An Effective Procedure for Computing “Uncomputable” Functions

Dr. Kurt Ammon has just published his most recent paper on creative systems on the internet. You can find it on http://arxiv.org/pdf/1302.1155v1.pdf.

I consider this to be an epoch-making paper.

Basically, the paper contains a proof showing that and in which sense Church’s thesis is wrong. Church’s thesis is a hypothesis that states that every computable function is recursive. In essence this means that every computable function can be described by an algorithm or a finite formal theory. This is often understood to mean that every computer program is an algorithm. Ammon’s paper shows that this is not so. There are programs that are not algorithms and that can develop out of the scope of validity of any given formal theory, computing functions that are not turing-computable. So the generally held assumptions that computable equals turing-computable and that algorithm equals program are wrong.

You can contact Dr. Kurt Ammon on http://csyst.org.

Watch this space.

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13 comments

  1. Since the paper is quite technical, I am planning to publish a series of blog articles on this blog in an attempt to translate Ammon’s results into a form understandable by a wider audience and to explore what this means for philosophy in general.

    This project will, take some time. However, I think it is important since I consider this is an epoch-making paper.

  2. Reblogged this on The Asifoscope and commented:

    I have just started a new blog for more “technical” philosophical articles. As a start, I am happy to announce there the publication today of Dr. Kurt Ammon’s most recent paper.
    I will generally reblog articles from that blog here or at least publish links to articles I publish there.

    While I am blogging quite regularly on The Asifoscope and use it as a personal blog containing a wide range of topics, my new blog “Creativistic Philosophy” is reserved for more sincere philosophical and scientific articles. I will publish there only occasionally.

  3. I sometimes read your blog and wonder how on earth it is that I found your blog, liked it and have become such a fan of yours. lol

    1. 🙂 Well, the content of my other blog is quite mixed, so there are a lot of different people reading it for different reasons. I know I would bore some of them with the things I am going to publish here, that is why I started this separate blog for this kind of stuff. I will just put links to articles here on the other one and sometimes reblog an article.

      1. How many blogs do you have?

        1. Only these two are active. There are some older attempts from several years ago but I never really had the time back then. The articles that where good on those ones I have already reblogged and I am going to close them.

  4. […] literature on this topic. However, I suspect here a link to creativity. Following the works of Kurt Ammon, I view creativity as the ability to break out of any given formal system or algorithm. In […]

  5. […] to create computer programs that are creative in the sense of his definition. And in his article An Effective Procedure for Computing “Uncomputable” Functions he has shown that such computer programs are indeed […]

  6. […] Ammon provided a mathematical proof showing the possibility of computer programs to develop out of the scope of any given formal theory […]

  7. Reblogged this on "The Whole Hurly Burly" and commented:
    this is what i’m talking about! Yippee! Couple it with:

  8. […] no algorithm exist. So the common assumption that every program is an algorithm is wrong. (see AN EFFECTIVE PROCEDURE FOR COMPUTING “UNCOMPUTABLE” FUNCTION). Algorithms appear as components of creative systems but such systems as a whole cannot be viewed […]

  9. […] creativiticphilosophy.wordpress.com/2013/02/06/an-e%EF%AC%80ective-procedure-for-computing-uncomputa… […]

  10. […] is so because it has been shown that computers are not limited to what Turing-machines can do (see http://creativiticphilosophy.wordpress.com/2013/02/06/an-e%EF%AC%80ective-procedure-for-computing-un&#8230😉 and that instead it should be possible to implement creative system in computers, i.e. systems for […]

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