I assert that there are no three sided squares. I can proof it. Why claim that non-existence can't be proven?

Question

Definiton: A square is an equiangular, equilateral construct consisting of four line segments and their terminating points, such that they construct an Euler circuit, and all meet at right angles.

S = Set of all polygons.
X = Polygons with 3 sides
Y = Polygons with 4 sides.
X is disjoint Y, both of which are subsets of S.

There does not exist a three sided square.

Suppose not (proof by contradiction):

Suppse there exists a square with three sides.

S = Set of all polygons.
X = Polygons with 3 sides
Y = Polygons with 4 sides.
X is disjoint Y, both of which are subsets of S.

Such a square is in in set X, as a three sided polygon.
Since a square by definition has four sides, it is in set Y.
Thus, a three sided square is in both set X and set Y.

This is a contradiction. Since X and Y are disjoint, no element can be held in common.

Therefore, the supposition is false. There are no three sided squares.

Thus, the non-existence is proven.

Footprints:

Nice way to miss the point, guy.

My point is, people run around here saying, "You cannot prove non-existence!!!" You can, in fact, prove non-existence, given traits and definitions.

How someone defines their sky pixie can leave them vulnerable to having their particular version proven non-existent.

Wow, lots of people putting non-existent concepts into my question.

I merely point out that non-existence CAN be proven. I do not say for any given case it can, or that it can for any arbitrarily selected case.

Only that it is possible, at least for some things, to prove non-existence.

Yeash people, pay attention. I didn't mention a deity until Footprints brought it up.

TTC:

Love it. :)

Answer 1

Excellent question. Negatives certainly can be proven, subject to appropriate definitions.

It's trivial to prove the non-existence of a tri-omni deity:

If an omnipotent, omniscient, omnibenevolent deity existed, then human evil could not exist. Since human evil unarguably does exist, the classical monotheistic deity cannot exist.

Answer 2

You are proving that BY DEFINITION of a square, a 3 sided square doesn't exist. What if someone were to say that they had faith and belief in 3 sided squares, and just because you couldn't feel them or understand them, didn't mean they don't exist?

Frustrating right?

A loving God BY DEFINITION cannot exist either, all one has to do is read the bible and then think through the implications of a having a creator with complete knowledge of the futue to understand that in Creating Lucifer, God by definition created evil.

Therefore a Loving God cannot exist.

There is no evidence for any God, loving or otherwise, so comparing a solid, fully defined object to a belief in a being that isn't static is not a good fit.

I loved the question though, really made me think.

Answer 3

so what, it's a circular word game, doesn't prove nothing, not even that non-existence can be proven. It may prove that the use of categories makes sense, but that's about it.
We define that all polygons with exactly 4 sides are called squares. Consequently if it has more or less sides it's not called a square, anybody surprised? Only those with a defective short term memory. What point did you want to make?
But as you are so good in proving non-existence, how about trying your wits with the famous flying teapot in outer space? Or the flying spaghetti monster. Your choice, but please, please, disprove just one on them.

Answer 4

I was with you until the sky pixie comment. I know Footprints brought it up but sometimes I wish beliefs were treated a little more respectfully, even if they are completely the opposite of one's own. Good argument though for proving a negative. Although I think it would be quite difficult to use for something intangible.

Answer 5

Actually there are three sided "squares".

If I make date squares (or any other kind of cookie/cake like dessert called a square) I can cut them into three-sided portions, but they would still be by definition "squares".

The Market "Square" in my hometown was situated where three major roads converged. It has three sides, but is still officially named the Market Square.

A set-"square" is a three-sided drawing tool, A speed-"square" is a triangular measure tool used to mark perpendicular lines for cutting materials.

So your assertion that there are NO three sided squares is incorrect-- it is only true is using the very narrow, geometric definition that you have decided to use. Since your argument is largely one of semantics, there is no justification for limiting the definition of "square" to the purely geometric.

Answer 6

You only proved a 3-sided shape can not be called a square...you did not prove the non-existance of 3-sided shapes.

That is only argument by semantics and definition.

~ Eric Putkonen

Answer 7

Fine, you win. Proving non-existence is possible when there is only one proposition acting on one definition. A basic tenet of logic can be proven or disproven. However, given infinite definitions and infinite propositions, disproving that becomes impossible.

I agree with the above. Proving a Biblical God given the definitions of All loving all powerful etc. is possible, as it is a contradiction. Disproving the existence of a being with those defintions, not the propositions about him, is impossible though.

Answer 8

What you're essentially showing there is that a concept (the three-sided square) is incoherent, sort of like the Christian god (who is a three-godded god, sort of).

The "can't prove a negative" assumes a coherent thing to look for, and the question is one of existence in reality, not in concept (which is not the same thing unless you're a platonist or something).

Hence, it's different to say "Yahweh does not exist" or "three-sided squares don't exist" than it is to say "there are no black swans."

Answer 9

Only the non-existance of three-sided squares

Answer 10

lot of typing just to say there are no 3 sided squares(haha) it takes 4 for a square