We have definitions for both a square and a circle. By definition, I understand that it's impossible to have a square circle. However, why does the word 'square' have to necessarily mean 'a plane figure with four equal sides'? Conceivably, the word square could have been defined as a 'round plane'? Thus making 'a square circle is metaphysically impossible' false?

I'm new to philosophy. So if this question is pathetic I apologize.

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    Welcome to Philosophy SE! It's a good question! Quine notwithstanding, the meaning of the words, or what they describe is what matters and what can be said to be possible or impossible, not the words themselves. Once the meaning is fixed, some things may become impossible. For example, married bachelors are impossible because "bachelor" means unmarried man. You could define bachelor to mean something other than the "standard" definition, but you wouldn't be showing that married bachelors are possible, you'd just be showing that married <whatever-you-define-bachelor-to-mean>s are possible. Commented Apr 5, 2019 at 21:00
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    I wish philosophers would choose a different example. The unit circle is a square in the taxicab metric. en.wikipedia.org/wiki/Taxicab_geometry. What the saying means is that a definition is a definition. You can't have a married bachelor because a bachelor is unmarried by definition. But you can have a square circle!
    – user4894
    Commented Apr 5, 2019 at 21:15
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    The word "square" is a string of letters, it can mean whatever people agree it to mean. So it is vacuous to ask what is "metaphysically possible" for a string of letters to mean. Anything. Therefore, when people talk about metaphysical possibility they do not refer to strings of letters, but to the senses currently attached to them, see SEP on Metaphysical Possibility.
    – Conifold
    Commented Apr 5, 2019 at 21:18
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    @user4894 Very neat. But I'd argue that "everyday" geometry is implicitly Euclidean, and so we should give the "square circle" example a charitable interpretation. I think it's like someone saying 1+1=10 is impossible, and you objecting that it's a bad example because 1+1=10, in base 2. The everyday reading of numbers is base 10, and that is how they meant to be implicitly understood. Commented Apr 5, 2019 at 22:01
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    Although it is pretty nearly universally accepted that a square circle is metaphysically impossible, there doesn't seem to be any agreement that I can find as to why. I suspect a lot of people will point out that we can deduce a logical contradiction from the definitions/axioms in Euclidean geometry, but then we're introducing additional terms/symbolism so that the "square circle" itself doesn't strictly entail a logical contradiction. For my own part, I'd simply say I have no way to make sense of a square circle, and I intuit from this its metaphysical impossibility. But that's me : )
    – Ben W
    Commented Apr 5, 2019 at 23:18

1 Answer 1


It depends complety in what definition of square and circle, do you use. If you use the standard definition of square (|x| + |y| = c) and the standard definition of circle (x^1 + y^2 = k), then it is a logical contradiction, therefore it methaphysicaly cannot exists. But if you as a example define square as any geometric shape and use the standard definition of circle, then it can exists.

  • As soon as you generalize the definition of the circle to ‖(x,y)‖ = k (that is, a circle is the set of all points for which the norm of the vector (x,y) is k), the square and the diamond are in fact special cases of the circle: You get the diamond if ‖(x,y)‖ denotes the 1-norm, the usual circle if it denotes the 2-norm, and the square if it denotes the infinity norm.
    – Uwe
    Commented Oct 22, 2021 at 10:22
  • @Uwe You can't call circle to all these things. Commented Oct 22, 2021 at 10:49
  • Of course I can: "Definition 3.1: Let k be a positive real number, let ‖_‖ be a norm. We call the set { (x,y) | ‖(x,y)‖ = k } a circle with diameter k."
    – Uwe
    Commented Oct 22, 2021 at 13:25
  • @Uwe generalized circle* Commented Oct 22, 2021 at 20:41
  • Have a look at user4894's comment above on the taxicab geometry.
    – Uwe
    Commented Oct 22, 2021 at 22:30

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