The Law of Identity

[Skepdick]

....

This is perhaps the biggest own goal you could possibly score; in fact - it's equating contradictions with falsehood/absolute nothingness.

This robs you of the distinction in directionality:

Contradictions (proofs of negation): g: Any → not(Any) proceed from something TO its negation.
They contain rich proofs that show how various propositions lead to contradiction - algorithms, knowledge, logical structure It's the act of taking substantive claims and showing how they collapse.

Ex nihilio constructions: f: ⊥ → Any proceed from nothing TO anything.
It's the explosion principle and requires already having ⊥ as a starting point. It's pure vacuous generation.

By equating contradictions with absolute nothingness and rendering them informationally empty (classical falsehood), you destroy the very mechanism you needs for your metaphysical argument to work.

You destroy your own cognitive/logical machinery. You end up unable to think clearly about contradiction, negation, or generation because your equation erases the very distinctions that make these concepts meaningful.

[Scott Mayers]

I use an argument from absolute nothingness in metaphysics

Ex nihilo nihil fit

If you start with absolute nothingness - you can't get anything other than absolute nothingness.

f : Prop → Prop

If you read properly, I granted that this included in the argument. But funny that you'd now embrace the 'classical' interpretation that requires those laws that you were arguing against. You'd have to assume the very 'consistency' of an Identity to make such claims. I was actually showing HOW you can assume any 'mechanism' to draw conclusions still utilizes the laws.

This was not a debate about Absolute Nothingness but about logic. I used that it to show that Totality itself does not need an apparent 'logic' but that you can derive it even using contradiction. [It acts as a 'force' to compel change] Either you opt to remain consistent within your present logical frame and interpret a contradiction as a means to STOP that line of further reasoning OR you can use it to derive newer dimensions where the paradox persists.

Totality, not this Universe, is what could have a foundation in 'absolute' nothingness because it is the only thing that guarantees a contradiction that requires resolution which becomes a foundation for 'order'. So the contradiction is necessary as a paradox with respect to Totality at the very least. The 'explosion' of such a contradiction leading to 'Absolute Infinity' is thus fine. And so you can flip it around and assume Absolute Infinity and be sure that that guarantees Absolute Nothingness as absolutely Something.

And it is to the infinity of possibilities that exist to which you can 'construct' reality without any essential consistency on the level of Totality. So you can instead lay out all the possibilities exhaustively in each and every possible position and arrangement before finding any patterns. The 'patterned' worlds are what leads to a formulation of logic. That is, you can certainly find worlds that have exclusive patterned structures consistently. And if you reduce these patterns to a most generic set of 'rules' they become the stage for defining a logical system.

in which I first show that reality can manifest from contradiction itself

Ex falso quodlibet

If you start with a falsehood - you can derive anything.

f: ⊥ → Any

So not only are your two premises a non-starter; your third one; the one you remained silent/implicit about (where you've equated nothingness with contradiction) is not true either.

By assuming "Absolute nothingness ≡ Contradiction" you are smuggling in classical logic through the back door; because in Classical logic a contradiction is indeed the same as Falsum (⊥).

Contradictions (proofs of negation) contain information. They proceed in the direction g: Any → ⊥
Absolute nothingness does not. It proceeds in the other direction: f: ⊥ → Any

So are you starting with absolute nothingness; or are you starting with something that leads to absolute nothingness?

Our disagreement runs much deeper. You simply have no grasp that the "x = y" expressions have no truth-value.
x=y is a mere proposition. Either it has a constructive proof (a transformation from x -> y and from y -> x) or it doesn't.

Can you transform 1 into 0; and 0 into 1? Yes.. 1-1 is 0; and 0+1 is 1.
OK so then 1=0 holds under that interpretation.

Mathematics is about formal relationships and proofs, not about correspondence to some external "truth"
Truth (whatever that is) simply doesn't come into it.

I don't agree with your interpretation. You missed the point of it used regarding Absolute X's here. And oddly
your plain denial of Absolute Nothingness now seems to suggest you ARE using some 'identity' rule.

0 = 0 and 1

is an identity you just showed you understand using your own stance to be against Absolute Nothingness. The right side of it is just a substitution of an IDENTICAL expression in meaning. This is because you denied that Absolute Nothingness can lead to anything. So it cannot exist WITH anything,...including '1'. And so ....

1 = 1 or 0 is the dual of the above using DeMorgan's; This is an identity law for what 1 is or what '1 or 0' means.

If anything is true, then adding absolutely nothing to it will not change its identity. So using this last expression, just remove the 'or 0' and you have....

1 = 1

So you proved that you actually AGREE to this identity as ABSOLUTELY essential requirement to all "logic" systems.

....and why I assumed you might have some other reason for disagreeing.

[Scott Mayers]

....

This is perhaps the biggest own goal you could possibly score; in fact - it's equating contradictions with falsehood/absolute nothingness.

This robs you of the distinction in directionality:

Contradictions (proofs of negation): g: Any → not(Any) proceed from something TO its negation.
They contain rich proofs that show how various propositions lead to contradiction - algorithms, knowledge, logical structure It's the act of taking substantive claims and showing how they collapse.

Ex nihilio constructions: f: ⊥ → Any proceed from nothing TO anything.
It's the explosion principle and requires already having ⊥ as a starting point. It's pure vacuous generation.

By equating contradictions with absolute nothingness and rendering them informationally empty (classical falsehood), you destroy the very mechanism you needs for your metaphysical argument to work.

You destroy your own cognitive/logical machinery. You end up unable to think clearly about contradiction, negation, or generation because your equation erases the very distinctions that make these concepts meaningful.

Actually it has served me quite well. I am uncertain of your symbolism here with the "⊥".

Material Implication is a paradoxical one that implies given anything, it is implied by anything else.

Given A, then (X implies A)

It relates similarly to Or-inclusion rule in propositional calculus. Given anything assigned 'true', then you can conclude that true OR anything else, because it would not change the fact of the disjunct:

Given A, then (A or X)

Now let A = absolutely nothing and X = Something (or anything) else. Then

Given (Absolutely Nothing), Something exists Material implication.

And

Given (Absolutely Nothing), (Absolutely Nothing) exists OR (Something) exists.

These here show two different expressions involving 'implication' and 'or with Absolutely Nothing, and it still proves Something is derivable within the system beginning with absolutely nothing.

Totality itself is a 'contradiction' if we begin with absolutely nothing. But that is a GOOD thing because at the extremely large (a proper class) is something that doesn't sit still. AND my proposal regarding physics is that this ultimate Contradiction (Totality == Absolutely Nothing) IS the universal means of driving reality. The constant state of Totality contradicting itself beginning as absolutely nothing is partly related to Hegelian logic or Marx's Dialectic Materialism.

[They touched on 'contradiction' in politics as that which creates wars that need resolving as a 'new' agreement'. But they show that regardless of re-beginning 'anew' reign for political leadership, it may begin vital and functioning but loses it in time due to how humans concentrate ownership power in fewer hands while the political 'elect' settle into a nepotistic dynasty of leaders who lacked the prior suffering of their parents. So spoiled, their means of power become corrupt which initates the new future conflict in cycles.

This is extraneous but relates to a foundation of multivariable logics that use some contradiction as the initiator of change to a new 'dimension'. To be at x = 3 and not at x = 3 for instance, a contradiction, is resolved by the perpendicular line vertical from x = 3 in the y-axis dimension at all points except ON the literal X-axis. So x =3 is the solution except at y = 0 when in two or more dimensions. So something contradictory is the foundational force in my physics.]

[Skepdick]

I use an argument from absolute nothingness in metaphysics

Ex nihilo nihil fit

If you start with absolute nothingness - you can't get anything other than absolute nothingness.

f : Prop → Prop

If you read properly, I granted that this included in the argument. But funny that you'd now embrace the 'classical' interpretation that requires those laws that you were arguing against. You'd have to assume the very 'consistency' of an Identity to make such claims. I was actually showing HOW you can assume any 'mechanism' to draw conclusions still utilizes the laws.

This was not a debate about Absolute Nothingness but about logic. I used that it to show that Totality itself does not need an apparent 'logic' but that you can derive it even using contradiction. [It acts as a 'force' to compel change] Either you opt to remain consistent within your present logical frame and interpret a contradiction as a means to STOP that line of further reasoning OR you can use it to derive newer dimensions where the paradox persists.

Totality, not this Universe, is what could have a foundation in 'absolute' nothingness because it is the only thing that guarantees a contradiction that requires resolution which becomes a foundation for 'order'. So the contradiction is necessary as a paradox with respect to Totality at the very least. The 'explosion' of such a contradiction leading to 'Absolute Infinity' is thus fine. And so you can flip it around and assume Absolute Infinity and be sure that that guarantees Absolute Nothingness as absolutely Something.

And it is to the infinity of possibilities that exist to which you can 'construct' reality without any essential consistency on the level of Totality. So you can instead lay out all the possibilities exhaustively in each and every possible position and arrangement before finding any patterns. The 'patterned' worlds are what leads to a formulation of logic. That is, you can certainly find worlds that have exclusive patterned structures consistently. And if you reduce these patterns to a most generic set of 'rules' they become the stage for defining a logical system.

You have absolutely missed the forrest for the trees. All I am talking about here is property preservation under continuous transformations

Input -> Transformation -> Output.
That is what f : Prop → Prop means.
That is what the negation operator DOES constructively.

I am not assuming any logical system. Not classical. Not non-classical.

That is what the symbol "=" represents. A collection of continuous processes!

1 = 0 says the same thing as "There exists f: 1 -> 0 and g: 0 -> 1"

Whatever 0 represents.
Whatever 1 represents.
Whatever "->" represents (one or infinitely many different transformations).

Equality is strictly about bidirectional property preservation.

Equality is process not state!
This is why we can't bridge the ontological divide.

There's no "ontological totality"!

You'd have to assume the very 'consistency' of an Identity to make such claims.

No! I do not have to do that! I can treat both consistency; and identity (whatever the fuck those are) as properties/propositions.

f : Prop → Prop

If I start with A (which has an "identity") and I arrive at B (which has NO "identity") that violates property preservation!
If I start with A (which has an "consistency") and I arrive at B (which has NO "consistency") that violates property preservation!

ANd now for the kicker. THe reason I am NOT assuming any logic is precisely because "validity" may well be one of those properties that get lost!

If I start with A (which has "validity") and I arrive at B (which has "NO" validity) that violates property preservation!
If I start with A (which has NO "validity") and I arrive at B (which has "validity") that violates property preservation!

If you start with nothing and you arrive at something -> violation!
If you start with something AND nothing and you arrive at only nothing; or only something - violation!

If you start with system which has NO "violations" and you arrive at a system with "violations" -> this violates property preservation!
If you start with system which has "violations" and you arrive at a system with NO "violations" -> this violates property preservation!

You are operating on the premise that identity is some kind of unification principle (a TOTALITY).
And I am simply rejecting the very need for unification.

[anthonypaulrobinson]

A is never anything, but a first letter Uralic-Altaic word.

I know this, because I’m Venetian Iranian.

A is the root note of an A chord

-Imp

Ah yes, the route of trickery.