When we must have certainty, we must rely upon deductive inferences. When a new bridge or a space shot depends upon the mathematics, we don’t think, “Well, math is unreliable, but that’s okay because our equations are likely to be true.” No! There is enough unreliability in our construction and engineering projects already, but that is not because of the mathematics!

When we measure angles for a roof or other construction project, we don’t think that the Pythagorean Theorem is “pretty reliable.” No! We know that the Pythagorean Theorem is always exactly right. Of course, most of the angles we measure are not perfect. But that is not because of some unreliability in the Pythagorean Theorem. It is because our measuring instruments are very crude compared to the infinite precision of geometry.

When we think about the nature of justice, about how laws should work, about whether or not a particular political system is legitimate, about forms of government, about religion, science, and ethics, and about a host of other subjects that we think are very important, philosophers do not think that induction is a reliable method. Instead, we turn to deductive arguments and argument analysis to discuss such subjects.

Deductive arguments provide literal proofs, while inductive arguments can at most provide a certain probability that our conclusions is true.