Paradoxes-Archiv - Hansruedi Straub

Paradoxes and self-reference

Paradoxes are contradictions in logic. Some can be solved inside the the logical system, while others resist this attempt. Some contradictions are not solvable in principle, as K. F. Gödel proved hundred years ago. These true paradoxes all show the same formal kernel. The kernel contains typically a re-entry or self-reference. This phenomenon of re-entry or self-reference is at the core of all true paradoxes and a ticklish challenge for formal logic. Simple instruction for generating paradoxes The trick with which classical logical systems can be invalidated consists of two instructions: 1: A statement refers to itself. 2: The

By Hans Rudolf Straub|2026-01-06T10:22:10+00:0025. February 2025|Categories: Logic, Paradoxes, Self-Referentiality|Tags: Barber paradox, Meta-level, Model selection, Paradox, Self-reference, Zenon|0 Comments

Logic kernels in true paradoxes

In logic there is a single basic pattern, found in every true paradox. The kernel of each true paradox consists of a selfreferential move, which arises from a logical statement and re-enters it from outside. This logical selfreference is found behind the severe mathematical problems adressed by K. F. Gödel. A try to solve the problem on the basis of a new formalism was done by George Spencer-Brown. His formalism helps to describe contradictions in formal logic. "Draw a Distinction" Spencer-Brown introduces the elementary building block of his formal logic with the words ‘Draw a Distinction’. Figure 1 shows

By Hans Rudolf Straub|2026-01-06T10:23:09+00:0022. August 2024|Categories: Information, Logic, Paradoxes|Tags: Barber paradox, Distinction, paradoxes, Re-Entry|0 Comments

Logic and Paradoxes

It is a widely accepted believe that logic systems should be free of contradictions. In reality, however, we are always faced with contradictions and even seemingly unsolvable contradictions which we call paradoxes. How can we handle them? Logic in Praxis and Theory Computer programs consist of algorithms. Algorithms are instructions on how and in what order an input is to be processed. Algorithms are nothing more than applied logic and a programmer is a practising logician. But logic is a broad field. In a very narrow sense, logic is a part of mathematics; in a broad sense, logic is everything