Harold Walsby

Soon after the discovery of the calculus by Newton and Leibniz, problems of consistency in mathematics arose which centred around the concept of “infinity,” i.e. “infinitesimals” or “infinitely small quantities.” The inconsistencies, together with ensuing disputes among mathematicians and philosophers, were not allayed until the middle of the last century. Whether or not Weierstrass, Dedekind… read more »

Aristotle’s Principle, as we have just seen, implies the existence of some contradictions and denies the existence of others. This would account for the otherwise inexplicable fact that it is sometimes called “the Principle of Contradiction” and sometimes “the Principle of Non-contradiction,” titles which are in flat contradiction of one another! Strictly, of course, since… read more »

The limits one may set to the term “contradiction” are to some extent arbitrary, since the word is normally used in different senses. I shall use the term in the widest sense compatible with my immediate object. This follows excellent precedent. For example, Aristotle’s Principle is generally applied to “contraries” (such as “black” and “white”)… read more »

It will be useful to take a look in broad-perspective at what we are about to do. I must therefore say a word about the historical role of the principle of Non-contradiction. The usual view of logic is that “natural logic” – sometimes called “native wit” – is inborn, somehow “given” by nature (or Divine… read more »

Art does not exactly imitate that which can be seen by the eyes, but goes back to that element of reason of which Nature consists and according to which Nature acts. (Goethe) For generations now many artists, poets and mystics have expressed their deep conviction that human reason cannot be bounded by what has often… read more »

Harold Walsby Design Research Project Paper No. 1 January 1967 Communicating mathematical ideas is a problem even among mathematicians. Many leading mathematicians are distressed over a style of mathematical writing that has become commonplace in the last decade or two. Mathematical papers are compressed to the limit, until all intuitive ideas are squeezed out. As… read more »

Special Announcement to Potential Subscribers: In the first days of my Design Project a few people wrote: “This all seems most abstract. What does your Paradox Principle actually do? What are its practical consequences? Has it any concrete effects on our daily lives?” The short answer is, Yes, it has potentiality for very practical results… read more »