Can we describe round square, which doesn't exist?

Question

Definitely, a round square doesn't exist.

Then, can we describe a round square?

E.g. A round square isn't green. A round square is big. A round square is round.

Can we meaningfully describe like this? If so, could they be true?

Answer 1

It is true that there exists no entity which instantiates the set squares which has the characteristic round.

It is true that there exists no entity which instantiates the set squares which has the characteristic round and which has the characteristic green.

It is false that there exists an entity which instantiates the set squares which has the characteristic round.

It is false that there exists an entity which instantiates the set squares which has the characteristic round and which has the characteristic big.

It is false that there exists an entity which instantiates the set squares which has the characteristic round and which has the characteristic round.

Answer 2

Square wheels

Does this aid you in your quest?

Answer 3

Sometimes, some of us have an intuition that statements like, "The round square is round," or, "The round square is square," are "analytically" true. Such statements seem like instances of, "The F x is F," or similar "tautological" claims. Take, "The round square is round and a square," as (1), then consider:

Taking (1) as simply lacking in truth-value calls to mind the truthvaluelessness approach to category mistakes. In that article and section, they go over some other theories about such mistakes which have a similar thematic significance: meaninglessness and contentlessness views. So those are other options for describing round squares:

• No description is possible because one of the fundamental conditions of describability, i.e. logical possibility, has been transgressed upon. We might say, "For a contradictory subject of a sentence/proposition, every predication is a meaning-defeating category mistake." Or, less aggressively, "For such subjects, predications are content-defeating," or "are truth-value-defeating," etc.

Yet another option is to distinguish between kinds of predications. We might try out Zalta's encoding/exemplifying distinction (which is on a par with the difference between stipulative and ostensive definitions, we will note), in which case we can situate noncontradictoriness relative to exemplifying while leaving the door open to objects encoding for otherwise mutually displacementary attributes. So we wouldn't say, "The round square is round," but, "The round square encodes roundness," and, "The round square doesn't exemplify roundness." For more on Zalta's gloss of the matter specifically with respect to fictional objects, see Klauk[14] (for some outside analysis); see also Zalta[81] (of course) as well as Luporini[22] or even Linsky and Zalta[96].

Finally, there might be some mathematical domain of discourse^R where "round square" functions like "digon," i.e. as a degenerate expression, or something similar (think perhaps of obgenerate cases of a category as ones with too much of what the degenerate case has too little of). That is, a square might be framed as a degenerate circle, or a circle as an obgenerate square, etc. (This is a rather speculative option, I confess, seeing as I am not a good enough abstract geometer to offer this speculation wholeheartedly; but so I leave it to our more well-informed audience to decide the merits of this proposal.)

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^ROr take the trivial ring where 1 = 0 and analogize this to a space where a square = a circle, perhaps.

Answer 4

Sometimes propositions are called "truth barers" where their truth or falsity depend on some state of affairs in the world (a particular spatiotemporal location). for e.g. the proposition that "Paris is the capital of France" is true now but thousands of years ago it would be false. So seeing that it is impossible that round squares can exist then any proposition about them would always be false.