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26 Μαρ 2004 · Aristotle uses mathematics and mathematical sciences in three important ways in his treatises. Contemporary mathematics serves as a model for his philosophy of science and provides some important techniques, e.g., as used in his logic.
- The Infinite
Aristotle accepts this notion as well. The infinite series...
- Place and Continuity of Magnitudes
In Physics iv.1-5 Aristotle distinguishes four notions as...
- Aristotle and Greek Mathematics
Aristotle discusses the definitions of numerous mathematical...
- The Infinite
Aristotle discusses the definitions of numerous mathematical entities and properties, such as point, line, plane, solid, circle, commensurate, number, even and odd, three, etc., and uses others in interesting ways, such as prime and additively prime (not the sum of two numbers, i.e., 2 and 3, since 2 is the first number) in a definition of ...
Aristotle and First Principles in Greek Mathematics. It has long been a tradition to read Aristotle's treatment of first principles as reflected in the first principles of Euclid's Elements I. There are similarities and differences.
There is no one Aristotelian text devoted to mathematics. Instead, Aristotle’s views can be found in Posterior Analytics, Metaphysics, De Anima, and Physics. These texts show that Aristotle believed first that we could have mathematical knowledge and second that mathematics is an ideal science. These two points are not disputed by
Aristotle denied this hypothesis by building a theory of continuity and infinite divisibility. He claimed that a line comprising of an infinite number of potential points is equivalent to saying that a line can be divided anywhere on it, bringing potential points to actuality.
Aristotle thought that the objects in the natural world do not perfectly instantiate mathematical properties: a physical sphere is not truly spherical; a straight edge is not truly straight. In con- sequence, though commentators see Aristotle as railing against a Platonic ontology of geometrical and arithmetical objects, they see
29 Ιουν 2023 · Aristotle solves the difficulty by noting that how one systematizes one’s thought makes all the difference: “geometry considers the physical line, but not as physical, whereas optics [considers] the mathematical line, yet not as mathematical but as physical.”
