Proof by example


In logic and mathematics, proof by example is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof.
The structure, argument form and formal form of a proof by example generally proceeds as follows:
Structure:
Argument form:
Formal form:
The following example demonstrates why this line of reasoning is a logical fallacy:
The flaw in this argument is very evident, but arguments of the same form can sometimes seem somewhat convincing, as the following example suggests:
In the common discourse, a proof by example can also be used to describe an attempt to establish a claim using statistically insignificant examples. In which case, the merit of each argument might have to be assessed on an individual basis.

Valid cases of proof by example

In some scenarios, an argument by example may be valid if it leads from a singular premise to an existential conclusion. For example:
These examples outline the informal version of the logical rule known as existential introduction, also known as particularisation or existential generalization:
;Existential Introduction
In mathematics, proof by example can also be used to refer to attempts to illustrate a claim by proving cases of the claim, with the understanding that these cases contain key ideas which can be generalized into a full-fledged proof.