Is it possible to reconcile rationalism and empiricism? If so, how? If not, why?
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Perhaps the greatest attempt to reconcile rationalism and empiricism was Immanuel Kant's construction of what he called "transcendental idealism" in his Critique of Pure Reason. During the Enlightenment, the debate between rationalism and empiricism was represented by philosophers like Rene Descartes (rationalism) and John Locke (empiricism).
In his Cartesian Meditations, Descartes believed he had proven that the mind had knowledge independent of the senses, and he established a philosophical "proof" for the existence of the self, God, and the world. One of his famous examples is watching a candle burning. While the "substance" of the candle wax changes form, from hard to melted liquid and is also vaporized as fuel in the fire, the mind is able to track the different permutations of the wax even though the sensory input changes with the burning of the wax. Descartes concluded that the mind has knowledge of the candle wax that does NOT come from the senses, because the sensory input changes over time. If knowledge came from the senses, ...
This solution addresses how Kant reconciles rationalism and empiricism with his transcendental idealism from the Critique of Pure Reason, and also addresses the issue generally. It covers the rationalism of Descartes, and the empiricism of John Locke, and brings the issue up-to-date with some comments on quantum physics.