Immanuel Kant (1724–1804) is a nexus of modern philosophy. He brings together everything that came before him, and is the starting point for everything that came after him. The philosophy of the 17th and 18th centuries is generally characterized as being split between empiricists (most of whom were British) and rationalists (most of whom were French or German). While Kant was taught in a thoroughly rationalist tradition, he was able to use the best philosophy of both groups and reconcile their differences.
The rationalists placed a heavy emphasis on metaphysics and knowledge gained through the exercise of the unaided intellect. They were skeptical about knowledge acquired from experience, arguing that the senses are unreliable. Knowledge from experience, they argued, cannot carry the certainty and necessity that characterizes the abstract reasoning of mathematics or geometry. Thus, they set about seeing what other certain or necessary truths they could learn through abstract reason alone. The result was a great deal of energetic speculation as to the nature of God, the ultimate constituents of matter, and the soul. Among the most significant rationalists were Descartes, Spinoza, and Leibniz.
The empiricists, on the other hand, believed strongly in experiential knowledge. John Locke asserted that the mind is a blank slate at birth, and that all our knowledge comes from experience. Even mathematics, he suggests, is built from inferences and generalizations we make regarding experience. The goal of an empiricist is to systematize our knowledge from experience, to show how the complexities of human knowledge are built up from simple sensations. George Berkeley asserted that nothing exists except in experience—"being is being perceived." David Hume argued that we have no rational justification for inferring any general laws about experience, and that our "knowledge" of cause and effect is more a matter of custom than necessity.
Kant said that Hume's skeptical challenge is what first spurred him toward his critical philosophy. Hume asks how we can make inferences regarding experience: how can I predict what will happen in the future based on what has happened in the past? In order to do so, Hume suggests, I must know some sort of "uniformity principle" that says that events in the future will follow the same sorts of general laws that they have followed in the past. But how can I know this uniformity principle? It isn't logically or necessarily true, so I can't simply infer it prior to experience like I can with mathematical knowledge. However, I fall into a vicious circle if I claim that I know it from experience, since I need to already have the uniformity principle in order to infer that—the uniformity principle has been true in the past, and it will continue to be true in the future. Thus, Hume concludes that we cannot know that future events will follow the same laws as past events: we just get into the habit of expecting it.
Kant first answers Hume's skepticism and reconciles rationalism and empiricism in his magnum opus, the Critique of Pure Reason, published in 1781. This book is long, dense, and difficult, and was generally misunderstood. Kant published the Prolegomena two years later as a primer, hoping to make his ideas more accessible.
One gathers the impression from what is here, that Kant's not terribly compelling, or plausible, whatever his historical importance. I think this is debatable.
About the claim that is made here, that Frege was the first to point out that geometry is not synthetic a priori. Well, this implies that indeed, geometry is not synthetic a priori. However, Some believe that Frege was wrong. I'll note that I'm also reading, here, about how this position 'was given a boost by Einstein's relativity..' That is to say, that Einstein's relativity<... Read more→