What are the salient differences among rationalism, empiricism, and the Scottish common sense school of philosophy?
In Europe during the Early Modern period, philosophy began to diverge from theology and look for secular and material answers to important philosophical answers about being, knowledge, nature, and ethics. The philosophies of this period diverged in epistemological assumptions, i.e. what they thought were the ways in which knowledge was obtained.
Rationalists like Descartes thought that we could obtain knowledge by making deduction from self apparent first principles. Those principles could be arrived at by reason alone (thus: "rationalist"). His Meditations record this process beginning with his famous cogito, ergo sum (I think therefore I am)
Empiricists, on the other hand, argued that knowledge could only be obtained through the senses. They thought that the mind begins as a tabula rasa (a blank, or erased, slate) and that we gradually arrive at knowledge by combining pieces of experience. General principles are merely averages of many experiences, and should not be trusted.
Kant and the Common Sense school combined the two positions through seeing knowledge as a combination of innate ideas with experience.