On the Scope of Diagonal Argument and on Contradictory Equivalence. Cantor's Paradox
نویسنده
چکیده
Restriction on the scope of diagonal argument will be set using two absolutely different proof techniques. One of the proof techniques will analyze contradictory equivalence (R ∈ R ↔ R ∉ R) in a rather unconventional way.
منابع مشابه
Diagonal arguments and fixed points
A universal schema for diagonalization was popularized by N.S. Yanofsky (2003), based on a pioneering work of F.W. Lawvere (1969), in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function. It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema. Here, we fi...
متن کاملParadox and Relativism
Since the time of Plato, relativism has been attacked as a self-refuting theory. Today, there are two basic kinds of argument that are used to show that global relativism is logically incoherent: first, a direct descendent of the argument Plato uses against Protagoras, called the peritrope; and, second, a more recent argument that relativism leads to an infinite regress. Although some relativis...
متن کاملExpanding HTA – Correcting a Misattribution, Clarifying the Scope of HTA and CEA; Comment on “Ethics in HTA: Examining the ‘Need for Expansion’”
Abrishami, Oortwijn, and Hofman (AOH) attribute to me a position I do not hold and an argument I did not make. The purpose of this note is make clear what my position actually is and to clarify the main differences between health technology assessment (HTA) and cost-effectiveness analysis (CEA).
متن کاملCantor's Problem
What is born on Sacred Cows is as much religion as is any theology. Abstract: In 1891 a paper by Georg Cantor was published in which he addressed the relative cardinality of two sets, the set of integers and the set of real numbers, in effort to demonstrate that the two sets were of unequal cardinality. This paper offers a contrary conclusion to Cantor's argument, together with implications to ...
متن کاملDiagonalizing by Fixed-Points
A universal schema for diagonalization was popularized by N. S. Yanofsky (2003) in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function. It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema. Here, we fit more theorems in the universal schema of diagonalization, such a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011