Essence, Plenitude, and Paradox

POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a Problem Posed by Kaplan

In this paper I discuss a paradox, due to David Kaplan, that in his view threatens the use of possible worlds semantics as a model-theoretic framework for intensional logic.1 Kaplan’s paradox starts out from an intuitively reasonable principle that I refer to as the Principle of Plenitude. From this principle he derives a contradiction in what he calls Naive Possible World Theory. Kaplan’s meta...

The paradox of the unity and duality of the kidneys according to Chinese medicine: kidney essence, yin, yang, qi, the mingmen--their origins, relationships, functions and manifestations.

This paper explores the relationship between Kidney Essence, Yang, Yin and Qi, and the Mingmen, their origins, the variety of functions they provide to the human organism, mentally, physically and spiritually, and the fundamental paradox they represent in terms of unity and polarity. This exercise is part of an ongoing personal exploration in the service of a more complete understanding of the ...

Indefinite Divisibility

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a “definite totality” but rather is “indefinitely extensible”. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this pictur...

Scaling—a Plenitude of Power Laws - Principles of Complex Systems | @pocsvox CSYS/MATH 300, Fall, 2015 | #FallPoCS2015

Bertrand’s Paradox Revisited: More Lessons about that Ambiguous Word, Random

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...