The Law of Identity

[Skepdick]

I cannot convince you of anything and won't waste any further time, still no offense to you personally.

That is the only sensible thing you've said. For somebody who pretends to value time you are temporally blind in your formalisms.

x=x doesn't ALWAYS hold.

When you stop trying to convince me that I am wrong and you start convincing yourself that you are wrong; only then can the dialogue resume.

[Skepdick]

To you, "1 = 1" if and only if "1 = 0".

See, this is where your temporal blindness comes in.

In your view with standard Peano Axioms 1=0 specifies a falsehood. An empty set with no exemplars. It's dark, dead and void of any meaning.

Whereas in my view x=y (such as 1=0) specifies a rich computational multiverse of paths, equivalences, higher-dimensional structure and infinity toposes. The space of all possible continuous transformations from 1 to 0. Only some of them are empty; but they still have topological/categorical structure.

x=y means nothing other than you start at one place (x := 1) and you end at another ( y:= 0).

Your formalisms are ontologically impoverished because you've forgotten that reality is pure process.
I am so sorry that you live in your head. It must be such a dull place.

Perhaps read some Whitehead as a good intro to process philosophy.

[Magnus Anderson]

x=x doesn't ALWAYS hold.

And that is blatantly false. "x = x" is not an open statement. Yet, you keep treating it like one.

[Skepdick]

And that is blatantly false. "x = x" is not an open statement. Yet, you keep treating it like one.

It absolutely is an open/incomplete statement! It doesn't eve have a type!

You can equip it with a type by saying "x = x is a Boolean"

And then you can have its two closures/completions:

1. x = x is true
2. x = x if false.

[Magnus Anderson]

2. Alternative logics aren't just possible - they're implementable

I am waiting for you to show us a thing that is both what it is and what it is not at the same time.

You've given us pretty stupid examples in the past, e.g. "It's raining and it's not raining" where by "It's raining" you mean "It's raining on this side of the street" and by "It's not raining" you mean "It's not raining on the other side of the street". That's not an example of a thing existing in two different states at the same time but a magic trick meant to deceive. So I am expecting you to do A LOT BETTER this time.

[Magnus Anderson]

It absolutely is an open/incomplete statement.

No, it is absolutely not. You dreaming that it is doesn't change the fact.

[Skepdick]

I am waiting for you to show us a thing that is both what it is and what it is not at the same time.

And I am waiting for you to stop being stupid.

[Skepdick]

No, it is absolutely not. You dreaming that it is doesn't change the fact.

You dreaming that it's closed doesn't make it closed.

The very fact that we are disagreeing about it shows you that there are multiple possible closures.

Your closure is x=x is always true.
My closure is x=x is NOT always true.

[Magnus Anderson]

And I am waiting for you to stop being stupid.

This is a very intelligent response.

[Skepdick]

And I am waiting for you to stop being stupid.

This is a very intelligent response.

I know.

Are you still you; or have you changed in that instant?

[Magnus Anderson]

You dreaming that it's closed doesn't make it closed.

But I'm not dreaming. It's closed for real. Ask around. It's been known for ages. The Law of Identity has never been anything other than a closed statement.

The very fact that we are disagreeing about it shows you that there are multiple possible closures.

Oh my God. So you don't even know what an open statement is.

There is a guy on ILovePhilosophy.com who argues that 1 = 0. I disagree with him. Does that mean 1 = 0 is an open statement?

[Magnus Anderson]

Are you still you; or have you changed in that instant?

Did you have a brain surgery while I was away?

[Skepdick]

Oh my God. So you don't even know what an open statement is.

Why are you lying?

There is a guy on ILovePhilosophy.com who argues that 1 = 0. I disagree with him. Does that mean 1 = 0 is an open statement?

Of course 1=0 is an open statement! It identifies ALL syntactic systems A such that A ⊢ 1 = 0

On a homotopical/topological view that's the space where continuous transformations from 1 to 0 exist.

Perhaps you need a brain surgery?

1=0 can be viewed as an open statement. Or it can be viewed as a closed statement.

If you want to view it as a closed statement - you need to provide the closure.

[Magnus Anderson]

Of course 1=0 is an open statement! It identifies ALL syntactic systems A such that A ⊢ 1 = 0

Yikes. You really are beyond help.

[Skepdick]

Of course 1=0 is an open statement! It identifies ALL syntactic systems A such that A ⊢ 1 = 0

Yikes. You really are beyond help.

Medice, cura te ipsum!

1=0 is an open specification. It identifies ALL possible Mathematical universes in which 1=0 is a meaningful Mathematical expression.

Perhaps what you are interested in is Mathematical universes where 1≠0?
A universe where there are NO continuous functions between 1 and 0?

You want universes where the path space between 1 and 0 is empty - where there are no identifications, no continuous deformations, no ways to get from 1 to 0.

Not even on the Real number line.

You want to live in a discontinuous universe. Shame!