Deductive and Inductive Arguments
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 (assumptions) 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 to be sound.
Here is a valid deductive argument: It's sunny in Singapore. If it's sunny in Singapore, he won't be carrying an umbrella. So, he won't be carrying an umbrella.
Here is a mildly strong inductive argument: Every time I've walked by that dog, he hasn't tried to bite me. So, the next time I walk by that dog he won't try to bite me.
An inductive argument is an argument that is intended by the arguer merely to establish or increase the probability of its conclusion. In an inductive argument, the premises are intended only to be so strong that, if they were true, then it would be unlikely that the conclusion is false. There is no standard term for a successful inductive argument. But its success or strength is a matter of degree, unlike with deductive arguments. A deductive argument is valid or else invalid.
The difference between the two kinds of arguments does not lie solely in the words used; it comes from the relationship the author or expositor of the argument takes there to be between the premises and the conclusion. If the author of the argument believes that the truth of the premises definitely establishes the truth of the conclusion (due to definition, logical entailment, logical structure, or mathematical necessity), then the argument is deductive. If the author of the argument does not think that the truth of the premises definitely establishes the truth of the conclusion, but nonetheless believes that their truth provides good reason to believe the conclusion true, then the argument is inductive.
Some analysts prefer to distinguish inductive arguments from conductive arguments; the latter are arguments giving explicit reasons for and against a conclusion, and requiring the evaluator of the argument to weigh these considerations, i.e., to consider the pros and cons. This article considers conductive arguments to be a kind of inductive argument.
The noun "deduction" refers to the process of advancing or establishing a deductive argument, or going through a process of reasoning that can be reconstructed as a deductive argument. "Induction" refers to the process of advancing an inductive argument, or making use of reasoning that can be reconstructed as an inductive argument.
Because deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises, if the argument is a sound one, then the truth of the conclusion is said to be "contained within" the truth of the premises; that is, the conclusion does not go beyond what the truth of the premises implicitly requires. For this reason, deductive arguments are usually limited to inferences that follow from definitions, mathematics and rules of formal logic. Here is a deductive argument:
John is ill. If John is ill, then he won't be able to attend our meeting today. Therefore, John won't be able to attend our meeting today.
That argument is valid due to its logical structure. If 'ill' were replaced with 'happy', the argument would still be valid because it would retain its special logical structure (called modus ponens). Here is the form of any argument having the structure of modus ponens:
P
If P then Q
So, Q
The capital letters stand for declarative sentences, or statements, or propositions. The investigation of these logical forms is called Propositional Logic.
The question of whether all, or merely most, valid deductive arguments are valid because of their structure is still controversial in the field of the philosophy of logic, but that question will not be explored further in this article.
Inductive arguments can take very wide ranging forms. Inductive arguments might conclude with some claim about a group based only on information from a sample of that group. Other inductive arguments draw conclusions by appeal to evidence or authority or causal relationships. Here is a somewhat strong inductive argument based on authority:
The police said John committed the murder. So, John committed the murder.
Here is an inductive argument based on evidence:
The witness said John committed the murder. So, John committed the murder.
Here is a stronger inductive argument based on better evidence:
Two independent witnesses claimed John committed the murder. John's fingerprints are