Resolution of Paradoxes (Final Version)

H

Huseyn

Registered Member
Abstract: A paradox arises when the degree of Positional Dependence (PD) of the dependent concept within the scope of a given question is not taken into account in relation to the leading concept within the same scope.

Example 1 — The Egg and the Hen:

  • The dependent: “Egg,” relying on the leading “Hen,” in the maximally possible PD in both of its states:
    • Initial (as laid by the hen),
    • Final (as incubated by the hen).
  • In the perspective of the question “Which came first?” the leading concept is revealed in the minimally possible PD of combinatorial concepts suitable for choice.
  • Thus, the paradox is resolved by distinguishing between maximal and minimal PD roles.
Example 2 — Achilles and the Tortoise:

  • Achilles moves only to the mark left by the leading “moving tortoise.”
  • He cannot overtake it, relying in both states on the maximal PD of the tortoise.
  • The paradox dissolves once the positional dependence is redefined.
Example 3 — The Liar:

  • The dependent “I” in the final state, relying on the leading “Lie” in minimal PD, becomes sequentially negated in both states.
  • The paradox is resolved by shifting the PD role.
Example 4 — The Cretan:

  • The dependent “Cretan” in the final state, relying on the leading “set of Cretans not represented by this Cretan as non-liars,” becomes sequentially negated in both states.
  • Again, the paradox is resolved through PD adjustment.
Example 5 — The Barber:

  • The dependent “Barber” relies on the leading “those who shave themselves” in maximal PD, and on “those who do not shave themselves” in minimal PD.
  • The paradox is resolved by recognizing the change of PD degrees.
Example 6 — The Arrow:

  • The dependent “Arrow” relies on the leading “state of motion” in maximal PD, and on “state of rest” in minimal PD.
  • The paradox is resolved by situating the arrow within the change of PD degrees.
Example 7 — Socratic Knowledge:

  • The dependent “Knowledge” relies on the leading “knowable.”
  • The paradox of Zeno is resolved by clarifying the positional dependence of knowledge.
Source (original publication, 26 November 2018): Resolution of Paradoxes (Final Version) — Pikabu

Note: This is only a translation into English, made exclusively by AI for Sciforums. The original conceptual framework, theses, and axioms belong to the author.

If one link is not sufficient, please see here for a broader set of references where the work has long been published:Search results — Решение парадоксов (окончательная версия) /Resolution of Paradoxes (Final Version)/
 
Huseyn said:
Abstract: A paradox arises when the degree of Positional Dependence (PD) of the dependent concept within the scope of a given question is not taken into account in relation to the leading concept within the same scope.

Example 1 — The Egg and the Hen:

  • The dependent: “Egg,” relying on the leading “Hen,” in the maximally possiblePD in both of its states:
    • Initial (as laid by the hen),
    • Final (as incubated by the hen).
  • In the perspective of the question “Which came first?” the leading concept is revealed in the minimally possible PD of combinatorial concepts suitable for choice.
  • Thus, the paradox is resolved by distinguishing between maximal and minimal PD roles.
Example 2 — Achilles and the Tortoise:

  • Achilles moves only to the mark left by the leading “moving tortoise.”
  • He cannot overtake it, relying in both states on the maximal PD of the tortoise.
  • The paradox dissolves once the positional dependence is redefined.
Example 3 — The Liar:

  • The dependent “I” in the final state, relying on the leading “Lie” in minimal PD, becomes sequentially negated in both states.
  • The paradox is resolved by shifting the PD role.
Example 4 — The Cretan:

  • The dependent “Cretan” in the final state, relying on the leading “set of Cretans not represented by this Cretan as non-liars,” becomes sequentially negated in both states.
  • Again, the paradox is resolved through PD adjustment.
Example 5 — The Barber:

  • The dependent “Barber” relies on the leading “those who shave themselves” in maximal PD, and on “those who do not shave themselves” in minimal PD.
  • The paradox is resolved by recognizing the change of PD degrees.
Example 6 — The Arrow:

  • The dependent “Arrow” relies on the leading “state of motion” in maximal PD, and on “state of rest” in minimal PD.
  • The paradox is resolved by situating the arrow within the change of PD degrees.
Example 7 — Socratic Knowledge:

  • The dependent “Knowledge” relies on the leading “knowable.”
  • The paradox of Zeno is resolved by clarifying the positional dependence of knowledge.
Source (original publication, 26 November 2018): Resolution of Paradoxes (Final Version) — Pikabu

Note: This is only a translation into English, made exclusively by AI for Sciforums. The original conceptual framework, theses, and axioms belong to the author.

If one link is not sufficient, please see here for a broader set of references where the work has long been published:Search results — Решение парадоксов (окончательная версия) /Resolution of Paradoxes (Final Version)/
Click to expand...
You don't learn do you?
 
Huseyn said:
A paradox arises when the degree of Positional Dependence (PD) of the dependent concept within the scope of a given question is not taken into account in relation to the leading concept within the same scope.
Click to expand...
What's "positional dependence"?
 
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