1. Inference
Logic

2. As a way to truth Truth or falsity is a property of judgment
Basis for truth or falsity
Evidence of the senses
It is raining today
The chair is on my right.
Analysis (analytic statements)
A triangle is a polygon with three sides.

3. As a way to truth Authority Persons in authority Inference
Propositions 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

4. 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

5. Types of inference Immediate inference Mediate 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

6. Examples Immediate inference Mediate 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.

7. Types of Immediate Inference
Oppositional Inferences
Contradiction
Contrariety
Subcontrariety
Subalternation
Eduction
Obversion
Conversion
Contraposition
Inversion

8. 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

9. 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.

10. Oppositional Inferences
Contradiction
Opposition between propositions that differ in quality and quantity
Every 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. +)
Example
Every flower is red.
Ergo, not every flower is red.

11. Contradiction Example Every 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.

12. Oppositional Inferences
Contrariety- the opposition between universal propositions that differ in quality.
Every S is P. (A, univ +)
No S is P. (E, univ. -)
Example
Every rose is a flower.
Ergo, no rose is a flower.
No plant is a mammal.
So, every plant is a mammal.

13. 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.

14. 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 -)
Example
Some vegetables are delicious.(true)
Ergo, not all vegetables are delicious.
Not all citizens are voters.(true)
So, some citizens are voters.

15. 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.

16. 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. +)
Example
Every circle is round. (true)
Ergo, some circles are round.
No square is a circle. (true)
So, some squares are not circles.

17. Subalternation Some 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.

18. Summary A E I O CONTRARIETY S S U U B B A A L L T T E E R R N N I I O
CONTRADICTION
SUBCONTRARIETY

19. Summary At Af A? Ef Et E?
I t If It I? Of Ot O?