(October 30, 2015 at 3:48 am)Irrational Wrote: The law of noncontradiction is not something that is discovered but is invented? Therefore, squares-circles can exist with the right mindset? Married bachelors?
Just trying to understand your view more.
Square circles cannot exist because a circle is also a concept. A square circle therefore violates a rule that we have already invented.
A circle matches so closely with reality that it's easy to mistake it as feature of reality, but perfect spheres do not exist in nature.
A circle therefore is an approximation. A concept that we use as shorthand when we don't want to describe a shape down to its smallest detail. The power of Maths and logic lies in it being an abstraction of the real world.
Take numbers. If someone wants to argue that Maths exists as a feature of the universe then they need to explain why 1 is not a prime number, or why zero raised to the zeroth power equals one
Quote:Zero raised to the zero power is one. Why? Because mathematicians said so. No really, it’s true.
[...]
But if this is the case, then how can mathematicians claim that 0^0=1? Well, merely because it is useful to do so. Some very important formulas become less elegant to write down if we instead use 0^0=0 or if we say that 0^0 is undefined.
