The principles that AN INSTANCE OF A CLASS IS THE CLASS and A CLASS IS AN INSTANCE OF ITSELF allow for the so called LAWS OF THOUGHTIDENTITY - WHAT IS, IS.CONTRADICTION - NOTHING BOTH IS and IS NOT.EXCLUDED MIDDLE - EVERYTHING IS or IS NOT.and allow us to adopt a bivalent system. Everything essential for primary logic is provided.Though this is not the place to discuss it, it should be noted that the development of general logic with its current theories (...) of class, identity and natural numbers could take a very different course from the one it currently pursues.Human thought would have had to evolve to a high level of development before any systematic attempt to analyse it could have been made. It seems it was in the floruit of the Greek civilisation that this attempt was first made. The issues in this paper were of prime concern to those ancient thinkers and their achievements were considerable. Since those times further developments have occurred, many of which they would not have dreamed, but to this day there are still great issues that have not been resolved. The state of the art leaves much to be desired and it is my hope that this paper will contribute to its progress.If the ideas in this paper are true, then it seems we have come across the very origins of human rationality. (shrink)

Until the second half of the 19th century the natural numbers were regarded as given and not further analysable. The concept of a class as defined by mathematicians of the time, Seeming more fundamental, Was then used to define the natural numbers. Their definitions of a class are unsuitable because of paradoxes and other difficulties. In this paper a new definition of a class is stated, And from this the natural numbers are defined.

If true, this is one the the most important papers in the history of mathematics. the natural numbers are defined and one to one correspondence between the natural numbers is made precise. the paper deals with the very fundamentals of arithmetic and the logical principles differ quite markedly from those used by georg cantor.

The paradoxes act as restraints on undisciplined or erroneous reasoning and so perform a valuable role. The fact that they have resisted solution for so long suggests that the current systems of logic are defective. The paradoxes of set theory, in my opinion, completely condemn all the current forms of set theory and their associated definitions of the natural numbers. Nothing short of a complete review of the whole area seems capable of remedying the situation.

The argument of this paper suggests that for the last hundred years or so fundamental premisses of logic have been incorrect. From these premisses a vast superstructure has been developed which, it would seem, is no more meaningful than a game such as chess.The basic errors in current class theory, it seems to me, have impeded progress in the fields of mathematics and logic. I am certain that on the theory proposed, the correct definition of a natural number can be (...) provided. I can, in fact, provide this. What benefits it will bring to logic only time will tell.Of the greatest importance is the fact that if the theory is true, at last, there will be a firm link between the Humanities and the Sciences. (shrink)

The aim of this book is to explain human rationality. The fundamental principles of human thought are stated in terms of Balzer's Principles, and their operations in everyday life are illustrated. The natural numbers are defined and explained in a fresh fashion. Paradoxes, including those of class theory and material implication, which have signaled that all is not well in our logical systems, are laid to rest here. The explanation of human rationality has more than logical interest, for it touches (...) upon the human values embedded in our rationality. The book carries the message that all human beings are fundamentally equal. (shrink)

The aim of this book is to explain human rationality. The fundamental principles of human thought are stated in terms of Balzer's Principles, and their operations in everyday life are illustrated. The natural numbers are defined and explained in a fresh fashion. Paradoxes, including those of class theory and material implication, which have signaled that all is not well in our logical systems, are laid to rest here. The explanation of human rationality has more than logical interest, for it touches (...) upon the human values embedded in our rationality. The book carries the message that all human beings are fundamentally equal. (shrink)