The Laws of Logic Negate Through Self-Referentiality

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Eodnhoj7
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The Laws of Logic Negate Through Self-Referentiality

Post by Eodnhoj7 »

As stands the laws of logic negate when self-referencing:



1. There is either the law of identity or the law of non-contradiction when applying the law of excluded middle, this is considering both equality and non-equality are opposites. If the law of identity stands, and the law of non-contradiction does not, then A=A and A=-A. If the law of non-contradiction stands, and the law of identity does not, then A equals an infinity of things thus is indefinite and obscure: A=B,C,D,E.... (under this the law of non-contradiction is also valueless as A and -A equal an infinity of things).



2. The law of identity necessitates the law of excluded middle being the law of excluded middle and the law of non-contradiction being the law of non-contradiction. At first glance this makes sense but the contradiction occurs in the respect that now there are multiple laws of excluded middles and multiple laws of non-contradiction as equality is dyadic, A and A as A=A, at minimum while being polymorphous when taken to the extreme, A and A and A and... as A=A=A=.... This multiplicity of the single law regresses, or rather progresses, infinitely thus is indefinite as ((A=A)=(A=A))... or (A=A=A...). Dually each of these laws, grounded in the variable of A or -A, can equivocate to an infinite number of things as A or -A are variables which encompass an infinite number of meanings; this infinity of meanings is indefiniteness with this infinity of meanings resulting from a self-reference.



3. The law of non-contradiction necessitates that the law of identity does not equal the law of excluded middle considering the "equals" function is the complete opposite of the "or" function; "or" is difference thus is an absence of equality. This again makes sense at first glance however the contradiction ensues further considering "equality" stands in contrast to "or" thus making "or" equivocate to "not-equals", therefore repetitively stating "equality" does not equal "non-equality" and the law of non-contradiction becomes itself as "not equaling" "not equals" or rather (=)=/=(=/=). The law of non-contradiction as the law of non-contradiction equivocates as the law of identity yet both are opposites as the law of identity is "equality" and the law of non-contradiction is "non-equality"; in stating (=/=)=(=/=) we are necessitating "equality" is inseparable from "non-equality" yet both must be distinct if identity of non-contradiction is to hold.
alan1000
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by alan1000 »

I shouldn't wonder.
Flannel Jesus
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Flannel Jesus »

Eodnhoj7 wrote: Thu May 12, 2022 12:47 am As stands the laws of logic negate when self-referencing:



1. There is either the law of identity or the law of non-contradiction when applying the law of excluded middle, this is considering both equality and non-equality are opposites.
I don't think this has been demonstrated clearly enough. Why can't all three stand at the same time?
Skepdick
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Skepdick »

Flannel Jesus wrote: Mon Jul 18, 2022 11:59 am I don't think this has been demonstrated clearly enough. Why can't all three stand at the same time?
They can. As long as you don't mind trivialising your formal system. In actual fact - you should learn NOT to mind trivialising your formal system because all formal systems are just ellaborate tautologies.

Non-contradiction is defined as: ¬(P ∧ ¬P) ↔ ⊤
The symbol " ↔" works in exactly the same way as the Mathematical symbol "=".
It means "Any time you encounter the pattern on the left you can substitute it with the pattern on the right - they mean the same thing" e.g they are identical.

And then there's this thing in Mathematics called the Univalence axiom: identity is equivalent to equivalence. If A and B are identical (as in law of identity - identical) then A and B are equivalent. Nothing outrageous here either. A rose is a rose is a rose. 1 = 1 = 1.

So far - so good. The "law" of non-contradiction depends on the law of identity.
But the law of non-contradiction is itself a proposition. it proposes THAT ¬(P ∧ ¬P) is identical to ⊥

So be it.

But THEN the law of excluded middle comes in and fucks shit up because it says either ¬(P ∧ ¬P) is identical to ⊥ or it isn't.

None of this is particularly interesting from the view-point of Mathematics though. The "law" of excluded middle is the same thing as having a choice: A or B - choose one (without getting bogged down into the details of HOW we choose A or B).

IF you admit choice into your formal system then you can trivially derive the law of excluded middle using this theorem.

And IF you admit choice into your formal system then you can trivially (and axiomatically) choose whether ¬(P ∧ ¬P) is identical to ⊤ or not.

You could (axiomatically) choose that ¬(P ∧ ¬P) is identical to ⊥
Last edited by Skepdick on Mon Jul 18, 2022 1:09 pm, edited 2 times in total.
Skepdick
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Skepdick »

In fact, the OP itself is a tautology. Boring and trivial.

Everybody understands (or, I hope - should understand) that self-evaluation causes paradox.

The paradigm case being: This sentence is false.

And so any rule-based system (*cough* Logic/Mathematics *cough*) which evaluates its own rules suffers from this. We know, of course. Wittgenstein told us.
This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule.

Wittgenstein, Philosophical Investigations §201 a"
And most recently, Girard tried to tackle this issue in "Locus Solum: From the rules of logic to the logic of rules".

But this is a whole lot of prose/poetry. Here is a direct example of ¬(P ∧ ¬P) ↔ ⊥
lnc-ruby.png
lnc-ruby.png (40.96 KiB) Viewed 2229 times
bobmax
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by bobmax »

The three principles boil down to just one: the principle of identity.
From which the other two descend.

The identity principle is the foundation of all rational thinking.
Which is determined thought.

Not respecting this principle, thought fades into the indeterminate.

Therefore it is necessary to hold firmly to this indispensable principle in order to be able to think.

Although... it's not absolute.
Because in reality A is never equal to A.
Skepdick
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Skepdick »

bobmax wrote: Mon Jul 18, 2022 3:24 pm Not respecting this principle, thought fades into the indeterminate.

Therefore it is necessary to hold firmly to this indispensable principle in order to be able to think.
This is not true (and I don't mean false).

As Schrödinger observed a century ago physics works just fine without it.

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_logic

In practice, rejecting the law has absolutely no side-effects on other logical/mathematical operations one might perform with the symbol. Simply don't compare a thing to itself (because it's meaningless to do so).

I am not I. Time has passed.
fuck-identity.png
fuck-identity.png (32.9 KiB) Viewed 2215 times
Eodnhoj7
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Eodnhoj7 »

Skepdick wrote: Mon Jul 18, 2022 12:51 pm In fact, the OP itself is a tautology. Boring and trivial.

Everybody understands (or, I hope - should understand) that self-evaluation causes paradox.

The paradigm case being: This sentence is false.

And so any rule-based system (*cough* Logic/Mathematics *cough*) which evaluates its own rules suffers from this. We know, of course. Wittgenstein told us.
This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule.

Wittgenstein, Philosophical Investigations §201 a"
And most recently, Girard tried to tackle this issue in "Locus Solum: From the rules of logic to the logic of rules".

But this is a whole lot of prose/poetry. Here is a direct example of ¬(P ∧ ¬P) ↔ ⊥
lnc-ruby.png
If self evaluation causes paradox, and it does as presented by the op, then a continual progression is paradoxical as well considering:

1. The "continual progression" must progress past itself if "the progression" is universal; this is a self-negation.

2. The "continual progression" must not progress past itself if "the progression" is to progress; this progression is not universal thus self-referentiality (paradox) is a part of truth as an absence of progression occurs.

3. Either way, as presented in points 1 and 2, we result in paradox.
Eodnhoj7
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Eodnhoj7 »

Skepdick wrote: Mon Jul 18, 2022 3:41 pm
bobmax wrote: Mon Jul 18, 2022 3:24 pm Not respecting this principle, thought fades into the indeterminate.

Therefore it is necessary to hold firmly to this indispensable principle in order to be able to think.
This is not true (and I don't mean false).

As Schrödinger observed a century ago physics works just fine without it.

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_logic

In practice, rejecting the law has absolutely no side-effects on other logical/mathematical operations one might perform with the symbol. Simply don't compare a thing to itself (because it's meaningless to do so).

I am not I. Time has passed.

fuck-identity.png
Self-referentiality is unavoidable considering "everything" has no comparison but itself.
Eodnhoj7
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Eodnhoj7 »

bobmax wrote: Mon Jul 18, 2022 3:24 pm The three principles boil down to just one: the principle of identity.
From which the other two descend.

The identity principle is the foundation of all rational thinking.
Which is determined thought.

Not respecting this principle, thought fades into the indeterminate.

Therefore it is necessary to hold firmly to this indispensable principle in order to be able to think.

Although... it's not absolute.
Because in reality A is never equal to A.
The necessity of "or", because of the distinctions it necessitates allowing for form to occur, can be the relative starting point as well....beginning points are relative.
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Astro Cat
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Astro Cat »

Skepdick wrote: Mon Jul 18, 2022 12:39 pm
Flannel Jesus wrote: Mon Jul 18, 2022 11:59 am I don't think this has been demonstrated clearly enough. Why can't all three stand at the same time?
They can. As long as you don't mind trivialising your formal system. In actual fact - you should learn NOT to mind trivialising your formal system because all formal systems are just ellaborate tautologies.

Non-contradiction is defined as: ¬(P ∧ ¬P) ↔ ⊤
The symbol " ↔" works in exactly the same way as the Mathematical symbol "=".
It means "Any time you encounter the pattern on the left you can substitute it with the pattern on the right - they mean the same thing" e.g they are identical.

And then there's this thing in Mathematics called the Univalence axiom: identity is equivalent to equivalence. If A and B are identical (as in law of identity - identical) then A and B are equivalent. Nothing outrageous here either. A rose is a rose is a rose. 1 = 1 = 1.

So far - so good. The "law" of non-contradiction depends on the law of identity.
But the law of non-contradiction is itself a proposition. it proposes THAT ¬(P ∧ ¬P) is identical to ⊥

So be it.

But THEN the law of excluded middle comes in and fucks shit up because it says either ¬(P ∧ ¬P) is identical to ⊥ or it isn't.

None of this is particularly interesting from the view-point of Mathematics though. The "law" of excluded middle is the same thing as having a choice: A or B - choose one (without getting bogged down into the details of HOW we choose A or B).

IF you admit choice into your formal system then you can trivially derive the law of excluded middle using this theorem.

And IF you admit choice into your formal system then you can trivially (and axiomatically) choose whether ¬(P ∧ ¬P) is identical to ⊤ or not.

You could (axiomatically) choose that ¬(P ∧ ¬P) is identical to ⊥
Are you using character map to get logic symbols to work on the forum? What’s your secret to getting those? I can get negation with alt+0173 (or similar, I’m typing on a phone and I more have it memorized from hand position than actual number) and I was able to find the existential operator (the backwards E) in character map, but I can’t find for instance the universal operator (upside down A) and the and symbol you’ve pasted here (^).

Would also be nice to have arrows for material implication and the like. How are you doing it?
Skepdick
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Re: The Laws of Logic Negate Through Self-Referentiality

Post by Skepdick »

Astro Cat wrote: Sat Aug 13, 2022 1:36 pm Are you using character map to get logic symbols to work on the forum? What’s your secret to getting those? I can get negation with alt+0173 (or similar, I’m typing on a phone and I more have it memorized from hand position than actual number) and I was able to find the existential operator (the backwards E) in character map, but I can’t find for instance the universal operator (upside down A) and the and symbol you’ve pasted here (^).

Would also be nice to have arrows for material implication and the like. How are you doing it?
Copy/paste.

I have a note/document (accessible with a simple shortcut) which has most of the symbols I need.
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