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Two mutually constraining methods Rationalism and Empiricism
Rationalism - Descartes' method of doubt together with his subsequent arguments are exemplary of a style of thinking that has come to be knows as Rationalism. Some other prominant philosphers of the period who embraced Rationalism include Spinoza and Leibniz. Rationalists' arguments, preceding largely on the basis of deductive reasoning from first principles, are to be contrasted with
Empiricists' arguments which tend to proceed inductively on the basis of sensory experience. Some empiricist philosophers of the period include Locke, Berkeley and Hume.
Things begin to get more complex now as we develop our mental maps with diverse categories.
We'll have a sidelong glimp at a few other figures along the way and then have a look at kant. But don't stress. I won't be expecting anyone to actually read the whole thing. It's a long and difficult read. So, we certainly won't have time to do him justice.
Post mid-term review