Logical Opposition

• Logical opposition – refers to the different relations that exist between propositions having the same subject and predicate but differing in quantity and quality.

• Knowing the value of a given proposition, we can immediately infer the value of its opposing proposition

• A, E, I, O have opposing relationships based on their quality and quantity.

Square of opposition

E

I O

A u n i v e r s a l

negative

Aff I rmative

p a r t i c u l a r

Four kinds of oppositions

1. Contradictory – this pertains to relationship between A and O; E and I.

2. Contrary terms – it pertains to the relationship between A and E.

3. Subcontrary – refers to the relationship between I and O proposition.

4. Subaltern opposition – opposition that exist

between two propositions that differ only in quantity. (A and I) (E and O)

E

I O

A c o n t r a r y

Subalterns

Subalterns

S u b c o n t r a r y

contradictory

1. Contradictory – this pertains to relationship between A and O; E and I. – Opposition between two that differ both in

quality and quantity.

– Only one proposition can be true.

(If one is true, the other is false.)

• If A is true, O is false

– All murders are criminals (A) (true)

– Some murders are not criminals (O) (false)

• If O is true, A is false

– Some birds do not fly (O)(true)

– All birds are flying animals (A) (false)

• If E is true, I is false

– If no student are listening (E) (true)

– Then, some students are listening (I) (false)

• If I is true, E is false

– If some students are dean’s listers (I) (true)

– Then, no students are dean’s listers (E) (false)

2. Contrary terms – it pertains to the relationship between A and E. (They differ only in quality)

the two cannot be both true but can be both false. – if one is true, the other is false

– If one is false, the other is doubtful (either true or false)

– If A is true E is false • All books are useful (true)

• No books are useful (false)

• If E is true, A is false

– No dogs are cats (True)

– All dogs are cats (False)

• If A is false, E is doubtful (may either true or false)

– All women are men (false)

– No women are men (true)

– All women are pregnant(false)

– No women are pregnant(false)

• If E is false, A is doubtful (may either true or false)

–No voters are citizen (false)

–All voters are citizen (true)

–No citizens are activist (false)

–All citizens are activist (false)

3. Subcontrary – refers to the relationship between I and O proposition. (they differ only in quality)

– If one is false, the other is true

– If one is true, the other is doubtful

– If I is false, O is true • some animals are plants (false)

• Some animals are not plants (true)

– If O is false, I is true • Not all cellphones are electronic device (false)

• Some cellphones are electronic device. (true)

• If I is true, O is doubtful(may either true or false)

– If some flowers are plants (true)

– Then, some flowers are not plants (false)

– If some lawyers are liars (true)

– Then some lawyers are not liars (true)

• If O is true, I is doubtful

– If some students are not varsity players (true)

– Then, some students are varsity players (true)

– If some animals are not plants (true)

– Then, some animals are plants (false)

4. Subaltern opposition – opposition that exist between two propositions that differ only in quantity. (A and I) (E and O)

• Rules:

– if A or E proposition is true, I or O proposition is true.

– if A or E proposition is false, I or O proposition is doubtful.

– If I or O proposition is true, A or E proposition is doubtful.

– If I or O proposition is false, A or E proposition is false.

If A or E proposition is true, I or O proposition is true. A that is true: if A is true I is true

(A and I) • All cats are animals. (true) • Some cats are animals. (true)

– E that is true: if Eis true O is true

(E and O) • All priests are not nuns (true) • Some priests are not nuns (true)

if A or E proposition is false, I or O proposition is doubtful.

A that is false: if A is false I may be true or false.

(A and I)

– If, everyone in the class is actively participating (false)

– Then, few in this class are actively participating (true)

( A and I)

– If, all creatures are immortals (false)

– Then, some creatures are immortal (false)

E that is false: if E is false O may be true or false

(E and O)

– If, No women are pregnant (false)

– Then, some women are not pregnant (true)

– If, no orange are fruits (false)

– Then, some orange are not fruit (false)

If I or O proposition is true, A or E proposition is doubtful.

I that is true: if I is true, A may be true or false.

– If, some doctors are professionals (true)

– Then, all doctors are professionals (true)

– If, some students are smart (true)

– Then, all students are smart (false)

O that is true: if O is true, E may be true or false.

If, some criminals are not law abiding citizens (true)

Then, no criminals are law abiding citizens (true)

If , some artists are not singers (true)

Then, no artists are singers (false)

If I or O proposition is false, A or E proposition is false.

I that is false: if I is false, A is false.

If, some carrots are fruits (false)

Then, each carrot is a fruit (false)

O that is false: if O is false, E is false.

If, some pigs are not animals (false)

Then, all pigs are not animals (false)

Reasoning/ Inference

What is reasoning/inference?

– It is our capacity to understand complex reality.

– It is a mental operation wherein the mind infers a new truth drawn out from previous judgments.

– Therefore, reasoning is making conclusion from a given sets of propositions.

Two methods of Reasoning

• Deductive reasoning- reasoning from a universal or general idea to a particular or specific/individual conclusion.

Example:

– all murders are criminals, but Jonas is murderer, therefore Jonas is a criminal.

– No politicians are corrupt, but Mr. Stuart is a politician, therefore Mr. Stuart is not corrupt.

• Deductive reasoning is like an inverted triangle.

• Inductive reasoning - inductive reasoning is a type of reasoning wherein it draws its conclusion from particular or specific concepts to general or universal idea.

• Example:

Kyle is a good dancer.

Hannah is a good dancer.

Robin is a good dancer.

But, Kyle, Hannah, Robin are CVSU students.

Therefore, CVSU students are good dancers.

Jane is smart.

But, Jane is a tourism student.

Therefore, tourism students are smart.

Inductive reasoning maybe likened

to an upright triangle.

Deductive VS Inductive Reasoning

• Deductive reasoning – if the premises are true it absolutely guarantees the truth of its conclusion. (gives 100% certainty)

• Inductive reasoning – the truths of its premises makes it likely and probable that its conclusion is also true. (at least 51% certainty)

How to make inference?

• Inference is a spoken or written expression of reasoning.

• Parts of inference:

– Premises: part of inference from which conclusion is drawn or the new knowledge is derived. Premises is also know as antecedent.

– Conclusion: is the final statement derived from premises. It is also called consequent.

– Sequence: the necessary connection between the premises (antecedent) and the conclusion (consequent).

Man is a rational being; but Socrates is a man; hence, Socrates is a rational being

Antecedent (premises)

Inference sequence

consequent (conclusion)

• Invalid inference:

– Roses are red, violets are blue; therefore I am Filipino.

– Some men(gender) are leaders; but, Jessie is a leader; therefore Jessie is a man.

• Note: there must always be a logical/necessary connection to make a valid or sound inference.

Valid Inference:

– All men are mortal, but you are a man, therefore you are mortal.

– Philosophers are seekers of wisdom, but Socrates is a philosopher, so, Socrates is seeker of wisdom.

– All students are learners; but CVSUans are students; hence, CVSUans are learners.

Two types of Inference

1. Immediate inference: – The conclusion passes from one proposition

– Without medium

– New proposition but not new truth

Example: • No bees are flies; so, no flies are bees.

• All men are mortal beings; thus, some mortal beings are men.

(it change the arrangement the subject and predicate in order create new proposition, but the meaning or essence is still the same.)

2. Mediate inference:

– The conclusion passes from two proposition

– Through a medium

– New proposition and new truth

Example:

• All men are free; but I am a man; thus, I am free.

• All voters are citizen, but Aldrin is a voter; therefore, Aldrin is a citizen.

(mediate inference uses two propositions from which conclusion will be drawn out. Mediate inference creates new propositions as well as new knowledge.)

Foundations of Thought (Reasoning)

• There are three basic Laws of Thought, also known as Principles in logic.

• 1st Law of identity: – It in an imperative that says that “whatever is, is.”

• A is A

• Boys are boys

• Table are table

• 2nd Law of Contradiction:

– It says that the co-existence of mutually exclusive realities in one entity simultaneously is logically impossible.

– “it is impossible for the same thing both to be and not to be.”

– Nothing is both A and not-A

– Hanna can never be present and absent in my class at the same time.

• 3rd the Law of Excluded Middle:

– States the there is no third alternative in the presence of mutually exclusive realities or contradictory. (there is no middle ground)

– “Everything must neither be or not be.”

– Nothing is neither A nor not-A.

– Either you are mortal or immortal.

– Jake is either alive or dead.