Logic is Grounded in Self Referential Tautologies
Logic is Grounded in Self Referential Tautologies
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 "notnot 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)
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 "notnot 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)

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Re: Logic is Grounded in Self Referential Tautologies
I don't recognise any of those symbolic formulae as being the grounding of Logic.
You seem confused, Eodnhoj.
You seem confused, Eodnhoj.
Re: Logic is Grounded in Self Referential Tautologies
">" thereforemickthinks 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.
"( )" 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.

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Re: Logic is Grounded in Self Referential 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 NonContradiction as example;
Note the mentioned of "psychological" elements involved.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.
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 thoughtgrounded only and thus erroneous.
Re: Logic is Grounded in Self Referential Tautologies
That is not true. There is empirically verifiable evidence for God. All of reality/existence. Including the dog. Including you.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 thoughtgrounded only and thus erroneous.
But since the Godlanguage 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.
Re: Logic is Grounded in Self Referential Tautologies
Translation: The way you formulate logic is not the way I formulate logic.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: 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 notP".
or is it ヨP, which translates in English into "there doesn't exist P"
It's the problem of Operator precedence.
 Arising_uk
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Re: Logic is Grounded in Self Referential Tautologies
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))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. ...?
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.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 notP".
or is it ヨP, which translates in English into "there doesn't exist P"
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.
Yawn.
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.
Re: Logic is Grounded in Self Referential Tautologies
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?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
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.
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?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))
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 CurryHowardLambek 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
So, even that's not the case from the viewpoint of eval().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.
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.
Re: Yawn.
Ooooh! And what does "intelligence" imply?
So, are the semantics of "being" different to the semantics of "existence"?
Well, you have a Masters degree, no? Since you are overqualified 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 "nonmaterial 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 logicbased 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 "proofsasprograms," we now talk about "theoriesassystems." This change of scale has led to a new class of problems and challenges discussed throughout this project summary.
Re: Yawn.
You'd have to ask someone who believes in god.
As you said Skepdick:
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.
Re: Yawn.
Not at all. I simply have to ask somebody who believes humans have intelligence.
That's you then.
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.
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.
Re: Yawn.
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.
No it isn't, after all:
Short answer no, but I put my case here: https://philosophynow.org/issues/133/Ph ... _Millennia
Re: Yawn.
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
Re: Yawn.
You said it yourself Mr Skepdick:
What does intelligence mean in this context?
In the current context I doubt there is much difference between what you mean by awareness, and my meaning of intelligence.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...