Kant Vs. Mill On Mathematics Essay

1424 Words3 Pages

To what extent has Philosophy shaped Mathematics?

Kant vs Mill

Preface

There was of course considerable philosophical action after Aristotle and through the Middle Ages, but there was very little focused on mathematics. The seventeenth century saw major revolutions in science and mathematics, through the work of Descartes, Newton and Leibniz. This meant that when Kant began his philosophy in the eighteenth century, he was in a position to build on philosophy after the scientific developments. In particular, physics began to grow in importance and popularity. This lead to new branches in mathematics and new conceptions in the traditional branches. These mathematical revolutions included new ways of linking geometry with algebra and arithmetic (Fermat and Descartes), and the development of the calculus, through the work of Newton and Leibniz, which was needed for the study of gravitation and motion. …show more content…

On the European continent, rationalists like Descartes, Spinoza and Leibniz were plato’s natural heirs. They emphasised the importance of reason, as opposed to sensory experience in obtaining knowledge. The rationalist model for knowledge-gathering is mathematics - mathematical demonstration in particular. Demonstrating this, Spinoza’s Ethics has the same format as Euclid’s Elements, containing ‘propositions’ and ‘demonstrations’. It is thought science is supposed to be founded on philosophical first-principles. Descartes attempted a mathematical-style derivation of the laws of motion.

Empiricism, the main opposition to rationalism, is an attempt to base knowledge on experiences from the five senses. During this period, the major writers were Locke, Berkeley, Hume and Reid, all of whom lived in the British Isles. A common theme in empiricism is that ultimately anything we know about the world around us must come from our only access to the world - through our eyes, ears, and so

Open Document