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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?

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    See "Colorless green ideas sleep furiously" for the well-known example of a sentence that is grammatically well-formed, but semantically nonsensical. Commented Nov 17, 2023 at 8:13
  • You should like Meinongian theories:"Concrete objects are said to exist and subsist. Abstract objects are said not to exist but to subsist... ‘The round square is round’ is a true sentence and therefore its subject term stands for an object." The round square still does not exist, only subsists, and you need a lot of logical acrobatics to avoid contradictions, but still.
    – Conifold
    Commented Nov 17, 2023 at 9:41
  • 1
    @Conifold logical acrobatics give people something to do in their spare time, I guess?
    – Scott Rowe
    Commented Nov 17, 2023 at 13:15
  • Topologically, one might speak of a square that is a circle in the way that we sometimes joke that a donut and a coffee mug are "the same" (because they can be transformed into each other minus excessive breakage of whichever original shape). Or imagine a square projected onto a sphere, or a circle with distinguished points inserted so as to split the circle into four arcs = sides. These are not round squares per se, perhaps, but they might be what our mind tries to "compute" when it tries to "compute" the phrase "round square"... Commented Nov 17, 2023 at 14:40
  • I'm with Conifold. You might enjoy the Meinongian jungle.
    – J D
    Commented Nov 17, 2023 at 15:31

4 Answers 4

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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:

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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 discourseR 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.)


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

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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.

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  • So, are "round square is green" and "round sqaure is round" false?
    – user68943
    Commented Nov 17, 2023 at 4:09
  • @Collins when translated into an unambiguous sentence that can mean what is probably meant by "a round square is...", yes.
    – g s
    Commented Nov 17, 2023 at 4:10
  • @g s I'm sorry, but then "round square isn't green" and "round square isn't round" are true?
    – user68943
    Commented Nov 17, 2023 at 4:13
  • @collins yes, when likewise translated into a more unambiguous sentence.
    – g s
    Commented Nov 17, 2023 at 4:16
  • @g s What do you mean by "when translated into an unambiguous sentence"? I'm sorry but I'm not an English speaker so it's a bit hard to understand.
    – user68943
    Commented Nov 17, 2023 at 4:17
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Square wheels

Square wheels

Does this aid you in your quest?

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  • They just demonstrated that all wheels need to be round, which doesn't mean that square wheels are round.
    – NotThatGuy
    Commented Nov 17, 2023 at 9:30
  • Point. I was mistaken.
    – Hudjefa
    Commented Nov 17, 2023 at 10:02
  • * I meant "not all wheels", but I guess that was obvious.
    – NotThatGuy
    Commented Nov 17, 2023 at 10:05
  • THIS. Given enough time and money, you can achieve the impossible.
    – Scott Rowe
    Commented Nov 17, 2023 at 13:19
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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.

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