In the study of logical reasoning, arguments can be separated into two categories: deductive and inductive. Deductive reasoning is sometimes described as a "top-down" form of logic, while inductive reasoning is considered "bottom-up."

What is a Deductive Argument?

A deductive argument is one in which true premises guarantee a true conclusion. In other words, it is impossible for the premises to be true but the conclusion false. Thus, the conclusion follows necessarily from the premises and inferences. In this way, a true premise is supposed to lead to a definitive proof truth for the claim (conclusion). Here is a classic example:

Socrates was a man (premise) All men are mortal (premise). Socrates was mortal (conclusion)

The essence of the argument, mathematically, is: If A = B, and B= C, then A = C.

As you can see, if the premises are true (and they are), then it simply isn't possible for the conclusion to be false. If you have a correctly formulated deductive argument and you accept the truth of the premises, then you must also accept the truth of the conclusion; if you reject it, then you are rejecting logic itself. There are those that argue, with some irony, that politicians are sometimes guilty of such fallacies—rejecting deductive conclusions against all logic.

What is an Inductive Argument?

An inductive argument, sometimes considered bottom-up logic, is one in which premises offer strong support for a conclusion, but one that is not a certainty. This is an argument in which the premises are supposed to support the conclusion in such a way that if the premises are true, it is improbable that the conclusion would be false. Thus, the conclusion follows probably from the premises and inferences. Here is an example:

Socrates was Greek (premise). Most Greeks eat fish (premise). Socrates ate fish (conclusion).

In this example, even if both premises are true, it is still possible for the conclusion to be false (maybe Socrates was allergic to fish, for example). Words which tend to mark an argument as inductive—and hence probabilistic rather than necessary—include words like probably, likely, possibly and reasonably.

Deductive Arguments vs. Inductive Arguments

It may seem that inductive arguments are weaker than deductive arguments because in a deductive argument there must always remain the possibility of premises arriving at false conclusions, but that is true only to a certain point. With deductive arguments, our conclusions are already contained, even if implicitly, in our premises. This means that a deductive argument offers no opportunity to arrive at new information or new ideas—at best, we are shown information which was obscured or unrecognized previously. Thus, the sure truth-preserving nature of deductive arguments comes at the expense of creative thinking.

Inductive arguments, on the other hand, do provide us with new ideas and possibilities, and thus may expand our knowledge about the world in a way that is impossible for deductive arguments to achieve. Thus, while deductive arguments may be used most often with mathematics, most other fields of research make extensive use of inductive arguments due to their more open-ended structure. Scientific experiment and most creative endeavors, after all, begin with a "maybe," "probably" or "what if?" mode of thinking, and this is the world of inductive reasoning.