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#### Can Truth Be Known?

A question that immediately precedes this one is: “Can anything be known?” There have been several periods of history that have been called periods of enlightenment, but the primary one we associate with the term “Age of Enlightenment” or simply “Enlightenment” was a cultural movement of intellectuals living generally in Europe in the latter half of the 17th and 18th century. Its purpose was to reform society using reason, to challenge ideas grounded solely in tradition and faith, and to advance knowledge through the scientific method. It promoted not only scientific thought, but also skepticism, and intellectual interchange. Many people of the time believed that until the Age of Enlightenment, the power of knowledge had been held by too few. People of all classes, great minds and simple folk alike, were encouraged to question and challenge everything they believed they knew. Was it really true? The question itself was not new to this time, but its pervasiveness and the methods employed in the search for truth were changed.

In an earlier article, we were asked, “On what do we base truth?” Most people seem to accept things as true if they are put forth as such by the fields of science or mathematics. In actuality, scientists would be among the first to tell you that they can prove nothing as true. They are actually in the business of proving things to be false. Much like our system of justice promotes innocence until guilt is proven, scientists theorize things to be true unless and until they are proven false. The scientific method depends on sensory observation and experimentation.

The development of mathematical formulas includes neither observation nor experimentation. The mathematician and politician Pythagoras (c. 570 BC – c. 495 BC) developed an abstract and rational method of answering questions about reality. Observation played no part in his search for truth. His method was founded on mathematical equations and was largely intuitive.

We have already examined the fact that Doubt is the Beginning of All Knowledge. Doubt, questioning and debate are all good means to approach fact, but reason suggests that if we are totally skeptical, nothing can be known for certain, making examination futile. On the other hand, if we can agree on any one thing as truth, then we can inquire as to how that truth came to be known and extrapolate the method to learn other truths.

Many centuries before the Enlightenment, there existed a group called Sophists. Plato describes them as follows, “...the art of contradiction making, descended from an insincere kind of conceited mimicry, of the semblance-making breed, derived from image making, distinguished as portion, not divine but human, of production, that presents, a shadow play of words—such are the blood and the lineage which can, with perfect truth, be assigned to the authentic Sophist”. In a dialogue titled Meno, Plato describes a conversation between the Sophist Meno and Socrates.

Meno asks Socrates whether virtue is acquired by teaching or practice, or perhaps, it resides within us by nature. What Meno is testing is the sense in which anything can be known. In response, Socrates speaks with Meno’s young and uneducated servant and asks him questions about finding the area of a square. Through this process of questioning, the uneducated boy is able to determine that the length of the diagonal drawn through it determines the area. So the answer Socrates gives to Meno is that knowledge is reminiscent. The boy knew the answer all the time, but didn’t realize he knew it. The answer was already inside him.

There are two distinct kinds of knowledge: knowledge of the facts of daily life and truth. Facts come from observation of daily life, much like the scientific method. Truth, on the other hand, is that which has always has been and always will be true. Observation of daily life cannot yield this type of knowledge. We cannot observe what has always been or what will always be. Furthermore, our knowledge of the facts of daily life is learned by experience through our encounters with matter. Since we are encountering matter and matter is in constant flux and subject to imperfect observation, knowledge gained in this way cannot yield truth that always has been and always will be.

Socrates and his student Plato both point backwards to Pythagoras and the universal truths of mathematics. The answer to the question “What is a right-angle triangle?” is: “Any and every figure that satisfies the statement a2 + b2 = c2.” That formula is a truth. It never changes. That always has and always will describe a right-angle triangle. A true right-angle triangle is about that specific relationship. The length of the sides is immaterial as long as the relationship exists.

What is it that is within us, within our rationality that can make contact with that type of truth? We can’t come up with mathematical truths experientially. Surely, Pythagoras did not derive that formula by measuring apparent right angles in his environment. The walls and floors of our homes all seem to come together at right angles, but if you have ever had to make home repairs or fit wallpaper to those corners, you know they are not squared off and do not actually come together at right angles.

Obviously, these truths must exist in an a priori manner. That is, they are knowable without appeal to particular experience. They are derived without reference to particular facts. The process is largely intuitive, but also reasoned and deductive. Plato was satisfied that the truths of mathematics were sufficient to put to rest the arguments of the total skeptic who might suggest there is no such thing as unchanging truth.

So, as indicated above, if we can agree on any one thing as truth and the mathematical statement a2 + b2 = c2 is universally accepted as true, then we can inquire as to how that truth came to be known and extrapolate the method to learn other truths. Mathematical truth shows that we need not rely solely on experience for truth. Experience can’t get at certain truths. But if all truth cannot be reached through experience, what is left? Mathematics has shown that an intuitive, reasoned and deductive approach also yields truth.