SHVAĆANJE PREDMETA MATEMATIKE U OKVIRU ARISTOTELOVA REALIZMA
UNDERSTANDING OF MATHEMATICAL OBJECTS WITHIN ARISTOTLE’S REALISM

Summary/Abstract: The authors deal with Aristotle’s understanding of mathematical objects within his realistic approach,with special emphasis on his work Metaphysics. According to Aristotle, mathematical objects do not exist separately from their perceptible substance, moreover, mathematical objects are not,neither may be, substance. If they were substance, then it would be possible to put together some material substance from lines, dots and numbers. When mathematical science observes its objects, it sees them as if they were substance, even though they are really not. Although mathematical objects are not in the mode of being - οὐσίαι, Aristotle would say that they are being- ὄντα, because it is true to say that they are beings (which are separated), as well as the things which the substance is the foundation of - which are not separated, but what is not separated is also some being - τὸ ὄν.Here is included the criticism of Plato’s understanding of mathematical objects because Plato understands mathematical objects as real and separated from perceptible or visible areas. With regard to the interpretation of Aristotle’s realistic philosophy of mathematics, the authors point out that it can be labeled as abstractionism, fictionalism and qua theory. In the end the authors touch upon the nature of mathematics from Aristotle’s time to the 18th century, noting that during that period mathematics was understood as a science of sizes, those uninterrupted (continuous) - to be studied by geometry, and those interrupted (separated, discontinuous) - to be studied by arithmetic.

• Details
• Contents