A Notion of Zero in the Philosophy of Aristotle

ABSTRACT: This article shows that Aristotle created the first notion of a zero in the history of human thought. Since this notion stood in evident contradiction to the basic principles of his metaphysics and logic, he rejected it.

The origin and development of mathematical symbols was closely connected with the development of mathematics itself and development of philosophy. It resulted from the fact that philosophy provided the motivation for investigations and creation of adequate and good mathematical symbols. Moreover, being one of the cultural factors, (1) it played a significant role in the process of accepting or rejecting certain notions.

This article aims at producing evidence that particular ideas of Hellenic philosophy made it impossible for Hellenic thinkers to accept notion of a zero. The following considerations will be preceded by brief information on the ancient notations.

The ancient numeric systems aimed at ascribing to a singular whole number or written symbol (up to a point determined by practical needs). This symbol was a combination of a limited number of signs, produced on the basis of more or less regular laws. (2) Three ancient groups of people: the Babylonians, the Chinese and the Mayas discovered a position principle, that is one of the prerequisites leading to discovering a zero and considering it a number. (3) The first appeared in the Babylonian numeration in the 3rd century BC as a result of overcoming ambiguity in the notation of numbers. The sign for a zero that is the so-called diagonally drafted double nail ( ) indicated, first of all, a lack of units of some "sixty" order. It was also treated as kind of an arithmetic operator, since adding it at the end meant multiplication by "sixty". But neither the Babilonian mathematicians nor astronomers treated zero as a number. A diagonally drafted double nail was conceived of as an empty place, that is a lack of unites of a respective order.

Hellenes people used two systems of denoting numbers. The Athenian system was mathematically equal to the Roman system, whereas the Ionic system, just like the Hebrew system, was a system of an alphabetic type. In both systems, just like in the Egyptian hieroglyphic system or the Hebrew numeration, numbers had their established values regardless of the place they were put in. (4) None of the Hellenic system was based on a position principle, none of them used a symbol of zero, either.

ABSTRACT: This article shows that Aristotle created the first notion of a zero in the history of human thought. Since this notion stood in evident contradiction to the basic principles of his metaphysics and logic, he rejected it.

The origin and development of mathematical symbols was closely connected with the development of mathematics itself and development of philosophy. It resulted from the fact that philosophy provided the motivation for investigations and creation of adequate and good mathematical symbols. Moreover, being one of the cultural factors, (1) it played a significant role in the process of accepting or rejecting certain notions.

This article aims at producing evidence that particular ideas of Hellenic philosophy made it impossible for Hellenic thinkers to accept notion of a zero. The following considerations will be preceded by brief information on the ancient notations.

The ancient numeric systems aimed at ascribing to a singular whole number or written symbol (up to a point determined by practical needs). This symbol was a combination of a limited number of signs, produced on the basis of more or less regular laws. (2) Three ancient groups of people: the Babylonians, the Chinese and the Mayas discovered a position principle, that is one of the prerequisites leading to discovering a zero and considering it a number. (3) The first appeared in the Babylonian numeration in the 3rd century BC as a result of overcoming ambiguity in the notation of numbers. The sign for a zero that is the so-called diagonally drafted double nail ( ) indicated, first of all, a lack of units of some "sixty" order. It was also treated as kind of an arithmetic operator, since adding it at the end meant multiplication by "sixty". But neither the Babilonian mathematicians nor astronomers treated zero as a number. A diagonally drafted double nail was conceived of as an empty place, that is a lack of unites of a respective order.

Hellenes people used two systems of denoting numbers. The Athenian system was mathematically equal to the Roman system, whereas the Ionic system, just like the Hebrew system, was a system of an alphabetic type. In both systems, just like in the Egyptian hieroglyphic system or the Hebrew numeration, numbers had their established values regardless of the place they were put in. (4) None of the Hellenic system was based on a position principle, none of them used a symbol of zero, either.