Logic-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

Self-reference 1

Self-reference plays a crucial but widely underestimated role in logic. Douglas Hofstadters 'Gödel-Escher-Bach' In the 1980s, I read Douglas Hofstadter's cult book ‘Gödel-Escher-Bach’ with fascination. Central to it is Gödel’s incompleteness theorem. This theorem shows the limit of classical mathematical logic. Gödel proved this limit in 1931 in conjunction with the fact that it is insurmountable for all classical mathematical systems as a matter of principle. This is quite astonishing! Is mathematics imperfect? As inheritors of the Age of Enlightenment and convinced disciples of rationality, we consider nothing to be more stable and certain than mathematics. Hofstadter's book impressed me. However, at certain

By Hans Rudolf Straub|2025-12-25T16:05:39+00:0025. February 2025|Categories: Logic, Self-Referentiality|0 Comments

Ijon Tichy meets artificial Intelligence

Stanislaw Lem on entropy (littering) Littering in space had been a concern long before Elon Musk's Starlink programme, and various methods for cleaning up the growing clutter in Earth's orbit are currently under discussion. The task is not easy because - due to the second law, the inevitable increase in entropy - all littering tends to increase exponentially. If one of the thousands of pieces of scrap metal in space is hit by another piece of scrap metal, the one piece that was hit creates many new pieces that fly around at insane speeds. Space pollution is therefore a self-perpetuating

By Hans Rudolf Straub|2026-01-06T10:22:35+00:0011. February 2025|Categories: Artificial Intelligence, Information, Logic|Tags: AI, Artificial Intelligence, entropy, Ijon Tichy, Stanislaw Lem, Starlink|0 Comments

Georg Spencer-Browns Distinction and the Bit

continues paradoxes and logic (part 2) History Before we Georg Spencer-Brown's (GSB's) distinction as basic element for logic, physics, biology and philosophy, it is helpful to compare it with another, much better-known basic form, namely the bit. This allows us to better understand the nature of GSB's distinction and the revolutionary nature of his innovation. Bits and GSB forms can both be regarded as basic building blocks for information processing. Software structures are technically based on bits, but the forms of GSB (‘draw a distinction’) are just as simple, fundamental and astonishingly similar. Nevertheless, there are characteristic differences. Fig. 1:

By Hans Rudolf Straub|2025-11-15T12:33:39+00:0023. August 2024|Categories: Information, Logic, Bits|Tags: Bit, Distinction, entropy, Information content|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

By Hans Rudolf Straub|2026-01-06T10:24:06+00:0021. August 2024|Categories: Information, Logic, Paradoxes|Tags: Barber paradox, Kurt Gödel, Laws of Form, Logic, mathematics, Paradox|0 Comments

The bit has no meaning

The bit is the basis of IT Our information technology is based on the bit. Everything that happens in our computers is based on this smallest basic element of information. If someone asks you what a single bit means, you may well answer that the bit can assume two states, of which one means 0 and the other means 1. As is generally known, this enables us to write numbers of any size; all we have to do is to line up a sufficient number of bits. But is this really true? Does the one state in the bit

By Hans Rudolf Straub|2025-12-30T14:59:24+00:0029. November 2020|Categories: if-then, Information, Semantics|0 Comments

The theory of the three worlds

The theory of the three worlds, according to Roger Penrose connects different fields of science and philosophy. The three worlds are: Die platonic world contains objects that are non-local and "timeless". The physical world contains objects which can be examined from outside. The mental world is how we experience things in our head. Music in the three worlds Musical scales are part of all three worlds

By Hans Rudolf Straub|2025-11-15T13:19:40+00:0029. September 2020|Categories: Logic, music, Theory of the Three Worlds|0 Comments

The theory of the three worlds (Penrose)

The theory of the three worlds There are practical questions which concern our specific lives, and there are theoretical questions which seemingly don’t. However, there are also theoretical considerations which definitely concern our practical everyday lives. One of these is the three worlds theory, which deals with questions as to which worlds we specifically live in. On what foundation is our everyday existence based? The theory of the three worlds points to the fact that we simultaneously live in three completely different worlds. Practically, this does not constitute a problem for us; theoretically, however, the question arises as to how

By Hans Rudolf Straub|2025-09-23T12:44:32+00:0028. September 2020|Categories: Logic, Theory of the Three Worlds|1 Comment

Static and dynamic IF-THEN, Part 2

The dynamic IF-THEN differs from the static one by the fact that includes a time-span between IF and the THEN. The THEN is in the dynamic IF-THEN always after the IF, while both are simultaneous in the static IF-THEN of the Boolean algebra. This article continues the introduction to the dynamic IF-THEN and shows some of the problems of the conventional static IF-THEN. Several IF-THENs in a logical competition Let’s have a look at the following situation: IF A, THEN B IF A, THEN C If a conclusion B and, at the same time, a conclusion C can be drawn