Category History

Translation of an Article by Gottlob Frege

Originally posted on Creativistic Philosophy:
I have published an article by German philosopher, mathematician and logican Gottlob Frege, and also an English translation of it. The English translation was prepared in a joint effort together with Tina Forsee. It replaces an earlier translation that I had published earlier this year. Several mistakes of the previous…

Thoughts in a Museum

Originally posted on The Asifoscope:
? Visiting a newly opened collection of modern art in Hannover’s the recently extended Sprengel Museum, it seemed to me that the history of 20th century art can be described as a series, or rather, a network of reflective steps of thinking or perceiving. Any knowledge we are using, either…

Formalism vs. Creativism

A generally intelligent system should be universal in the sense that it can produce arbitrary knowledge. The proof essentially shows that an algorithm cannot be generally intelligent in this sense. The reason why, after about 60 years of research, general intelligence did not show up among the systems built by the artificial intelligence community is […]

“Formalizability” in the English Language

It is a peculiar feature of the current English language that the word “formalizable” is nearly non-existent. The word feels awkward. When looking up the equivalent of the German word “formalisierbar” in one of the online-dictionaries I am using, it turned out there was no corresponding English word in that dictionary. However, there was a […]

Basic Concepts 9 – Productive Sets and Productive Functions

In a previous article, I have sketched a proof that shows that the set of computable total functions (as well as the sets of programs calculating them, and of the Gödel numbers of such programs) is not enumerable. I want to look into this matter in more detail here. All of these sets are not enumerable, […]

Basic concepts 7 – Formalizations of Computability

In order to turn the intuitive concepts discussed in the previous article into exact concepts, one would have to define exactly what a program is. Different mathematicians (including Alan Turing, Alonzo Church, Stephen Cole Kleene and others) have come up with different formalisms in order to define exactly what a computable function is and thus […]