Categorical Logic

Read pp. 215 – 219

Logical Connectives for Categorical Logic

All, Some, Are, and Not

Example of Categorical Logic

P1) All consistent opponents of killing are opponents of capital punishment

P2) No opponents of capital punishment are orthodox traditional Catholics

C) Therefore, No consistent opponents of killing are orthodox traditional Catholics

Logical Form

P1) All S are M

P2) No M are P

C) Therefore, no S are P

Universal Affirmation

All S are P (all dogs are mammals)

Universal Negation

No S are P (no dogs are reptiles)

Particular Affirmation

Some S are P (some dogs are brown)

Particular Negation

Some S are not P (some dogs are not brown)

Square of Opposition

1) All S are P 2) No S are P

3) Some S are P 4) Some S are not P

Diagonals are Contradictories

(1) is denial of (4)

(2) is denial of (3)

Horizontals are Contraries

(1) and (2) can’t both be true, but both could be false

Venn Diagrams
(See In Class Examples of The Following)

All S are P

No S are P

Some S are P