This paper critically examines the Cantor Diagonal Argument (CDA) that is used in set theory to draw a distinction between cardinality of natural numbers and real numbers. The CDA discussed here using consensus from forms found range recently published sources. Four points critical are raised cast doubts on its validity general applicability. Also, contrary conclusion conventionally drawn CDA, ...

€ ∉ impredicable. Now, letting ‘V’ denote the collection of all properties, impredicable can be defined as follows:

[26] argues that the diagonal argument of the number theorist Cantor can be used to elucidate issues that arose in the socialist calculation debate of the 1930s. In particular he contends that the diagonal argument buttresses the claims of the Austrian economists regarding the impossibility of rational planning. We challenge Murphy’s argument, both at the number theoretic level and from the sta...

would like to thank Mark Watson for correcting a mistake in his summary of Cantor’s argument. 1A note on citations: Mises’s article appeared in German in 1920. An English translation, “Economic Calculation in the Socialist Commonwealth,” appeared in Hayek’s (1990) collection Collectivist Economic Planning in 1935. 2The current paper assumes a basic familiarity with the socialist calculation deb...

This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. Gödel’s theorem on Entscheidungsproblem, Turing’s halting problem or Chaitin-Gödel’s theorem). The fact, that a formal system contains a sentence, which introduces reflexitivity, does not imply, that the same system does not contain a sentence or a proof procedure which solves t...

Simion has a conjecture concerning the number of lattice paths in a rectangular grid with the Ferrer's diagram of a partition removed. The conjecture concerns the unimodality of this number over a sequence of rectangles with the sum of the length and width being constant and with a constant partition. This paper demonstrates this unimodality if the partition is symmetric or if the Ferrer's diag...