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Re: The Liar's paradox
Posted: Thu Feb 07, 2019 3:17 pm
by Logik
Walker wrote: ↑Thu Feb 07, 2019 3:15 pm
x is x
y is y
There are not grammatically correct propositions in type theory.
x = x ⇒ True
or
x = x ⇒ False.
It's just a choice.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 3:18 pm
by Walker
Whatever, but,
x is x
y is y
x is not y
Sky is Sky
Blue is Blue
Sky is not Blue
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 3:19 pm
by Logik
Walker wrote: ↑Thu Feb 07, 2019 3:18 pm
Whatever, but,
x is x
y is y
x is not y
Sky is Sky
Blue is Blue
Sky is not Blue
OK, I know you are trying to be prescriptive about classical logc, BUT you can f*** off with your linguistic prescriptivism.
We are trying to solve Liar's paradox. And you are insisting on using the logic which causes it.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 3:20 pm
by Walker
I simply listed a series of truths.
Make of them what you will.
Now, you f*** off.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 3:21 pm
by Logik
Walker wrote: ↑Thu Feb 07, 2019 3:20 pm
I simply listed a series of truths.
Make of them what you will.
Now, you f*** off.
No. You listed a bunch of axioms.
If you accept them as 'true' then so be it. I reject your simpleton religion.
To solve Liar's paradox you need a high-order logic. Like Type Theory.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 4:50 pm
by Eodnhoj7
Logik wrote: ↑Thu Feb 07, 2019 3:21 pm
Walker wrote: ↑Thu Feb 07, 2019 3:20 pm
I simply listed a series of truths.
Make of them what you will.
Now, you f*** off.
No. You listed a bunch of axioms.
If you accept them as 'true' then so be it. I reject your simpleton religion.
To solve Liar's paradox you need a high-order logic. Like Type Theory.
You need a higher-order logic than type theory.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 4:56 pm
by Logik
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 4:50 pm
You need a higher-order logic than type theory.
Why?
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 5:48 pm
by Eodnhoj7
Logik wrote: ↑Thu Feb 07, 2019 4:56 pm
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 4:50 pm
You need a higher-order logic than type theory.
Why?
You cannot avoid paradox at the general level when paradox is the foundation for all phenomenon. All measurement begins with a localization of some facet of "being". This in itself is an act of seperation resulting in a base dualistic state:
1) "Identity Axiom 1" as "△•△"
where "•" equivocates to any symbolic notation of relation and "△" equivocates to any variable, observes a base dualism where the act of observing a relation results in a basic dichotomy of the variable "△ and △" thus leaving the symbolic notation of "•" effectively undefined. This is isomorphically reflected in Point 2 an as such is determined by it and observed as a divergence of and convergence to Point 3.
2) "Identity Axiom 2" as "•△•"
The symbol notatation of relation, observed as "•" is in itself a variable and as a variable and can only be defined by a dichotomy. This "symbolic" variable of relation in turn is defined by the variables through which it relates; hence results in a base dualism. This is isomorphically reflected in Point 1 and as such is determined by it and observed as a divergence of and convergence to Point 3.
3) "Identity Axiom 3" as "◬"
The nature of the symbol of relation as variable and the variable existing through relation necessitates a dualism of form and function as observed by the dualistic nature of Points 1 and 2. This is a contradiction as there is no equilibrium to maintain a balance. This Dualistic nature of form/function in symbolism requires a form of inherent synthesis from which the dualism of Points 1 and 2 converge and diverge as Point 3 with Point 3 proven through Points 1 and 2.
The dichotomy of form and function where variable can be observed in a noun and verb state, can be further observed in the "metaphysics of language" thread.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:04 pm
by Logik
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 5:48 pm
Logik wrote: ↑Thu Feb 07, 2019 4:56 pm
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 4:50 pm
You need a higher-order logic than type theory.
Why?
You cannot avoid paradox at the general level when paradox is the foundation for all phenomenon. All measurement begins with a localization of some facet of "being". This in itself is an act of seperation resulting in a base dualistic state:
1) "Identity Axiom 1" as "△•△"
where "•" equivocates to any symbolic notation of relation and "△" equivocates to any variable, observes a base dualism where the act of observing a relation results in a basic dichotomy of the variable "△ and △" thus leaving the symbolic notation of "•" effectively undefined. This is isomorphically reflected in Point 2 an as such is determined by it and observed as a divergence of and convergence to Point 3.
2) "Identity Axiom 2" as "•△•"
The symbol notatation of relation, observed as "•" is in itself a variable and as a variable and can only be defined by a dichotomy. This "symbolic" variable of relation in turn is defined by the variables through which it relates; hence results in a base dualism. This is isomorphically reflected in Point 1 and as such is determined by it and observed as a divergence of and convergence to Point 3.
3) "Identity Axiom 3" as "◬"
The nature of the symbol of relation as variable and the variable existing through relation necessitates a dualism of form and function as observed by the dualistic nature of Points 1 and 2. This is a contradiction as there is no equilibrium to maintain a balance. This Dualistic nature of form/function in symbolism requires a form of inherent synthesis from which the dualism of Points 1 and 2 converge and diverge as Point 3 with Point 3 proven through Points 1 and 2.
The dichotomy of form and function where variable can be observed in a noun and verb state, can be further observed in the "metaphysics of language" thread.
Why do you want to avoid paradox?
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:08 pm
by Eodnhoj7
Logik wrote: ↑Thu Feb 07, 2019 6:04 pm
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 5:48 pm
Logik wrote: ↑Thu Feb 07, 2019 4:56 pm
Why?
You cannot avoid paradox at the general level when paradox is the foundation for all phenomenon. All measurement begins with a localization of some facet of "being". This in itself is an act of seperation resulting in a base dualistic state:
1) "Identity Axiom 1" as "△•△"
where "•" equivocates to any symbolic notation of relation and "△" equivocates to any variable, observes a base dualism where the act of observing a relation results in a basic dichotomy of the variable "△ and △" thus leaving the symbolic notation of "•" effectively undefined. This is isomorphically reflected in Point 2 an as such is determined by it and observed as a divergence of and convergence to Point 3.
2) "Identity Axiom 2" as "•△•"
The symbol notatation of relation, observed as "•" is in itself a variable and as a variable and can only be defined by a dichotomy. This "symbolic" variable of relation in turn is defined by the variables through which it relates; hence results in a base dualism. This is isomorphically reflected in Point 1 and as such is determined by it and observed as a divergence of and convergence to Point 3.
3) "Identity Axiom 3" as "◬"
The nature of the symbol of relation as variable and the variable existing through relation necessitates a dualism of form and function as observed by the dualistic nature of Points 1 and 2. This is a contradiction as there is no equilibrium to maintain a balance. This Dualistic nature of form/function in symbolism requires a form of inherent synthesis from which the dualism of Points 1 and 2 converge and diverge as Point 3 with Point 3 proven through Points 1 and 2.
The dichotomy of form and function where variable can be observed in a noun and verb state, can be further observed in the "metaphysics of language" thread.
Why do you want to avoid paradox?
I am not avoiding one, just using it as a solution where it negates itself.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:13 pm
by Logik
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 6:08 pm
I am not avoiding one, just using it as a solution where it negates itself.
Why do you want paradox to negate itself?
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:16 pm
by Eodnhoj7
Logik wrote: ↑Thu Feb 07, 2019 6:13 pm
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 6:08 pm
I am not avoiding one, just using it as a solution where it negates itself.
Why do you want paradox to negate itself?
Why wouldn't a paradox negate itself, it wouldn't be paradoxical if it didn't.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:19 pm
by Logik
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 6:16 pm
Why wouldn't a paradox negate itself, it wouldn't be paradoxical if it didn't.
You are answering the question with a question.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:20 pm
by Eodnhoj7
Logik wrote: ↑Thu Feb 07, 2019 6:19 pm
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 6:16 pm
Why wouldn't a paradox negate itself, it wouldn't be paradoxical if it didn't.
You are answering the question with a question.
All questions are the contextualization of answers.
Re: The Liar's paradox
Posted: Thu Feb 07, 2019 6:29 pm
by Logik
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 6:20 pm
Logik wrote: ↑Thu Feb 07, 2019 6:19 pm
Eodnhoj7 wrote: ↑Thu Feb 07, 2019 6:16 pm
Why wouldn't a paradox negate itself, it wouldn't be paradoxical if it didn't.
You are answering the question with a question.
All questions are the contextualization of answers.
Why contextualise answers?