Identity Entails Logic
the inventors of the three laws of classical logic, never stated the laws relationships to each other.
The first law is the law of identity. It merely says that every time you talk about A, you mean the same identical thing.
The other two formulas are variations on the afeard Law of the excluded middle. Don’t try to use logic in a situation where the Law of the excluded middle does not obtain ... in other words where it is not ... err entailed. Identity entails it. That’s what the diagram says. For example If A might not be A, then not (not A) might not be A either. Here is another example of where identity is failing.
In other words: My diagram lays down a precise formula for when you can, and can not, apply the classical laws of logic. If my diagram does not do so, then i surely want to know.
“if you are inside a classical logic box, where those three axioms hold, then there is no need to even be aware of the relationship between the axioms … they are all of equal value. But what if you do not even know whether you are in a classical logic box or not ? That is where the law of identity comes into play first … if it holds, then you know the other two laws will hold as well … if identity does not hold, then you are outside of a classical logic box.”
But i seem to remember that you need all three axioms to prove anything. They are three independent axioms.
Your A is never exactly my A no matter how similar they may seem by all the communication we can use to compare them. There will always be some difference, and usually more individually aware difference than not. Binary logic only works inside one individual, or a computer, and sometimes not even either of those.
So then, what is the real logic of the verses?