The Black Vault

Can an omnipotent being draw a square circle or violate the laws of logic?

No. That would be nonsensical.

Might as well ask if an omnipotent being has the power to not exist. Wouldn't that be ironic? If God was so powerful, he made it so that he never existed, and in his almighty power, made the atheists right.

Here are some laws of logic:
http://en.wikipedia.org/wiki/Three_clas ... #Aristotle

http://en.wikipedia.org/wiki/Law_of_identity
http://en.wikipedia.org/wiki/Law_of_noncontradiction
http://en.wikipedia.org/wiki/Law_of_excluded_middle


Here are Euclid's five axioms which generates Euclidean geometry:
http://en.wikipedia.org/wiki/Euclidean_axioms#Axioms

As you know, Einstein made use of non-Euclidean geometry in his general relativity. The non- part comes in when the fifth axiom is no longer assumed.

What makes Euclid's five axioms flexible but Aristotle's three axioms of reason not flexible?

If I, for example, no longer assume the first axiom (of identity), then I can say S can be a square and a circle simultaneously.

Even QM is saying that one particle can exist in two places, which makes me suspicious of the axiom of identity.

The axioms of Aristotle have an application of course but I do not think they are inviolate, any more than Euclid's axioms can be bent or broken.

If everything requires proof, where is the proof of the three laws of thought? And if there is no proof, then they are axioms. Axioms are not inviolate.

In addition, btw, in a metric space with the taxicab metric, lots of circles are squares

I think it's more a problem of language. "Square" and "Circle" are man-invented descriptions. If S were a square and a circle simultaneously, it still would not be accurate to call it a "square circle", imo.

Everybody knows non-Euclidean geometry is a sure path to awakening the elder gods.
Ia Cthulhu! Ia Dagon!

humphreys wrote:I think it's more a problem of language. "Square" and "Circle" are man-invented descriptions. If S were a square and a circle simultaneously, it still would not be accurate to call it a "square circle", imo.

If something was square and circular why would calling it a square circle be inaccurate?

at1with0 wrote:If something was square and circular why would calling it a square circle be inaccurate?

One implies that is a shape is somehow both a square while simultaneously being a circle (square and a circle), while another implies the shape is a circle that is square in shape (a square circle).

A red bus is a bus that is red, not a bus that is also a red.

I guess I'm talking about something that is a square and circle simultaneously.

If one no longer assumes the law of identity, S can be both.

I would agree that God could create an object that is both a square and a circle then, yeah, but most of the challenges like "can God make a rock so big that he can't lift it?" are obviously impossible, and nonsensical.