Categorical Propositions

Categorical Propositions

• These can be classified into four standard types based on their quantity and quality

A Proposition

• The logical structure is "All S is P"
• The proposition is affirmative
• The subject term and proposition are universal, while the predicate term is particular
• Example: All flags are symbols of countries

I Proposition

• The logical structure is "Some S is P"
• The proposition is affirmative
• Both the subject and predicate terms, and the proposition are particular
• Example: Some graduates are honor students

E Proposition

• The logical structure is "No S is P"
• The proposition is negative
• Both the subject and predicate terms, and the proposition are universal
• Example: No lawyers are bar flunkers

O Proposition

• The logical structure is "Some S is not P"
• The proposition is negative
• The subject term and the proposition are particular, but the predicate term is universal
• Example: Some farms are not tourist spots

Argument

• A verbal expression of mediate inference containing interdependent propositions
• Propositions are arranged as either a claim (conclusion) or evidence (premises)
• Arguments consist of two types of statements: conclusions and the reasons/premises supporting them
• Premises are statements providing reasons or evidence
• Conclusions are statements presenting the main claims

Deductive Argument

• An inference where the conclusion follows with absolute necessity from the premises
• Evaluated as valid or invalid based on logical form rather than content
• Validity depends on the premises strongly supporting the conclusion with absolute certainty
• Example: All mothers are women; Catherine is a mother; Therefore, Catherine is a woman

Inductive Argument

• An inference where the conclusion proceeds from the premises with probability
• Inductive arguments are not evaluated for validity or invalidity
• Conclusions are assessed based on strength (good/bad, strong/weak)
• Example: Observation that multiple women can bear children, leading to the probable conclusion that all women can bear children

Inference

• The process of creating a new proposition directly related to a preceding one
• The truth-value of the new proposition implies the truth of previous propositions

Mediate Inference

• Involves three or more propositions
• Includes a middle proposition linking the premise and the conclusion
• The third proposition acts as the conclusion
• The conclusion presents a new meaning or truth implied by previous propositions
• Example: All Filipinos are Asians; All Ilonggos are Filipinos; Therefore, all Ilonggos are Asians

Immediate Inference

• Involves only two propositions
• Does not contain a middle proposition
• The second proposition is the equivalent proposition
• The equialent proposition retains the truth of the given proposition
• Example: Some youth are students; Some students are youth

Eductions

• Also known as equivalent propositions, immediate inferences, or restated propositions
• Involve two propositions with equivalent meaning

Obversion

• Retain the subject and its quantity
• Change the quality of the proposition (affirmative to negative, or vice versa)
• Substitute the predicate with a contradictory or complementary term
• Possible Schemes: A to E, E to A, I to O, O to I
• Example: Obvertend – All trees are plants. Obverse - No trees are non-plants

Conversion

• Interchange the subject and predicate terms
• Retain the quality of the proposition
• Do not extend any of the terms
• Possible Schemes: E proposition, I proposition, and A proposition
• Example: Convertend – No men are mortals. Converse – No mortals are men

Contraposition

• A combination of both conversion and obversion