Rules of Inference, Fallacies

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### Common Logical Forms

The table below shows the most general presentation for commonly occurring forms of valid arguments (rules of inference) and fallacies.

It is important to understand that the occurrence of a common form depends upon the relationship between its terms, not upon the names given to those terms.

For example, both of these arguments are Modus Ponens:
p→q
p
∴q

¬q→p
¬q
∴p

It is also important to understand that it doesn't matter which premise is listed first or which premise is listed second.

For example, both of these arguments are Modus Ponens:
p
p→q
∴q

¬q
¬q→p
∴p

VALID FORMSINVALID FORMS
Modus Ponens
p→q
p
∴q

One premise is an if...then statement, the other premise affirms the antecedent, and the conclusion affirms the consequent.
Fallacy of the Converse (Affirming the Consequent)
p→q
q
∴p

One premise is an if...then statement, the other premise affirms the consequent, and the conclusion affirms the antecedent.
Modus Tollens
p→q
¬q
∴¬p

One premise is an if...then statement, the other premise denies the consequent, and the conclusion denies the antecedent.
Fallacy of the Inverse (Denying the Antecedent)
p→q
¬p
∴¬q

One premise is an if...then statement, the other premise denies the antecedent, and the conclusion denies the consequent.
Hypothetical Syllogism
p→q
q→r
∴p→r

One premise is an if...then statement, another premise is an if...then statement whose antecedent matches the consequent of the other premise, and the conclusion results from this chain of reasoning.
Misuse of Hypothetical Syllogisms
p→q
p→r
∴q→r

p→q
r→q
∴p→r

An incorrect attempt at Hypothetical Syllogism, in which two conditional premises agree in the antecedent, or agree in the consequent.
Disjunctive Syllogisms
p∨q
¬q
∴p

p∨q
¬p
∴q

One premise is an "or" statement, the other premise denies part of the "or" statement, and the conclusion affirms the other part.
Disjunctive Fallacies (Affirming a Disjunct)
p∨q
q
∴¬p

p∨q
p
∴¬q

One premise is an "or" statement, the other premise affirms part of the "or" statement, and the conclusion denies the other part.

MORE VALID FORMS

VALID FORM
Disjunction Introduction
p
∴p ∨ q

Conjunction Elimination
p∧q
∴p

Conjunction Introduction
p
q
∴p∧q