There are not grammatically correct propositions in type theory.

x = x ⇒ True

or

x = x ⇒ False.

It's just a choice.

There are not grammatically correct propositions in type theory.

x = x ⇒ True

or

x = x ⇒ False.

It's just a choice.

Last edited by Logik on Thu Feb 07, 2019 3:18 pm, edited 1 time in total.

Whatever, but,

x is x

y is y

x is not y

Sky is Sky

Blue is Blue

Sky is not Blue

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 fuck off with your linguistic prescriptivism.

We are trying to solve Liar's paradox. And you are insisting on using the logic which causes it.

I simply listed a series of truths.

Make of them what you will.

Now, you fuck off.

Make of them what you will.

Now, you fuck 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 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?Eodnhoj7 wrote: ↑Thu Feb 07, 2019 5:48 pmYou 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.

I am not avoiding one, just using it as a solution where it negates itself.Logik wrote: ↑Thu Feb 07, 2019 6:04 pmWhy do you want to avoid paradox?Eodnhoj7 wrote: ↑Thu Feb 07, 2019 5:48 pmYou 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.