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This was the most manageable of Hume's many disputes, since here the enemy was only a bunch of philosophers, and a relatively small bunch at that—Descartes, Spinoza, Leibniz, Malebranche, and a few others. What did these men all have in common?
Well, they were all rationalists, meaning that they were united in the view that knowledge, at least of the most important or fundamental sort, could be arrived at through the use of reason alone—that is, just through reliance on logic. So, for example, Leibniz tried to show that the law of identity (a=a), properly understood, reveals the most amazing facts about the universe: that the world is made up ultimately of an infinite number of "monads"—substances that contain within themselves all their properties, past, present, and future, and that appear to interact with each other, though in reality they are completely independent of one another.
Does that sound a bit crazy to you? It sure did to Hume. He, of course, was into empiricism, the view that all knowledge is ultimately based on experience (not logic). He did not invent this notion; he built on the work of earlier British empiricists such as John Locke and George Berkeley. Hume argued that the only knowledge that could be arrived at through pure logic alone was, in effect, trivial. The truths of logic and mathematics he called "relations of ideas," and he said these told us nothing about the world; they only reflected the meaning of the terms involved.