point, and since in the cooperative language game it is used in such a fashion, the principle should be affirmed that particularly in discussions of rigid designators in fictional possible worlds, the benefit is to classify it as necessary, even if one can imagine in theory someone writing a story of Pegasus without wings which would largely function to violate the Gricean maxim of avoiding obscurity by presuming a definition (Pegasus without wings)..
    – J D
    Aug 7 at 19:07
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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:

  1. To be even number is to be divisible by two.
  2. To be is to be the value of a bound variable.
  3. To be Pegasus is to be capable of flying.

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.

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    I like your answer, and I suppose that since it is already long, you didn't want to include what Kripke might say. If Pegasus is a fictional thing in our world, or a real thing in a possible world where the Greek myths are true, then "Pegasus flies" is simply a contingent fact about Pegasus. Not all properties of a thing are essential to it. Even if the name Pegasus rigidly designates, there may be worlds where a counterpart of Pegasus does not fly. On this view, "Pegasus flies" only seems necessary because we use this fact to distinguish Pegasus from other horses that don't fly.
    – Bumble
    Aug 4 at 4:52
  • Thanks. I reckoned that the OP, having observed the Russellian vs. Fregean proposition debates, tangled with the question what if the case is that of a definition. Actually, my own view is divergent from them and the possible world analysis you've mentioned. Aug 4 at 11:23

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