CONTRADICTION OF IDENTITY
Philosophy is both a series of equations that occurs through these equations as definition through certain laws of definition. In simpler terms these equations are both self referencing and express themselves tautologically through further equations much in the same manner to define defintion requires the same laws of definition to define it. This is a spiral.
These equations act as identity laws, not just of philosophy but as philosophy itself. Philosophy is a tautology of identity laws that stem beyond Aristotelian principles of the Principle of Identity: (P-->P), The Law of Non-Contradiction (P=/=P) and the Law of Excluded Middle (P v -P).
Laws of identity are unavoidable in philosophy as an assumed context is constant, this assumed context is identity itself.
The nature of tautologies are expressed as points of awareness, a continual regress of assertions, and circularly self referencing. This triad is called the Munchausseen Trilemma. However the original Aristotelian laws of identity are contradictory if applied under the Munchauseen Trilemma:
1. "P" is an assumed variable as a point of view of the observer.
2. (P=P) leads to an infinite regress as ((((P=P)=(Q=Q))=(R=R))=(S=S))=....
3. (P=P) has the same premise as the conclusion thus is circular.
Dually each of the laws is subject to the trilemma:
(P=P) is subject to circularity as P is both the premise and conclusion.
(P=/=-P) is subject to infinite regress as -P equates to (R,S,T,...) as variables which are not P
(Pv-P) is subject to assumed assertions as P and -P are strictly taken without proof.
Dually the laws are contradictory if applied to themselves in a circular self referential manner:
((P=P)v(-P=-P)) necessitates under the law of excluded middle one principle of identity exists or the other thus negating the principle of identity into existing in seperate states of either one identity or the other.
(P=P)v(P=/=-P) necessitates that under the law of excluded middle either the law of identity exists or the law of non contradiction. ****If one is false, then P=-P either way. If (P=P) is false then (P=-P) and (P=/=-P) simultaneously. If (P=/=-P) is false then (P=P) and (P=-P) simultaneously
((P=P)=(-P=-P)) necessitates under the law of identity that two opposing values are equal through the law of identity thus negating the law of non contradiction where P cannot equal not P.
((P=P)=/=(-P=-P)) necessitates under the law of non-contradiction that two principles equal through the law of identity are not equal thus the law of identity is not equal to itself.
((P=P)=(-P=-P)) v ((P=P)=/=(-P=-P)) necessitates either the law of identity or the law of non contradiction results, thus negating either the fallacious use of the law of identity or the fallacious use of the law of non-contradiction but not both. Either the law of identity or the law of non contradiction is negated. If the law of non contradiction is negated then the law of identity ceases to exist as P = -P. If the law of identity is negated then the law of non contradiction is negated as P = -P.
On top of it, in physics, Newton's Law "For every reaction there is an equal and opposite reaction" necessitates P = -P. However the Aristotle's Principle of Non Contradiction states P =/= -P. A contradiction between Newtonian physics and Aristotelian logic occurs.
For "every action there is an equal and opposite reaction" demands two assertions: that of the action and that of the opposite reaction. The first action is thetical, the second is antithetical. One is the opposite of the other thus is its negation. For example a "ball moving to the right" is a thetical assertion. The "ball not moving to the right" necessitates its antithetical assertion.
The "ball does not move to the right" necessitates the "ball moving to the left" as an opposite movement. So while the "ball not moving to the right" does not necessitate "the ball moving to the left" (as the ball can move up or down), the "ball moving to the left" is still a negative and falls under an opposite.
These contradictions in identity occur precisely because of isomorphic and recursive contexts, yet isomorphism, recursion and contextuality are the grounding for all identity properties thus mandating original identity properities as faulty due to the absence of self referentiality.
Contradiction of Identity
Re: Contradiction of Identity
https://en.wikipedia.org/wiki/Non-class ... cal_logics
https://sci-hub.tw/10.1007/BF01057649
Axiom: ~(x=x)Non-reflexive logic (also known as "Schrödinger logics") rejects or restricts the law of identity;
https://sci-hub.tw/10.1007/BF01057649
Re: Contradiction of Identity
The identity laws can be negated by applying the laws to the laws. Recursive self referentiality negates the laws.Skepdick wrote: ↑Mon Jun 15, 2020 9:55 pm https://en.wikipedia.org/wiki/Non-class ... cal_logicsAxiom: ~(x=x)Non-reflexive logic (also known as "Schrödinger logics") rejects or restricts the law of identity;
https://sci-hub.tw/10.1007/BF01057649
Re: Contradiction of Identity
Because it sets the premise for new identity laws: isomorphism, recursion, contextual loops
Re: Contradiction of Identity
Read the first 2 pages of the paper I linked you to.
There very notion of "identity" is meaningless.
(A = A) means the left "A" is indistinguishable from the right "A" with respect to its characteristics.
They are not "the same" A.
Re: Contradiction of Identity
Identity is a loop. (A = A) is circular.
(A=B) is an isomorphism.
Re: Contradiction of Identity
It depends on what the operator "=" means.
https://ncatlab.org/nlab/show/equality#DifferentKinds
Here is a list of distinctions between different notions of equality, in different contexts, where possibly all the following pairs of notions are, in turn, “the same”, just expressed in terms of different terminologies:
the difference between axiomatic and defined equality;
the difference between identity and equality,
the difference between intensional and extensional equality,
the difference between equality judgements and equality propositions,
the difference between equality and isomorphism,
the difference between equality and equivalence,
the possibility of operations that might not preserve equality.
Re: Contradiction of Identity
P=PSkepdick wrote: ↑Mon Jun 15, 2020 11:05 pmIt depends on what the operator "=" means.
https://ncatlab.org/nlab/show/equality#DifferentKinds
Here is a list of distinctions between different notions of equality, in different contexts, where possibly all the following pairs of notions are, in turn, “the same”, just expressed in terms of different terminologies:
the difference between axiomatic and defined equality;
the difference between identity and equality,
the difference between intensional and extensional equality,
the difference between equality judgements and equality propositions,
the difference between equality and isomorphism,
the difference between equality and equivalence,
the possibility of operations that might not preserve equality.
=P=
P=
as
P(p)P
p(P)p
(P(p))
Last edited by Eodnhoj7 on Mon Jun 15, 2020 11:21 pm, edited 1 time in total.
Re: Contradiction of Identity
Identity is triadic considering the middle term is empty on its own terms and is defined through that which repeats under a circularlity. This can be seen under the example of P=P where "=" is empty of meaning except through the repetition of P. "=" is purely assumed and this assumption of "=" is defined through a repetition of P by a progression which is circular. The Munchauseen Trillema is reflected in this.
P=P, or more accurately P(p)P where "p" represents "-->", "<-->", "<--", etc., reflects a triadic nature in both structure and how it reflects through other assertions as p(P)p and (P(p)).
P(p)P, p(P)p, (P(p)) are all variations of the other as a cycling between assertions.
P(p)P where p is defined through P.
p(P)p where P is defined through p.
(P(p)) where P and p are defined through eachother.
One variable is expressed through a new one in a new variation. Under an expression of P(p)P where p can be defined as a variety of things as "therefore", "equals", "because", etc. the middle term is intrinsically empty and defined through the terms which repeat.
p(P)p observes this repetition inversely where P is defined through p.
The dualism between P(p)P and p(P)p observes P(p)P and p(P)p define eachother so that P and p are defined as existing strictly "as is" under (P(p)) where one context is defined as a tautology of the other as a variation of the original context.
"Equals" exists as a variation of "P" where a statement of "Cat equals Cat" reflects "Cat equals" in which "equals" is an action of "cat" as an extension of it. The dynamic state "equals" is the static state "Cat" expressed under a new variation where "Cat equals" observes "equals" as an action which is an extension of "Cat".