About the author of this site
Page last updated 12 Oct 2021
I live in Northern Ireland; I was born and reared in Dublin. 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 Proof. 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, then that 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.
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 proof that re-awakened my interest in the foundations of mathematics and logic and in Gödel’s proof. 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. For a proof that is purportedly a proof in one language about limitations of another language, this is quite extraordinary. 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 a new section on this website on infinity.
Once I discovered that the issues regarding levels of language that are evident in Gödel’s incompleteness proof also apply to misunderstandings about the diagonal argument, it became apparent that an entire branch of mathematics is based around the fallacious and contradictory notion that the impossibility of a one-to-one correspondence between two sets implies that their infinities must have different sizes.
Once one recognizes that this notion has absolutely no logical basis - as well as being contradictory - it becomes quite straightforward to show that this leads to a much better understanding and clarification of the notion of infinity, and also to the elimination of many paradoxical aspects of conventional mathematics.
I see it as my obligation to continue to demonstrate the illogical assumptions, the fallacies and the contradictions that are inherent in much of modern mathematics, so that the arcane notions that give rise to them can be expunged forever. Perhaps then we can have in the twenty-first century a mathematics that is worthy of human intellectual progress up to this point in time, rather than one so imbued with out-dated mystical beliefs that we would be ashamed to share it with an alien intelligence.