Traditional Logic Reference Sheet

The science of correct reasoning

A word or group of words that can serve as the subject or predicate of a proposition

The set of all things to which the term applies

The extension of 'dog' is all dogs

The set of attributes that define the term

The intension of 'dog' includes 'animal', 'domesticated', etc.

A term that refers to all members of a class (e.g., 'all dogs')

A term that refers to some (but not all) members of a class (e.g., 'some dogs')

A statement that gives the essential meaning of a term by stating its genus and specific difference

The broader class or category to which the term belongs

For 'dog', the genus is 'animal'

The characteristic that distinguishes the term from other members of the same genus

For 'human', genus = 'animal', specific difference = 'rational'

A statement that is either true or false

A (All S are P), E (No S are P), I (Some S are P), O (Some S are not P)

A-proposition (universal affirmative)

E-proposition (universal negative)

I-proposition (particular affirmative)

The term about which something is affirmed or denied

The term that is affirmed or denied of the subject

The linking verb ('is' or 'are') that connects subject and predicate

Two propositions that cannot both be true and cannot both be false (A vs O, E vs I)

Two propositions that cannot both be true but can both be false (A vs E)

Whether it is affirmative or negative

Whether it is universal or particular

When the proposition says something about every member of the class the term refers to

The subject of A-propositions and both terms of E-propositions are distributed

A diagram showing the logical relationships (contradictory, contrary, subcontrary, subaltern) between the four standard categorical propositions

A and O, E and I (diagonal pairs)

Contradictories cannot both be true and cannot both be false

A and E (both universal, one affirmative, one negative)

Contraries cannot both be true but can both be false

I and O (both particular)

Subcontraries can both be true but cannot both be false

The relationship between a universal and its corresponding particular (A to I, E to O)

If the universal is true, the particular must be true (in traditional logic)

It must also be TRUE (subalternation)

It could be either true or false (contraries can both be false)

E must be TRUE (since I and E are contradictories)

Switching the subject and predicate of a proposition

The converse of 'No cats are dogs' is 'No dogs are cats'

E and I propositions

'No S are P' converts to 'No P are S'; 'Some S are P' converts to 'Some P are S'

No dogs are cats

Changing the quality of a proposition and replacing the predicate with its complement

'All S are P' becomes 'No S are non-P'

No dogs are non-mammals (E)

Yes, obversion is valid for all four types

Switching the subject and predicate and replacing each with its complement

'All S are P' becomes 'All non-P are non-S'

A and O propositions

Some pets are birds

Because the predicate of an A-proposition is not distributed, so making it the subject of a universal claim is invalid

'All dogs are animals' does NOT mean 'All animals are dogs'

A deductive argument with two premises and a conclusion

Major term (predicate of conclusion), minor term (subject of conclusion), middle term (in both premises)

The premise containing the major term (predicate of the conclusion)

The premise containing the minor term (subject of the conclusion)

Man/men

The conclusion follows necessarily from the premises (regardless of whether premises are actually true)

It is both valid AND has true premises

4 (based on the position of the middle term)

The combination of proposition types (A, E, I, O) in its premises and conclusion

Example: AAA, EAE, AII, etc.

The middle term must be distributed at least once in the premises

When the middle term is not distributed in either premise, making the syllogism invalid

Example: All dogs are animals; all cats are animals; therefore all cats are dogs

A syllogism with at least one conditional (if-then) premise

If P then Q; P is true; therefore Q is true (affirming the antecedent)

Affirming the antecedent — the valid form

If P then Q; Q is false; therefore P is false (denying the consequent)

Denying the consequent — the valid form

Incorrectly reasoning: If P then Q; Q is true; therefore P must be true

If it rains the ground is wet; the ground is wet; therefore it rained (invalid — sprinklers could cause wet ground)

Incorrectly reasoning: If P then Q; P is false; therefore Q must be false

If it rains the ground is wet; it didn't rain; therefore the ground isn't wet (invalid)

If P then Q; if Q then R; therefore if P then R

The consequent of the first becomes the antecedent of the second

It rains

The ground gets wet

A syllogism with an either/or (disjunctive) premise

Either P or Q; not P; therefore Q (denying one disjunct affirms the other)

An 'or' statement where one or both options can be true

'You can have cake or pie' (you could have both)

An 'or' statement where exactly one option is true (not both)

'The light is on or off' (it can't be both)

The gardener did it

A syllogism with one premise or the conclusion left unstated (assumed)

All men are mortal

An enthymeme with the major premise omitted

An enthymeme with the minor premise omitted

Because people naturally leave out obvious or assumed premises to communicate more efficiently

An error in reasoning that makes an argument invalid

Attacking the person making the argument instead of the argument itself

Misrepresenting someone's argument to make it easier to attack

Assuming the truth of the conclusion in one of the premises

Introducing an irrelevant topic to divert attention from the original issue

Claiming something is true because an authority figure says so, even when they lack relevant expertise

Drawing a broad conclusion from too few examples

Presenting only two options when more exist

Claiming that one event will inevitably lead to a chain of negative consequences without justification

Using a word with two different meanings in the same argument to mislead

Arguing that something is true or good because many people believe it or do it

A conclusion that does not logically follow from the premises

Reasoning from general principles to specific conclusions (if premises are true, conclusion must be true)

Reasoning from specific observations to general conclusions (conclusion is probable, not certain)

Validity is about the structure of an argument; truth is about whether statements correspond to reality

A condition that must be present for an event to occur (but may not be sufficient alone)

Water is necessary for life but not sufficient

A condition that, if present, guarantees the event will occur

Being a dog is sufficient for being an animal

Yes, if one or more premises are false (valid only guarantees the conclusion follows from the premises)