Inductive Vs. Deductive Reasoning

Even if categories like “dog” and ‘table” could be accurately defined with sentences of the form all S is P, they have another important characteristic that makes it difficult for them to support logical reasoning. These categories are created by means of a process called induction, which is fundamentally different from the deduction used in logical reasoning. Deductive reasoning works best when it is applied to mathematics, because mathematical principles are necessarily true. We know, as the philosopher Kant said, not only that they are true, but that they cannot be otherwise. Consequently when we make statements like “all triangles have three angles whose sum is 180 degrees”, we don’t have to go out and measure hundreds of triangles to determine whether or not that statement is true. We can prove that it must always be true by using mathematical reasoning. But if we are making claims about all other sorts of objects, however, we never get that kind of certainty. For this reason, philosophers make a distinction between Mathematical Truths and Empirical Truths. Mathematical Truths ,such as the truths of deductive logic, are necessarily true. Empirical Truths, which we discover through our sense organs and through scientific experiments, are only contingently true i.e. it is possible that they could be false. Inductive reasoning gives us only contingent truths, not necessary truths.

Rationalists like Plato and Descartes believed that some necessary truths, such as the theorems of geometry, are facts about reality, which we grasp by intellectual…