The Significance of a Non-Reductionist Ontology for the Discipline of Mathematics: A Historical and Systematic Analysis |
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Authors: | D F M Strauss |
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Institution: | (1) University of the Free State, Bloemfontein, South Africa |
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Abstract: | An overview of the history of the concept of matter highlights the fact that alternative modes of explanation were successively
employed. With the discovery of irrational numbers the initial conviction of the Pythagorean School collapsed and was replaced
by an exploration of space as a principle of understanding. This legacy dominated the medieval period and had an after-effect
well into modernity—for both Descartes and Kant still characterized matter in spatial terms. However, even before Galileo
the mechanistic world view slowly entered the scene—the world as chaos, particles in motion. Elevating movement to become
the guiding principle in our understanding of matter dominated the main tendency of modern physics until the (end of the)
19th century. The discovery of irreversible processes (radio-activity for example) directed 20th century physics towards an
exploration of the meaning of energy-operation. It turned out that even within 20th century physics long-standing legacies
prevailed, because an account of the nature of matter continued to be torn apart by atomistic and holistic views—confronted
by the problem of constancy and change (radical transformability versus persistence). Concrete, material reality exceeds the
scope of any single mode of explanation—an insight that also serves a better understanding of the wave-particle duality. |
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