A square circle would be a shape or object in Euclidean space that is both square and circular. Philosophers, especially working in philosophy of language and metaphysics, use the phrase "square circle" as an example of a contradiction in terms, that is, a phrase (as opposed to a proposition), two parts of which describe qualities that cannot both exist in the same thing at the same time.
It is also often used as an example of an "impossible object." Probably the most interesting philosophical question about square circles, and other such "impossible objects," is whether they enjoy any sort of existence or being. The 19th century German philosopher, Alexius Meinong, famously held that while such objects obviously do not exist, they nevertheless enjoy a queer sort of "being." Other philosophers have held that "square circle" is literally nonsense, that is, lacks any significance or meaning. An interesting feature of that position, however, is that it denies significance despite the fact that the words "square" and "circle" do individually have meaning, and we can say what their truth conditions are (i.e., necessary and sufficient conditions of their being true).
"Clever schoolboys" may point out that a three-dimensional shape may be square on one plane, and circular on an orthogonal plane. To their disappointment, philosophers stipulate that does not count as a square circle.
Note that this does not have to do with the geometrical problem of squaring the circle, that is, constructing a circle that has the same area as a square using only a compass and straightedge. — Citizendium
There are two sides to every story and somewhere in the middle lies the truth. — Some guy
two parts of which describe qualities that cannot both exist in the same thing at the same time. — Citizendium
Law Of Noncontradiction! — TheMadFool
Consider now a 3D object, a right cylinder with height 4 units and diameter 4 units. Depending on the angle of the light you shine on it, the shape of its shadow will change. — TheMadFool
A contradictory proposition affirms that something has and does not have the same property. But a proposition that affirms that something looks like a circle from one perspective and does not look like a circle from another perspective is not a contradiction because the property of "looking like a circle from one perspective" is not the same property as "looking like a circle from another perspective".
Sometimes it is said for emphasis that a contradictory proposition affirms that something has and does not have the same property at the same time, and/or in the same sense, but these additions can be seen as already included in the meaning of the phrase "same property". — litewave
There's no contradiction here.
↪litewave Yep. Nothing to see here. — Banno
Thus, go further than reality could be. — javi2541997
Addendum
If a contradiction is being sought for, it's this: As litewave pointed out, some of us will observe T' as a square (S) and others will observe T' as as a circle (~S). Both parties are right: Square Circle. — TheMadFool
Square circle as a genuinely contradictory object would look like a square and like a circle from the same perspective (and at the same time and under all other same circumstances). Such an object cannot exist — litewave
If a contradiction is being sought for, it's this: As litewave pointed out, some of us will observe T' as a square (S) and others will observe T' as as a circle (~S). Both parties are right: Square Circle. — TheMadFool
Square circle as a genuinely contradictory object would look like a square and like a circle from the same perspective (and at the same time and under all other same circumstances). Such an object cannot exist — litewave
A square circle would be a regular polygon with four sides, the perimeter of which is equidistant from a given point on the same plane.
Draw me one of those. — Banno
This is what leads me away from reading your posts.
A square circle would be a regular polygon with four sides, the perimeter of which is equidistant from a given point on the same plane.
Draw me one of those. — Banno
Square circle as a genuinely contradictory object would look like a square and like a circle from the same perspective (and at the same time and under all other same circumstances). Such an object cannot exist. — litewave
But a circle and a square are NOT defined as each other's opposites, nor are they mutually exclusive at all. — fishfry
But a circle and a square are NOT defined as each other's opposites, nor are they mutually exclusive at all. People should stop using square circles as an example of a contradiction, because in fact there are square circles. — fishfry
In Euclidean space they are mutually exclusive and I tacitly assumed this kind of space. — litewave
The point I' making is that there are only apparent contradictions, not real ones — TheMadFool
A genuinely contradictory object cannot exist so any object in reality can be only seemingly contradictory. — litewave
In what kind of space are there square circles? I'm curious. — TheMadFool
There are no genuine contradictions. That's the law :point: The Law of Noncontradiction ~(p &~p), only apparent contradictions that can be resolved with anekantavada (many-sidedness/perspectivism). — TheMadFool
In the space with taxicab metric that fishfry mentioned. You may object that that is actually not a circle but he did use the standard definition of a circle: a set of points with a fixed distance from some point. — litewave
You can still formulate a genuinely contradictory proposition by insisting on the same perspective but such a proposition would not correspond to any object in reality — litewave
Even in physics, Euclidean distance is only a special case of a more general way of defining distance. — fishfry
That's wordplay. — TheMadFool
It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." — litewave
The “same thing” that belongs must be one and the same thing and it must be the actual thing and not merely its linguistic expression. For example, it is possible for someone to be a pitcher and not a pitcher where “pitcher” in the first instance refers to a baseball player and in the second to a jug that can hold beer
Aristotle meant to the object itself not the act of belonging to another.
The “same thing” that belongs must be one and the same thing and it must be the actual thing and not merely its linguistic expression. For example, it is possible for someone to be a pitcher and not a pitcher where “pitcher” in the first instance refers to a baseball player and in the second to a jug that can hold beer — javi2541997
Insistence on the same perspective was part of the meaning of a contradiction already in ancient Greece:
Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."
https://en.wikipedia.org/wiki/Contradiction
(emphasis mine) — litewave
I don't see that the article attributes the phrase "in the same respect" to the object. — litewave
An object can be potentially F and potentially not F, but it cannot be actually F and actually not F at the same time.
The point to all this being contradictions (square circles like atheism vs theism, physicalism vs nonphysicalism, etc.) are actually not contradictions. They're just different sides (anekantavada, many-sidedness, Jainism) of the same greater truth that resides in a world the next level up so to speak. — TheMadFool
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