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This page show how to make footnotes for your web pages that are very simple to insert and really easy to maintain, and which are accessibility friendly.

How to setup a Dark mode switch on a web-site which allows a user to switch to a dark or light mode or revert to the browser/system setting.

Why do intelligent people continue to defend beliefs that have no logical basis?

A fallacious argument that attempts to prove that consciousness cannot be the result of purely physical processes

A look at possible futures in view of the rise of artificial intelligence

Examining the claim that Gödel’s incompleteness proof is the most profound proof in the entire universe, and so we should send it out to alien intelligences

An attempt to use the concept of a magical non-intelligent machine to prove that a non-intelligent machine can pass any Turing type test

How some parts of mathematics are fabricated without any supporting logical basis

Roger Penrose’s bizarre claim that because of Gödel’s incompleteness proof our brains must be using quantum processes that a machine cannot replicate

A demonstration of the obvious error in John Searle’s argument that human consciousness might be something that is non-computable

What does it mean to “ select a real number at random ”?

When you remove grains of sand from a heap of sand, when does the heap stop being a heap?

How you can have different correct answers to a question that isn’t sufficiently well defined

Goodman claims that his paradox arises from scientific considerations, whereas it is a result of ambiguity of definition

A paradox that is reliant on the confusion of different levels of language

Based on the pretense that one can apply classical formal logic to a constantly changing real world

A claim that tries to prove that mathematical entities are real things that exist independently of any human concepts

The Platonist claim that numbers have an actual existence that is a s real as the existence of chairs, rather than being human constructs in the same way as unicorns are

The assumption that certain supernatural things exist and the assertion that humans can accurately describe these things even though humans have no way of confirming such descriptions

How it has been the source of irrational unfounded assumptions about the infinite

A book looking at how infinity is treated by modern mathematics and pointing out the logical fallacies involved

An English translation of the paper that initiated the notion that there must be undefinable real numbers

A definition of a sphere with infinitely dividing horns: what it is depends on the precise definition

Is there actually any proof that there are more real numbers than natural numbers?

How there can be a list of real numbers for which there is no Diagonal number

An analysis of what real numbers are when given a logical consideration of the language used to define them

A contradiction in a proof by Courant and Robbins that demonstrates the inherent contradictions that result from Platonist assumptions about the infinite

Another demonstration of an inherent contradiction in the concept that infinitely many numbers can be summated

How there is an inherent contradiction inherent in the concept that infinitely many numbers can be summated

Why do intelligent people continue to defend beliefs that have no logical basis

A complete logical analysis that demonstrates how several untenable assumptions have been made concerning the proof

How it has been the source of irrational assumptions about the infinite

Because Gödel’s proof appears paradoxical to many people, many people have tired unsuccessfully to find the flaw in it

A Review by Russell O’Connor of my paper on the flaw in Gödel’s proof

How Church makes the same error as in many incompleteness proofs

A key claim in many attempts at incompleteness proofs is the claim that a certain expression has a precise representation in the formal system

An examination of the claim that Gödel’s proof shows a formula to be true but unprovable in the given system

Roger Penrose’s bizarre claim that, because of Gödel’s incompleteness proof, our brains must be using quantum processes that a machine cannot replicate

A selection of claims for and against the notion that Gödel’s proof show that humans can deduce truths that machines cannot

An intuitive error by Gödel in another of his published papers

An explanation of Gödel’s incompleteness proof that falls down at the final hurdle

The key step in several incompleteness proofs and which contains an obvious error

The key part of his proof that he never actually proved, but simply assumed it to be correct

A step by step guide to Gödel’s proof for those wishing to investigate it in depth

A derogatory term that mathematicians sometimes apply to the work of others while ignoring the logical inconsistencies in their own work

Despite claims to the contrary, the reality is that much of mathematics has no logical basis

What a formal language is and what can be said within in and what can be said about it

Articles on various matters that do not fit into the above categories

A logical analysis of some paradoxes, demonstrating that in many cases the paradox is due to ambiguity of language

How the irrational belief in the actual existence of infinities has resulted in logical errors

How an error of intuition has triumphed over rational logic for almost 100 years

How the failure to consider the limitations of language causes logical errors

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