Deductive and Inductive Reasoning

Deduction: (Lat. de ducere, to lead, draw out, derive from; especially, the function of deriving truth from truth). Inference by which from general truths already known we advance to a knowledge of other particular truths necessarily implied in the former.

The typical expression of deductive inference is the syllogism. Granted the truth of the antecedent judgments, the consequent must follow; and the firmness of our assent to the latter is conditioned by that of our assent to the former. An example of decution is as follows...

1. Everything that has a beginning, has a cause.
2. The Universe has a beginning.
3. Therefore the universe has a cause.

Induction: Induction is the complement of deduction. In other words, it is inference by which from particular truths already known we advance to a knowledge general or universal truths supported by the former. In this form of reasoning, the premises of an argument support the conclusion but do not ensure it.

Example:

1. All observed crows are black
2. Therefore all crows are black

The conclusion is reasonably supported by the premise, but not absolutely proven in the strict sense. Unless we are certain that we have seen every crow (which is impossible), there may be one of a different color. Consequently, with inductive reasoning, the premises--at best--may predict a high probability of the conclusion, but do not absolutely ensure that the conclusion is true.

For example,

1. All observed beginnings have a cause
2. Therefore, all beginnings have a cause

Is an argument based upon inductive reasoning. Unless we have observed everything that had a beginning (which is impossible), we can only predict with high probability that everything which has a beginning has a cause. It is a reasonable conclusion, based upon the preponderance of evident. The "law of gravity" and other scientifc postulates such as the "Big Bang" theory of cosmology is also based upon inductive reasoning, as it infers a general conclusion from particular observed evidence.

Formal logic is deductive rather than inductive. However, inductive reasoning is cogent, and it is used in decision-making in all fields of study, such as civil and criminal law, philosophy, science, economics, politics, military studies, and theology.