Logic
Logical proofs only work in closed systems. Therefore we tend to build our understanding of the world on the basis of closed logical systems. Reality, however, is open, and our thinking is also better off being open than closed.
Open logical systems, on the other hand, are difficult to grasp. Due to their openness, they seem to resist formal clarity. While closed logical systems offer us a clear ground for proofs and calculations, they are unfortunately not able to include all necessary facts and details. Closed logical systems are incomplete, just by their closed nature.
I propose here, to study the phenomenon of open logic and to extend formal logic to include open and dynamic structures.
Selected articles from the topic «Logic»
Logic, Paradoxes, Self-Referentiality
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
Artificial Intelligence, Information, Logic
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
Information, Logic, 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
Information, Logic, 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
Information, Logic, Bits
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
if-then, Logic
It’s a commonly held belief that there’s nothing complicated about the idea of IF-THEN from the field of logic. However, I believe this overlooks the fact that there are actually two variants of IF-THEN that differ depending on whether the IF-THEN in question possesses an internal time element. Dynamic (real) IF-THEN For many of us,
