# Difference between deductive and inductive argument

In logic analysis of arguments, arguments can be separated into two categories: deductive and inductive. The former are studied by formal logic and the latter by informal logic.

## What is a deductive argument?

A deductive argument is one in which, if the premises are true, the conclusion will necessarily be true. In other words, it is impossible for the premises to be true and the conclusion false. Thus, the conclusion necessarily follows from the premises. Thus, a true premise must lead to definitive proof of the truth of the conclusion. Here is a classic example:

Socrates was a man (premise)

All men are mortal (premise).

Socrates is mortal ( conclusion)

As you can see, if the premises are true (and they are), then it is simply not possible for the conclusion to be false. If you have a deductive argument correctly formulated and accept the truth of the premises, then you must also accept the truth of the conclusion. If you reject it, you are falling into contradiction, it is as if you are saying that “Socrates, at the same time, is and is not mortal”.

## What is an inductive argument?

An inductive argument is one in which the premises offer strong support for a conclusion, but which do not fully guarantee it. This is an argument in which the premises support the conclusion in such a way that if the premises are true, the conclusion is unlikely to be false. Thus, the conclusion probably follows from the premises. 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 that the conclusion is false (perhaps Socrates was allergic to fish, for example). Expressions that tend to characterize an argument as inductive – and therefore probabilistic and not necessary – include words as likely, probable, possibly, and reasonably.

## Difference between deductive and inductive arguments

To summarize what has been said so far:

- deductive arguments have the conclusion
**necessarily**true, if the premises are true; - inductive arguments have the conclusion
**probably**true, if the premises are true.

In addition, there is another fundamental difference between them. In the deductive arguments, our conclusions are already contained, even if implicitly, in our premises. This means that a deductive argument does not offer an opportunity to come up with new information – at best, information that was obscured or not recognized in the premises is highlighted. Thus, the right nature, which preserves the truth, of deductive arguments comes at the expense of the expansion of knowledge. This becomes clear above example of deductive argument. In a way, the conclusion that Socrates is mortal was implicit in the premises.

Inductive arguments, on the other hand, draw conclusions that go beyond what is already said in the premises and this allows us to expand our knowledge of the world. It is the inductive reasoning behind science, for example. Newton’s law that says “two bodies attract each other with force proportional to their masses and inversely proportional to the square of the distance that separates their centers of gravity” is the conclusion of an inductive reasoning.

## References

Walton, Douglas. Informal Logic: A Pragmatic Approach. Cambridge: Cambridge University Press, 2008.