In Part 1 we learned that epistemology is the study of knowledge, and that since the time of Plato and Aristotle, JTB (justified true belief) has been the standard definition of knowledge. In Part 2 we learned that both logic and epistemology rely heavily on the distinction between true and false. And within epistemology, there are three theories which have been proposed regarding truth. They are 1) the correspondence theory of truth, 2) the coherence theory of truth, and 3) the pragmatic theory of truth.
Rationalism states that knowledge is gained, or at least best gained, by the use of reason. Empiricism states that knowledge is gained through experience and the senses. While Plato (427 – 347 BC) is usually considered the prototypical rationalist, his student Aristotle (384 – 322 BC) is usually considered the prototypical empiricist. And whereas Rene Descartes (1596 – 1650) the rationalist is often considered the father of modern philosophy, his contemporary Francis Bacon (1561 – 1626) the empiricist is considered a father of modern science.
Epistemology identifies a priori knowledge and a posteriori knowledge as two types of sources of knowledge. Knowledge that is gained independent of experience is a priori knowledge. Knowledge that is gained through experience and the senses is a posteriori knowledge. However, something is knowable only a posteriori if it cannot be known a priori.
In chapter nine “Epistemology” of their book Mathematics Through the Eyes of Faith, James Bradley & Russell Howell write, “A priori justification implies reasoning or some direct mental apprehension as opposed to sensory perception. For example, why does 2 + 2 = 4? An a posteriori justification would mean directly observing that under every circumstance, a collection of two distinct objects, when grouped with a collection of another two distinct objects, gives a collection of four objects. The problem here is that no one can observe ‘every circumstance.’ Instead, an a priori justification uses definitions and reasoning independent of the senses.”
Bradley and Howell continue, “For example, define 2 as the integer following 1, 3 as following 2, and 4 as following 3, and define addition a + b for positive integers as the bth integer after a. Then we have 2 + 2 = 2 + (1 + 1) = (2 + 1) + 1 = 3 + 1 = 4. This is an a priori justification.”
For more information, please see chapter three “Where Does Knowledge Come From?” in How Do We Know? An Introduction to Epistemology by James Dew and Mark Foreman.
You may also want to view “Descartes vs. Bacon on Rationalism vs. Empiricism” from Word on Fire by Peter Kreeft.
~ Boethius ~