Inference

Logic

As a way to truth

Truth or falsity is a property of judgmentBasis for truth or falsityEvidence of the senses

It is raining todayThe chair is on my right.

Analysis (analytic statements)A triangle is a polygon with three

sides.

As a way to truth

AuthorityPersons in authority

InferencePropositions are accepted as true

because other propositions can be found to serve as evidence for them. Truth or falsity is attained through the process called inference

Inference

• Is a process whereby from the truth-value of one or more propositions, we conclude to the truth value of another proposition.

• When we draw a conclusion from what we have asserted we make an inference

Types of inference

• Immediate inference– Proceeds from one proposition

directly to another proposition

• Mediate inference– Proceeds from two or more

propositions to another which is implied in the given propositions

Examples

• Immediate inference– It is true that some flowers are red.

Hence, it is false that no flower is red.

– Some animals are mammals. Thus, some mammals are animals.

• Mediate inference– Every person who is at least 18

years old is of legal age.– Monty is at least 18 years old.– So, he is of legal age.

Types of Immediate Inference

Oppositional InferencesContradictionContrarietySubcontrarietySubalternation

EductionObversionConversionContrapositionInversion

Matter and Form

• Material element (Matter)– Refers to the terms and propositions

that are used in the inference• Formal element (Form)

– Refers to the order or specific arrangement of the terms and propositions in the inference

Matter and Form

• Study the examples:– No Muslim is a Christian.– So, no Christian is a Muslim.– Some animals are dogs.– Ergo, some dogs are animals.

• The two examples have this form:– X is Y.– So, Y is X.

Oppositional Inferences

ContradictionOpposition between propositions

that differ in quality and quantityEvery S is P. (A, universal

affirmative)Not all S is P. (O, particular

negative)No S is P. (E, univ. -)Some S is P. (par. +)

ExampleEvery flower is red.Ergo, not every flower is red.

Contradiction

ExampleEvery man is immortal. (false)Ergo, not every man is immortal.No dog is a plant. (True)So, some dogs are plants.Not all turtles are animals. (false)Ergo, all turtles are animals.Some medicines are expired.

(true)Hence, No medicine is expired.

Oppositional Inferences

Contrariety- the opposition between universal propositions that differ in quality.

Every S is P. (A, univ +)No S is P. (E, univ. -)

ExampleEvery rose is a flower.Ergo, no rose is a flower.

No plant is a mammal.So, every plant is a mammal.

Contrariety

It is necessary that you go to school.(false)Ergo, it is not possible that you go to school.Georgia is always absent.(true)So, she is never absent.No plant has a sense of sight.(true)Ergo, every plant has a sense of sight.No book is thick. (false)Hence, every book is thick.

Oppositional Inferences

Subcontrariety- the opposition between particular propositions that differ in quality.

Some S is P. (I, par +)Not all S is P. (O, par -)

ExampleSome vegetables are delicious.

(true)Ergo, not all vegetables are

delicious.

Not all citizens are voters.(true)So, some citizens are voters.

Subcontrariety

Sometimes, Dario does not sing.(false)Ergo, sometimes Dario sings.Peter can go to Mindanao. (false)So, he does not need to go to Mindanao.Some grapes are sweet.(true)So, some grapes are not sweet.Not all fruits are yellow. (true)Hence, some fruits are yellow.

Oppositional Inferences

Subalternation--the opposition between propositions that have the same quality but different quantity.

All S is P. (A, univ +)Some S is P. (I,par. +)

ExampleEvery circle is round. (true)Ergo, some circles are round.No square is a circle. (true)So, some squares are not circles.

SubalternationSome papers are made from plants.(true)Ergo, all papers are made from plants.Not every employee is honest. (true)So, no employee is honest.Some dark things are white. (false)Hence, all dark things are white.Many college students are not literate. (false)Ergo, no college student is literate.Every paper is red. (false)Ergo, some papers are red.No ball is round. (false)So, some balls are not round.

Summary

A E

I O

CONTRARIETY

SUBCONTRARIETY

SUBALTERNATION

SUBALTERNATION

CONTRADICTION

Summary

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I t If It I?

Of Ot O? Ot