philosophy assignment

1. modus ponens For all these forms, below: the Greek

2. modus tollens letters are variables; they stand

3. conjunctive addition for complete declarative sentences

4. conjunctive subtraction (propositions). Think algebra.

5. disjunctive argument

6. conjunctive argument

7. double negation (2 forms)

8. chain

9. simple dilemma

10. complex dilemma

1. If Δ, then λ [fallacy = affirming the consequent] Δ a

therefore: λ

2. If Δ, then λ [fallacy = denying the antecedent] not λ a a

not Δ c f

3. Δ 4. Δ and λ λ Δ

Δ and λ (or λ)

5. Δ or λ

not Δ d

λ

6. Not both Δ and λ

Δ d

not λ

7. Δ dalso not not Δ d

not not Δ Δ

8. If Δ, then λ

If λ, then θ f

If Δ, then θ

9. Δ or λ

If Δ, then θ

If λ, then θ d

θ

10. Δ or λ

If Δ, then θ

If λ, then Φ

θ or Φ

Syllogistic logic (the logic of All, None, Some)

No Greek letters. Symbols (variables) are capital letters of the English alphabet (A, B, C, …).

Domain of the variables: predicates, properties, features.

E.g., All dogs have four legs = All things that have the property of being a dog are things that

have the property of having four legs.

All As are Bs. All dogs are mammals. All Bs are Cs. All mammals have hair. [ok, except dolphins] hence: All As are Cs. All dogs have hair. The above syllogism is valid (good deductive logic) but is not a "chain" argument, form #8 on the preceding page. Make sure you understand why. A fallacious argument: All As are Bs. All my relatives on my mother's side of the family are ugly. All Cs are Bs. All my relatives on my father's side of the family are ugly. hence: As are Cs. hence: mother's side relatives = father's side relatives? [nope]