Second Proof 1=0

[Eodnhoj7]

Actually the assumptions cannot be reduced to anything besides "forms" at there most basic level and the computer's basic input output operation is strictly a linear/cyclic form....even this is an "assumption" hence it is its own foundation that follow the same form and function of this "system".

This argument happened 100 years ago in Mathematics between the Platonists, Formalists and Intuitionists.

I am not really sure if anybody won or lost that argument. In the end you can interpret it whichever way you want because in the end Mathematics is just syntax. Semantics comes from interpretation.

My bias is Intuitionism. As I would say that a Formalist is a closet Intuitionist, so a Formalist would say I am a closet Formalist too.

If we can agree on each others' propositions - who cares?

And isn't it fun, considering the nature of space as fundamentally a priori and subjective, that intuitionism, in its basic symbolism, is grounded in symbols which require primitive geometric properties (arrows, angles, etc.)?

Intuitionist logic is very closely grounded to pure form.

¬ ¬
→ ↔
∨∧
⊥⊤
( ) [ ]
∩ ∪

[Skepdick]

Intuitionist logic is very closely grounded to pure form.

¬ ¬
→ ↔
∨∧
⊥⊤
( ) [ ]
∩ ∪

Quote the opposite. The above is just notation/grammar/syntax - no semantic.

The point of intuitionism is that it's not grounded. It produces models. Models that can and do change with time - like science should.

It's anti-foundationalism. It's coherentims. It's model-dependent realism and even anti-realism.

It's anything but 'grounded'. Nobody has figured out ontology yet.

[Eodnhoj7]

Intuitionist logic is very closely grounded to pure form.

¬ ¬
→ ↔
∨∧
⊥⊤
( ) [ ]
∩ ∪

Quote the opposite. The above is just notation/grammar/syntax - no semantic.

The point of intuitionism is that it's not grounded. It produces models. Models that can and do change with time - like science should.

It's anti-foundationalism. It's coherentims. It's model-dependent realism and even anti-realism.

It's anything but 'grounded'. Nobody has figured out ontology yet.

I don't know, I see where you are headed with it's absence of ontology...and "yes"...but it is a very "loose" "yes". The reason why I say "loose" is the basic symbolism used in intuitionism closely reflects basic "directional" properities and "contexts".

The simple "and" and "or" symbols, ∧∨, reflect a basic geometric symbol for converge (where two lines are directed toward and upward point of unity) and diverge (where two lines are directed away from a point of unity downwards to an inherent multiplicity)

¬, negation, observes an absence of any intrinsic direction unlike "tends towards",→, and "if and only if" ↔.

⊤, true observes the symbol of the tao cross which represents a synthetic unity which grounds truth.

⊤, false and inversion of this cross as an absence of synthesis where "falsity", as grounded in truths, observes an inherent disconnect of truths.


The reason I give these "explanations", is strictly because this "intuitionistic" logic may be in touch with deeper foundations of the subconscious than most might think...it may be a more..."human"...logic because of this. Many of these "symbols", grounded in a very abstract geometry are founded all over the world.

[Skepdick]

I don't know, I see where you are headed with it's absence of ontology...and "yes"...but it is a very "loose" "yes". The reason why I say "loose" is the basic symbolism used in intuitionism closely reflects basic "directional" properities and "contexts".

The simple "and" and "or" symbols, ∧∨, reflect a basic geometric symbol for converge (where two lines are directed toward and upward point of unity) and diverge (where two lines are directed away from a point of unity downwards to an inherent multiplicity)

¬, negation, observes an absence of any intrinsic direction unlike "tends towards",→, and "if and only if" ↔.

⊤, true observes the symbol of the tao cross which represents a synthetic unity which grounds truth.

⊤, false and inversion of this cross as an absence of synthesis where "falsity", as grounded in truths, observes an inherent disconnect of truths.


The reason I give these "explanations", is strictly because this "intuitionistic" logic may be in touch with deeper foundations of the subconscious than most might think...it may be a more..."human"...logic because of this. Many of these "symbols", grounded in a very abstract geometry are founded all over the world.

wtf pointed me to Ed Nelson, and so I shall borrow his language for it's good enough.

She: I have just proved ∃xA.
He: Congratulations! What is it?
She: I don’t know. I assumed ∀x¬A and derived a contradiction.
He: Oh. You proved ¬∀x¬A.
She: That’s what I said.

But he does not agree with her last statement; they have a different
semantics and a different notion of proof. This paper is an attempt to
understand the differences between them.

This is the best summary/analysis of intuitionism I have found ever/anywhere. https://web.math.princeton.edu/~nelson/papers/int.pdf

The focus on "completed communication" is spot on. Intuitionism is about semantic disambiguation.