Paradoxes

Self-reference 2 (Paradoxes)

Self-reference 2 (Paradoxes)

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 reference or the statement contains a negation. This constellation always results in a paradox. A famous example of a paradox is the barber who shaves all the men in the village, except of course those who shave themselves (they don't need the barber). The formal paradox arises from the question of whether the barber shaves himself. If he does, he's one of those men who shave themselves and, as the statement about

By Hans Rudolf Straub|2025-12-16T10:03:26+00:0025. February 2025|Categories: Logic, Paradoxes, Self-Referentiality|Tags: Barber paradox, Meta-level, Model selection, Paradox, Self-reference, Zenon|0 Comments

Paradoxes and Logic (Part 2)

continues Paradoxes and Logic (part 1) "Draw a Distinction" Spencer-Brown introduces the elementary building block of his formal logic with the words ‘Draw a Distinction’. Figure 1 shows this very simple formal element: Fig 1: The form of Spencer-Brown A Radical Abstraction In fact, his logic consists exclusively of this building block. Spencer-Brown has thus achieved an extreme abstraction that is more abstract than anything mathematicians and logicians have found so far. What is the meaning of this form? Spencer-Brown is aiming at an elementary process, namely the ‘drawing of a distinction’. This elementary process now divides the world into

By Hans Rudolf Straub|2025-11-25T18:26:54+00:0022. August 2024|Categories: Information, Logic, Paradoxes|Tags: Barber paradox, Distinction, paradoxes, Re-Entry|0 Comments

Paradoxes and Logic (Part 1)

Logic in Practice 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 that has to do with thinking. These two poles show a clear contrast: The logic of mathematics is closed and well-defined, whereas the logic of thought tends to elude precise observation: How do I come to a