Proof by example is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.

This fallacy has the following structure, and argument form:

Structure:

I know that X is such.

Therefore, anything related to X is also such.

Argument form:

I know that x, which is a member of group X, has the property P.

Therefore, all other elements of X have the property P.

The following example demonstrates why this is a logical fallacy:

I've seen a person shoot someone dead.

Therefore, all people are murderers.

The flaw in this argument is very evident, but arguments of the same form can sometimes seem somewhat convincing, as in the following example:

I've seen Gypsies steal. So, Gypsies must be thieves.

When valid

However, argument by example is valid when it leads from a singular premise to an existential conclusion. For example:

Socrates is wise.

Therefore, someone is wise.

(or)

I've seen a person steal.

Therefore, people can steal.

This is an informal version of the logical rule known as existential introduction (also known as particularisation or existential generalization).

Formally

Existential Introduction:

See also

• Modus ponens
  Modus ponens
  In classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...
  
  
• Affirming the consequent
  Affirming the consequent
  Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:#If P, then Q.#Q.#Therefore, P....
  
  
• Inductive reasoning
  Inductive reasoning
  Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
  
  
• Bayesian probability
  Bayesian probability
  Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...
  
  
• Proof by construction
• Anecdotal evidence
  Anecdotal evidence
  The expression anecdotal evidence refers to evidence from anecdotes. Because of the small sample, there is a larger chance that it may be true but unreliable due to cherry-picked or otherwise unrepresentative of typical cases....
  
  
• Counterexample
  Counterexample
  In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition "all students are lazy"....