Steven Milanese

Inductive reasoning is quite simply put an educated guess. It is reasoning based on a specific and/or set of observations from which a generalized conclusion is derived. The trouble with deriving “laws” from natural observation is that observation is unavoidably affected by individual perception. For example, a fish swimming inside of a fish bowl has a drastically different vantage point than an individual standing on the outside of the bowl looking in. Therefore, the perception of events being observed by one individual might not be the same as the perception of another. For this reason, the conclusions can at best be seen as likely but fails to produce the level of proof necessary for one to consider the conclusion to be absolute or “fact”.

Deductive reasoning is the process of using logical reasoning to argue from a general to a specific versus from a particular to a general, as is the case with inductive reasoning. Essentially it is an assumption. Simply put, one draws a logical conclusion based on an understanding of an established fact or observation. For example, if I observe an individual wearing a band style ring on their digitus medicinalis (ring finger) of their left hand, I can safely assume that the individual is or was at one point married. I draw this conclusion based on the fact that since ancient times bound or wed couples would wear a ring on this finger to symbolize their commitment to one another. (On an off note, the reason this finger was chosen was at the time it was believed that it contained a vein that ran directly to the heart.)

Deductive reasoning has led to some of the greatest discoveries of our time. One example is Newton’s corpuscle (particles) theory, which can be used to explain why light travels in a straight line and why it is refracted when traveling from one medium to another. He determined / deduced that based on his observation and understanding of how light traveled through the different mediums that light must be made up of corpuscles. Since he could not observe the particles themselves, he based his theory on logical deductive reasoning. I should note that this theory failed to account for “Newton’s Rings” which Newton himself observed. These were later explained by the wave theory and more specifically a phenomenon known as interference. Later, Einstein’s demonstration of the photoelectric effect showed that light in fact behaves as both particle and wave.

Mathematical Induction is a deductive methodology used to prove that a given statement will remain true for all non-negative integers. For example if you have a conjecture that you believe to be true for every positive integer greater than one, then you begin by first producing proof that the conjecture holds true for the number one. From there you would test for proof that the conjecture held true for two, and then three, and four, and so on. Many consider deductive reasoning as valid “proof” and it is in fact the basis of how geometric “proofs” are written. When a conjecture can be tested and proven using any given natural number (positive integer), the conjecture typically becomes an accepted theory or principle. At best, these remain likely theories but fail to reach the level of proof necessary to establish itself as fact.