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  1. All circles are round.
  2. All circles are not unround.

Then, is "unround circles don't exist" nonsense itself because "unround circles" is a contradiction?

I think even if circles don't exist, they still are round, so that unround circles don't exist doesn't make any sense because "unround circles" cannot indicate anything.

Likewise, can it (="unround circles") never be correctly predicated because there's already an error in the subject?

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    You could paraphrase it as, "No circle is unround," or, "If something is a circle, it isn't unround," or, "The number of unround circles is zero." Nov 14, 2023 at 3:09
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    What do you mean by round ? A curved surface or a full 360 degree circle ? Nov 14, 2023 at 11:14
  • @DheerajVerma A full 360 degree circle.
    – user68874
    Nov 14, 2023 at 11:55
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    "Unround circles" is not a contradiction because it is not even a sentence, it is just a predicate ¬ R(x) ∧ C(x). Predicates only become true or false when their variables are quantified over or object names are substituted for them. "Unround circles don't exist" is a true sentence and "Unround circles do exist" is a false sentence, but neither of them is a contradiction (both true and false).
    – Conifold
    Nov 14, 2023 at 12:48
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    I have circles of friends and circles of influence, neither are round. It's a semantic nit. Nov 14, 2023 at 16:00

5 Answers 5

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"In this sort of predicament, always ask yourself: How did we learn the meaning of this word ("good", for instance)? From what sort of examples? In what language-games? Then it will be easier for you to see that the word must have a family of meanings."

"The confusions which occupy us arise when language is like an engine idling, not when it is doing work."

-Wittgenstein, in Philosophical Investigations

So, what is the word 'unround' doing? Is it providing a useful reference category to communicate contrasts? I'd suggest it doesn't provide useful information. Does it mean angular? Flat? Are ellipses 'unround'? I would follow Wittgenstein, in looking at how the word/s are used. There might be contexts where your only concern is to sort between round or not, that it could be useful. A good comparable example is the 'unknot' in Knot Theory, where an apparently meaningless or contradictory term has taken on a specific point of useful meaning.

You could also make definitions, and apply set theory. Note though, 'unround circles' is a bit like 'unicorns', it can be a shared reference even though it's to something fictional, or by some definition impossible.

You might like to have a look at this related topic: Why is a square circle metaphysically impossible? or more generally look up the topic 'Square circle' for what you are talking about.

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This is a really a matter of idiom in language. Saying unround circles don't exist is just another way of saying all circles are round. It is like saying odd even numbers don't exist. The sort of combination of the adjectives typified by odd even is contradictory in one sense but quite common in everyday speech.

Of course, the foregoing assumes a particular meaning of the word 'exist'. You can say that odd even numbers exist as an abstract idea.

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Welcome!

Is the sentence you offer:

All circles are not unround.

nonsense? This is a good question.

The first thing you need to understand is that language is conventional. What that means is that what makes sense and what is useful and what language means is dependent on the context and the people using it. Consider how the sentence:

Uijt jt b djqifs.

seems to be utter nonsense at first glance, but might turn out to have meaning if it's a cipher of a single rotation. See how sense and nonsense are somewhat tricky? In fact, this notion that sentences might feel meaningful in the absence of a literal truth is famously enshrined in Chomsky's "Colorless green ideas sleep furiously.". So, I think it's fair to say that your sentence is mostly sensible and meaningful. The only part that is really challenging is the word 'unround'.

What does it mean to be 'unround'? Normally, school children run to a dictionary, which is full of what philosophers of language call lexical definitions. Does it have an entry as a reflection of use. In fact it does! (MW) But reading the definition quickly communicates that the sense offered here has to do with phonology and not geometry, so that gets us to the question, what do we do with a word that seems meaningful but doesn't have a dictionary entry? Well, if you're astute, you'll note that dictionaries are relatively modern inventions; people have been using words meaningfully long before a brave Scotsman started the OED.

One tool the philosopher has in his quiver is the stipulative definition. Here, for the point of the conversation we can simply stipulate that 'unround' is defined as 'not being round like a circle'. Here the problem is solved. Now, a square is unround by definition. And not unround would on the classical notions of logic (the law of excluded middle and principle of bivalence for instance) would be the opposite of unround which is round. So, we can see that 'not unround' can be transformed grammatically to 'round'. In the context of your claims, everything would seem to work out.

But what you are asking is, can I just stipulate definitions? If I do it, then anyone can do it right? And the answer is yes. In fact language use is highly democratic in this way. Countries often try to create language academies to regulate usage, but in the end, languages and dialects change. Modern English for instance differs from Middle and Old English which is related to Modern Frisian, but both part of the German families of language that are a branch on the PIE tree. It's hard to stop people from using language however they see fit, and that brings us to Wittgenstein and the notion of the language-game and the struggle of language prescriptivists who are constantly trying to get people to use a grammar according to a political agenda.

That brings us to the answer of your question. Like MarcoOcram noted, what you are talking about isn't a question of logic, so much a question of language. The use of 'unround' would be considered non-canonical or idiosyncratic or some would call it idiomatic. This is the idea that the language as presented is non-conventional. But on the whole, I'd say it's fairly meaningful, and I think 99 out of 1,000 people wouldn't have a problem responding to this as if it were conventional.

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    "If, moreover, the doshes are galloons, we know that some galloons are distimmed by the gostak. And so we may go on, and so we often do go on." en.wikipedia.org/wiki/Gostak
    – CriglCragl
    Nov 14, 2023 at 21:55
  • "What does it mean to be 'unround'?" Actually it could be Newspeak: a straight line is double plus unround. Nov 15, 2023 at 4:02
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"unround circles don't exist" is exactly the same sentence as "unround circle is a contradiction". In that sense, neither is more or less nonsensical than the other.

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    In this case it is a contradiction, because the definition of a circle makes it round. But there are many situations where "X that are not Y" could exist, but you would expect them to be very very rare, and they don't exist by chance.
    – gnasher729
    Nov 14, 2023 at 15:22
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Language is about what symbols mean in groups. Language games are possible because the same symbols in the same groups in informal language can have multiple different meanings.

That is:

"The X Y does Z" usually means the same thing as "There exists an entity which instantiates set Y which has characteristic X and also has the characteristic of Z-ing."

as in

"The tall man goes to the grocery store."

But sometimes it means:

"The elements of set Y which have characteristic X also have the characteristic of Z-ing"

as in

"Fictional Hobbits walk to Mordor in The Lord of the Rings."

and sometimes it means:

"There Z's an entity which instantiates set Y which satisfies characteristic X"

as in

"The square circle exists not."

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