Logic is Grounded in Self Referential Tautologies

What is the basis for reason? And mathematics?

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Eodnhoj7
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Logic is Grounded in Self Referential Tautologies

Post by Eodnhoj7 »

Logic is grounded in a self referential state which results in tautologies.

1. The "not cat exists therefore the not cat exists".

(-P --> -P)


2. The "not cat exists therefore the cat exists" considering the "cat" exists if there is a "not-not cat." The "not cat therefore the not cat" is a self referential double negative.

(-P --> -P) --> -(-P) --> P


3. The "cat exists therefore the cat exists".

(P --> P)


4. The "cat exists therefore the cat exists therefore x cat exists", necessitates the cat exists in different states thus a variation of cat occurs.

(P --> P) --> Q


5. The variation of "cat" observes a nature of "not cat" results considering a variation of the original variable necessitates the new variable as having a quality not of the original variable. The "cat" therefore "cat" is a self referential double positive.

(P --> P) --> (Q <--> -P)

6. The self referential state of the double negative through the law of identity, necessitates a positive variable which follows a double positive nature as self referential. The double positives and double negatives alternate resulting in continual variations of the original variables.

(-P --> -P) --> -(-P) --> (P --> P) --> (Q <--> -P)
mickthinks
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Re: Logic is Grounded in Self Referential Tautologies

Post by mickthinks »

I don't recognise any of those symbolic formulae as being the grounding of Logic.

You seem confused, Eodnhoj.
Eodnhoj7
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Re: Logic is Grounded in Self Referential Tautologies

Post by Eodnhoj7 »

mickthinks wrote: Sun Mar 29, 2020 12:08 am I don't recognise any of those symbolic formulae as being the grounding of Logic.

You seem confused, Eodnhoj.
"-->" therefore

"( )" brackets as contexts

https://en.m.wikipedia.org/wiki/Intuitionistic_logic

The law of identity is self referential and circular as the premise is the same as the conclusion. This self referentiality lends itself to double negation and double positives. Are double negation or double positives found in intuitionist logic? No. But rules and syntax are defined by the premises set forth, thus this logical system is made up.
Veritas Aequitas
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Re: Logic is Grounded in Self Referential Tautologies

Post by Veritas Aequitas »

Eodnhoj7 wrote: Sat Mar 28, 2020 11:39 pm Logic is grounded in a self referential state which results in tautologies.
...
Why the fuss?

Yes, logic ends up with "P is true because P is true"
So what??

Logic is merely a tool to organize thoughts but what counts is whatever the conclusion, it must be grounded empirical evidences, else it is merely empty illusory thoughts, e.g. God exists are real which is illusory.

Here is why Russell exemplify the points using the Law of Non-Contradiction as example;
Bertrand Russell in POP wrote:What we believe, when we believe the law of contradiction, is not that the mind is so made that it must believe the law of contradiction.
This belief is a subsequent result of psychological reflection, which presupposes the belief in the law of contradiction.

The belief in the law of contradiction is a belief about things, not only about thoughts.
It is not, e.g., the belief that if we think a certain tree is a beech, we cannot at the same time think that it is not a beech; it is the belief that if a tree is a beech, it cannot at the same time be not a beech.

Thus the law of contradiction is about things, and not merely about thoughts; and although belief in the law of contradiction is a thought, the law of contradiction itself is not a thought, but a fact concerning the things in the world.
Note the mentioned of "psychological" elements involved.

Thus whatever conclusion we arrive using logic, the ultimate is the conclusion must be supported by empirical evidences.
If we conclude a dog exists as real, then we bring an empirically real dog to be justified as true.

But when theists conclude 'God exists as real' they cannot bring a real God [like a real dog] for verification rather they are relying totally on logic which is merely thought-grounded only and thus erroneous.
Skepdick
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Re: Logic is Grounded in Self Referential Tautologies

Post by Skepdick »

Veritas Aequitas wrote: Sat Apr 04, 2020 8:16 am But when theists conclude 'God exists as real' they cannot bring a real God [like a real dog] for verification rather they are relying totally on logic which is merely thought-grounded only and thus erroneous.
That is not true. There is empirically verifiable evidence for God. All of reality/existence. Including the dog. Including you.

But since the God-language triggers you, I'll use a more subtle question: What verifiable evidence do you have for the existence of reality?

God. Existence. Reality. The Universe. They are all the synonymous, mystical words.
Skepdick
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Re: Logic is Grounded in Self Referential Tautologies

Post by Skepdick »

mickthinks wrote: Sun Mar 29, 2020 12:08 am I don't recognise any of those symbolic formulae as being the grounding of Logic.
Translation: The way you formulate logic is not the way I formulate logic.
mickthinks wrote: Sun Mar 29, 2020 12:08 am You seem confused, Eodnhoj.
Translation: I don't understand your language, Eodnhoj.

When using the symbol P in logic the existence of P is is implicit, not explicit. You could make existence explicit by using the existential quantifier ヨ, thus the English sentence "There exists P" translates into logic as ヨP.

The ambiguity arrises in deciding what -P means given that the ヨ is implicit, not explicit.
Is it ヨ-P , which translates in English into "there exists not-P".
or is it -ヨP, which translates in English into "there doesn't exist P"

It's the problem of Operator precedence.
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Arising_uk
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Re: Logic is Grounded in Self Referential Tautologies

Post by Arising_uk »

Skepdick wrote: When using the symbol P in logic the existence of P is is implicit, not explicit. You could make existence explicit by using the existential quantifier ヨ, thus the English sentence "There exists P" translates into logic as ヨP. ...?
Not the way I was taught it it doesn't, the existential quantifier is ヨX and it says "There is at least one X" with the X standing for a variable in a predicate proposition, so ヨX(p(X))
The ambiguity arrises in deciding what -P means given that the ヨ is implicit, not explicit.
Is it ヨ-P , which translates in English into "there exists not-P".
or is it -ヨP, which translates in English into "there doesn't exist P"
ヨX(-p(X)) says there is at least one X that does satisfy the predicate of not P and -ヨX(-p(X)) says there is not one X that satisfies the predicate of not P then of course you have ヨX(p(X)) and -ヨX(p(X)). In all cases the existence of such an object is up to whatever methods you wish to use to establish the truth of the objects or propositions of logic.

With respect to P in Propositional Logic that just stands for any proposition but generally declarative ones or fact assertions whose truth again is established by means other than logic. The only things in Logic that will necessarily be true or false are the tautologies and contradictions.
Last edited by Arising_uk on Mon Apr 20, 2020 2:58 am, edited 2 times in total.
uwot
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Yawn.

Post by uwot »

Skepdick wrote: Sat Apr 04, 2020 8:31 amGod. Existence. Reality. The Universe. They are all the synonymous, mystical words.
No they're not. 'Existence' and 'Reality' imply nothing; it's Parmenides 2500 year old observation that there isn't nothing - some shit exists. 'God' implies non human intelligence, and 'The Universe' suggests material being, both of which are the theory laden stuff any first year philosophy undergraduate who has been paying attention will be able to distinguish.
Skepdick
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Re: Logic is Grounded in Self Referential Tautologies

Post by Skepdick »

Arising_uk wrote: Sun Apr 19, 2020 9:10 pm Not the way I was taught it it doesn't, the existential quantifier is ヨX and it says "There is at least one X" with the X standing for a variable in a predicate proposition, so ヨX(p(X))

ヨX(-p(X)) says there is at least one X that does satisfy the predicate of not P
I think we are saying the same thing. You are using X to denote what I was denoting with P - an unbound variable. And you are using p(x) as a proposition satisfied by X. But the problem of reification doesn't go away. What does it mean "to satisfy a proposition"? Do you have a Satisfaction() predicate?

It you had such a predicate it seems it would mean something like "it evaluates to true" and so ヨX(p(X)) says "There exists X for which P(X) is true". But P(X) is a boolean, so then there also exists a different X (some other value) for which P(X) is false.

So then ヨX(-p(X)) means "There exists X for which -P(X) is true"

So both the proposition and its negation are satisfiable for different values of X?

That means "Existence" is a tautology.
Arising_uk wrote: Sun Apr 19, 2020 9:10 pm and -ヨX(-p(X)) says there is not one X that satisfies the predicate of not P then of course you have ヨX(p(X)) and -ヨX(p(X))
OK, but the ambiguity is in this. Does -ヨX(p(X)) mean the same thing as ヨX(-p(X)) ? Does the negation bubble up your stack?

See, I am treating everything as an expression. The only thing that is NOT explicit in my logic is my eval() function.
https://en.wikipedia.org/wiki/Eval
Arising_uk wrote: Sun Apr 19, 2020 9:10 pm With respect to P in Propositional Logic that just stands for any proposition but generally declarative ones or fact assertions whose truth again is established by means other than logic.

Right. Which makes Logic isomorphic to Type Theory and Category theory. Propositions are Types.

e.g the Curry-Howard-Lambek isomorphism. But at this point we are still talking about grammatical/syntactic identity.

We've spent all our time addressing points 1,2 and 3 - true to Wadler's law.

We have spent zero time on semantics. Which (to a computer scientist) is a design discussion around reification
Arising_uk wrote: Sun Apr 19, 2020 9:10 pm The only things in Logic that will necessarily be true or false are the tautologies and contradictions.
So, even that's not the case from the view-point of eval().

Whatever a "tautology" is, and whatever a "contradiction" is - if you can express it, you can eval() it.
Last edited by Skepdick on Mon Apr 20, 2020 2:50 pm, edited 6 times in total.
Skepdick
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Re: Yawn.

Post by Skepdick »

uwot wrote: Sun Apr 19, 2020 10:04 pm No they're not. 'Existence' and 'Reality' imply nothing; it's Parmenides 2500 year old observation that there isn't nothing - some shit exists. 'God' implies non human intelligence
Ooooh! And what does "intelligence" imply?
uwot wrote: Sun Apr 19, 2020 10:04 pm 'The Universe' suggests material being,
So, are the semantics of "being" different to the semantics of "existence"?
uwot wrote: Sun Apr 19, 2020 10:04 pm both of which are the theory laden stuff any first year philosophy undergraduate who has been paying attention will be able to distinguish.
Well, you have a Masters degree, no? Since you are over-qualified do you mind distinguishing them for us. What's the difference between "being", "existence", "The Universe" and "Reality" ?

How exactly is a "material being" different to "non-material being"?

The fact that all these things are "theory laden" is no problem for an undergraduate computer scientist. Because we understand that programming formalizes the notion of a "theory".

http://nuprl.org/Intro/intro.html

The project remains focused on logic-based tools to support programming and on implementing formal computational mathematics; we see these as inextricably linked activities. Over the years the scope of the project has expanded - from developing individual programs and theorems to constructing systems and theories. Starting with the slogan "proofs-as-programs," we now talk about "theories-as-systems." This change of scale has led to a new class of problems and challenges discussed throughout this project summary.
uwot
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Re: Yawn.

Post by uwot »

Skepdick wrote: Mon Apr 20, 2020 8:59 am
uwot wrote: Sun Apr 19, 2020 10:04 pm No they're not. 'Existence' and 'Reality' imply nothing; it's Parmenides 2500 year old observation that there isn't nothing - some shit exists. 'God' implies non human intelligence
Ooooh! And what does "intelligence" imply?
You'd have to ask someone who believes in god.
Skepdick wrote: Mon Apr 20, 2020 8:59 amSo, are the semantics of "being" different to the semantics of "existence"?
As you said Skepdick:
Skepdick wrote: Mon Apr 20, 2020 12:08 pmEverything is contextual.
Skepdick wrote: Mon Apr 20, 2020 8:59 amHow exactly is a "material being" different to "non-material being"?
Well, if you are referring to a material being, again, you'd have to ask someone who believes in such a creature. More generally idealism springs to mind, Susskind's holographic universe, brain in a vat, the Matrix, Descartes' evil dæmon. Take your pick.
Skepdick
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Re: Yawn.

Post by Skepdick »

uwot wrote: Mon Apr 20, 2020 2:05 pm You'd have to ask someone who believes in god.
Not at all. I simply have to ask somebody who believes humans have intelligence.

That's you then.
uwot wrote: Mon Apr 20, 2020 2:05 pm Well, if you are referring to a material being, again, you'd have to ask someone who believes in such a creature.
I am referring to "being" - the gerund (verb and a noun), and I am asking the person who insists that there is a difference between "being" and "existence".

That's you.
uwot wrote: Mon Apr 20, 2020 2:05 pm More generally idealism springs to mind, Susskind's holographic universe, brain in a vat, the Matrix, Descartes' evil dæmon. Take your pick.
Would it be fair to say that you think science is an idealistic establishment then? Since Maxwell's demon in statistical mechanics/thermodynamics is analogous to Descartes' evil one.

Both demons possess the property of omniscience/omnipotence/omnipresence which is necessary power for any entity in order to enable deception.
uwot
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Re: Yawn.

Post by uwot »

Skepdick wrote: Mon Apr 20, 2020 2:19 pm
uwot wrote: Mon Apr 20, 2020 2:05 pm You'd have to ask someone who believes in god.
Not at all. I simply have to ask somebody who believes humans have intelligence.

That's you then.
Well Skepdick, as per the other thread, intelligence is one of those phenomena that has a name, but isn't entirely understood. People who believe in god think there's something they can attribute to their god of choice. If you care to know, find someone who makes such a claim.
Skepdick wrote: Mon Apr 20, 2020 2:19 pm
uwot wrote: Mon Apr 20, 2020 2:05 pm Well, if you are referring to a material being, again, you'd have to ask someone who believes in such a creature.
I am referring to "being" - the gerund (verb and a noun), and I am asking the person who insists that there is a difference between "being" and "existence".

That's you.
No it isn't, after all:
Skepdick wrote: Mon Apr 20, 2020 12:08 pmEverything is contextual.
Skepdick wrote: Mon Apr 20, 2020 2:19 pmWould it be fair to say that you think science is an idealistic establishment then?
Short answer no, but I put my case here: https://philosophynow.org/issues/133/Ph ... _Millennia
Skepdick
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Re: Yawn.

Post by Skepdick »

uwot wrote: Mon Apr 20, 2020 3:39 pm Well Skepdick, as per the other thread, intelligence is one of those phenomena that has a name, but isn't entirely understood.
To claim that it's a phenomenon is to imply that you, as a phenomenologist, have experienced/observed it.

So, even if you don't understand it you have, at the very least, identified it/isolated it amongst all the other things which are present to your awareness. That is - you believe it exists, even if you lack the language/argument for it.

So you know - try put it in words...
uwot wrote: Mon Apr 20, 2020 3:39 pm Short answer no, but I put my case here: https://philosophynow.org/issues/133/Ph ... _Millennia
uwot
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Re: Yawn.

Post by uwot »

Skepdick wrote: Mon Apr 20, 2020 6:12 pm
uwot wrote: Mon Apr 20, 2020 3:39 pm Well Skepdick, as per the other thread, intelligence is one of those phenomena that has a name, but isn't entirely understood.
To claim that it's a phenomenon is to imply that you, as a phenomenologist, have experienced/observed it.
You said it yourself Mr Skepdick:
Skepdick wrote: Mon Apr 20, 2020 12:08 pmEverything is contextual.
What does intelligence mean in this context?
Skepdick wrote: Mon Apr 20, 2020 6:12 pmSo, even if you don't understand it you have, at the very least, identified it/isolated it amongst all the other things which are present to your awareness. That is - you believe it exists, even if you lack the language/argument for it.

So you know - try put it in words...
In the current context I doubt there is much difference between what you mean by awareness, and my meaning of intelligence.
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