Inductive and Deductive Reasoning

The information below is provided by the Internet Encyclopedia of Philosophy¹:

When assessing the quality of an argument, we ask how well its premises support its conclusion. More specifically, we ask whether the argument is either deductively valid or inductively strong.

A deductive argument is an argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument’s premises are true. This point can be expressed also by saying that, in a deductive argument, the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false. An argument in which the premises do succeed in guaranteeing the conclusion is called a (deductively) valid argument. If a valid argument has true premises, then the argument is said also to be sound. All arguments are either valid or invalid, and either sound or unsound; there is no middle ground, such as being somewhat valid.

Here is a valid deductive argument:

It’s sunny in Singapore. If it’s sunny in Singapore, then he won’t be carrying an umbrella. So, he won’t be carrying an umbrella.

The conclusion follows the word “So”. The two premises of this argument would, if true, guarantee the truth of the conclusion. However, we have been given no information that would enable us to decide whether the two premises are both true, so we cannot assess whether the argument is deductively sound. It is one or the other, but we do not know which. If it turns out that the argument has a false premise and so is unsound, this won’t change the fact that it is valid.

Here is a mildly strong inductive argument:

Every time I’ve walked by that dog, it hasn’t tried to bite me. So, the next time I walk by that dog it won’t try to bite me.

An inductive argument is an argument that is intended by the arguer to be strong enough that, if the premises were to be true, then it would be unlikely that the conclusion is false. So, an inductive argument’s success or strength is a matter of degree, unlike with deductive arguments. There is no standard term for a successful inductive argument, but this article uses the term “strong.” Inductive arguments that are not strong are said to be weak; there is no sharp line between strong and weak. The argument about the dog biting me would be stronger if we couldn’t think of any relevant conditions for why the next time will be different than previous times. The argument also will be stronger the more times there were when I did walk by the dog. The argument will be weaker the fewer times I have walked by the dog. It will be weaker if relevant conditions about the past time will be different next time, such as that in the past the dog has been behind a closed gate, but next time the gate will be open.

An inductive argument can be affected by acquiring new premises (evidence), but a deductive argument cannot be. For example, this is a reasonably strong inductive argument:

Today, John said he likes Romona.

So, John likes Romona today.

but its strength is changed radically when we add this premise:

John told Felipé today that he didn’t really like Romona.

The distinction between deductive and inductive argumentation was first noticed by Aristotle (384-322 B.C.E.) in ancient Greece. The difference between deductive and inductive arguments does not lie in the words used within the arguments, but rather in the intentions of the arguer. It comes from the relationship the arguer takes there to be between the premises and the conclusion. If the arguer believes that the truth of the premises definitely establishes the truth of the conclusion, then the argument is deductive. If the arguer believes that the truth of the premises provides only good reasons to believe the conclusion is probably true, then the argument is inductive. If we who are assessing the quality of the argument have no information about the intentions of the arguer, then we check for both. That is, we assess the argument to see whether it is deductively valid and whether it is inductively strong.

1. Fieser, James and Dowden, Bradley, editors. "Deductive and Inductive Arguments." The Internet Encyclopedia of Philosophy, University of Tennessee, https://www.iep.utm.edu/ded-ind/. Accessed 28 May 2020.