Analogy and diagonal argument

An Argument for Derivational Analogy

A common reason for the use of analogy in (computational) problem solving is the lack of appropriate object-level knowledge, e.g. rules, necessary to solve the problem from first principles. Hence, the absence of sufficient (object-level) domain knowledge is assumed in most case-based reasoning (CBR) systems. Even those CBR systems that combine rule-based and casebased reasoning rely on a simil...

Cantor’s Diagonal Argument: Proof and Paradox

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

Reflexivity and the diagonal argument in proofs of limitative theorems

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...

Cantor’s Diagonal Argument: an Extension to the Socialist Calculation Debate

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...

Legal Reason: The Use of Analogy in Legal Argument