Logic and Language

Logic and Language

Copyright © James R Meyer 2012 - 2017 www.jamesrmeyer.com

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I was born in Dublin in 1955. I remember in my first year at secondary school being faced with a choice between being taught Latin and additional maths. At that tender age, I chose Latin, for reasons quite unknown to me now. My mathematics teacher was horrified that I should make such a choice, since in his opinion I had shown considerable ability in mathematics. It turned out that my choice was immaterial, since the school decided that they had made a mistake, and that it was far too early to thrust such choices on the shoulders of children so young. And so I continued to learn both Latin and Maths as I had previously.

As I entered my last years of school life I was still indecisive as to what I wanted to do with the rest of my life. Academically I was quite capable, being among the first seven overall in Ireland in Physics in the Leaving Certificate examinations. I spent an extra year studying for the Entrance Scholarship to Trinity College Dublin, in which I came second overall, first in the scientific subjects.

After that I studied Veterinary Medicine at Trinity, and worked as a vet for a number of years. Then I decided to take an Engineering course in Queen’s University, Belfast. As I started re-immersing myself in study and reading around my subjects as well as the coursework, I became interested in the foundations of mathematics. It was at that time that I came across Gödel’s Incompleteness Theorem. I remember that, logically, the argument that Gödel’s proof, for any formal system, led to a statement that the formal system could not prove, but that Gödel’s proof did prove it, must lead to a contradiction - since if Gödel’s proof could be written down in a formal system, then it would be proving a statement, and at the same time proving that it could not prove it! I began to study it, but had to stop because it was taking up too much of my time. I left with a First Class Degree in Engineering in 1992.

After working as an engineer for some time, despite the fact that to outside observers it seemed that I was performing well in my second career, I still hadn’t found what I was looking for.

Then, entirely by chance, a few years ago, I came across a book about Gödel’s theorem that re-awakened my interest in the foundations of mathematics and logic and in Gödel’s theorem. I became determined that I should fully understand Gödel’s proof, and finally my efforts bore fruit. It was this that led to my writing a book, a book that I wanted to be able to reach out to as many people as possible (The Shackles of Conviction). I also published a paper on this website demonstrating the error in Gödel’s incompleteness proof. Since then, I have published several papers on this site demonstrating errors in various other incompleteness proofs.

My studies of these errors revealed that there is a major blind spot in what are normally referred to as logical arguments, in that no account is taken of the role of the limitations of language in such arguments. It is easy to show that many conventional arguments are flawed in this respect and much of the material on this website arises from the study of such flawed arguments. I have published another book, this time on Platonism and infinity (The Infinity Delusion) and new section on this website on infinity.

It has come to my notice that, when asked about the demonstration of the flaw in his proof (see A Fundamental Flaw in an Incompleteness Proof by Peter Smith PDF), Smith refuses to engage in any logical discussion, and instead attempts to deflect attention away from any such discussion. If any other reader has tried to engage with Smith regarding my demonstration of the flaw, I would be interested to know what the outcome was.

There is a new addition to the page Yet another flawed incompleteness proof, where Berto’s proof of incompleteness in his book *There’s something about Gödel* comes under scrutiny.

I found that making, adding or deleting footnotes in the traditional manner proved to be a major pain. So I developed a different system for footnotes which makes inserting or changing footnotes a doddle. You can check it out at Easy Footnotes for Web Pages (Accessibility friendly).

I have now added a new section to my paper on Russell O’Connor’s claim of a computer verified incompleteness proof. This shows that the flaw in the proof arises from a reliance on definitions that include unacceptable assumptions - assumptions that are not actually checked by the computer code. See also the new page Representability.

There is now a new page on Chaitin’s Constant (Chaitin’s Omega), which demonstrates that Chaitin has failed to prove that it is actually algorithmically irreducible.

13 May 2015 Good Math, Bad Math?

16th Mar 2015 Bishops Dancing with Pixies?

23rd Feb 2015 Artificial Intelligence

31 Mar 2015 Cranks and Crackpots

For convenience, there are now two pages on this site with links to various material relating to Gödel and the Incompleteness Theorem

– a page with general links:

– and a page relating specifically to the Gödel mind-machine debate:

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Please note that this web site, like any other is a collection of various statements. Not all of this web site is intended to be factual. Some of it is personal opinion or interpretation.

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Copyright © James R Meyer 2012 - 2017

www.jamesrmeyer.com