Unicorns also have the same two forms as the horse and the number four. When the word "unicorn" is mentioned, no doubt the image of a single horned horse comes to mind. This confirms that the unicorn has an archetypical form. A form within the mind and imagination that can consistently exist within the minds of people. To argue that a unicorn does not exist would be to disprove the very definition. While it is true that there is currently not a living form of unicorn, the fact that the image can be conjured means that it must exist. Should an image be non-configurable, then one could argue that the unicorn does not exist in any form. The second from that the unicorn takes, and the one that most people image is that from art. The creative manifestation of the archetypical form projected into a physical form. While the physical form may not breath, eat or move it is still existing just as the very computer that I am typing this paper on exists regardless of being alive. Secondly, the unicorn is not in violation of any universal rules. In both archetypical and physical from the creature would seem to have the same capabilities of the horse only with a horn atop its head. While some would argue that the unicorn does violate certain universal rules in that unicorns are said to be magical, this is not the case. There are legends formed about unicorns. These legends lend to the archetypical and physical definitions and once again are consistent with the actual form. There is no inconsistency. An inconsistency would be for example, if the unicorn's archetypical form was the traditional image, but the physical form looked like an umbrella. The final object, the square circle, does not nor cannot exist. There is absolutely no form that the square...

When attempting to visualize, it is easy to visualize a circle within a square or vise-verse, but not a square circle. Therefor, this object does not even exist within the archetypical form. The second part of the definition once again fails. Under the universal rules of geometry, a circle is a shape with no edges and no end. It simply continually goes around. A square on the other hand has four rigid sides all the same length and four points. These definitions contradict one another, therefor the square circle cannot exist because it contradicts universal the universal rules of geometry. Finally, because the square circle contradicts those universal rules, it also is in violation of universal truths. It cannot be refuted that a circle has no points and goes on continually. It is a universal truth. The combining of the square and the circle into one shape violates that truth.
So, as can be observed, existence does not rely on a living, breathing form that can be observed, but rather on any comprehensive form. While the horse exists in a physical, living form, the number 4 and the unicorn exist in an archetypical form consistent within the minds of people. The square circle on the other hand, can never exist and will never exist because it does not have any form and is in direct violation of universal laws and truths of mathematics.

References

Boche-ski, I.M. "Ancient Formal Logic." Amsterdam: North-Holland Publishing Company 1951.

Chappell, V. "Aristotle's Conception of Matter." Journal of Philosophy 70: 679 -- 696. 1973.

Dancy, R., 1986, 'Aristotle and Existence', in Knuuttilla & Hintikka 1986, pp. 49 -- 80.

GE.R. Lloyd. "Early Greek…