4. Proofs

Question 1

Derivation / Proof (3)

Answer 1

A) Sequence of annotated clear and truth-preserving inference steps, which preserve truth in the whole sequence.
B) There is not a unique derivation for each argument, one can be crafty and produce many
C) 1) Derivation: Valid 2) Proof: Sound (Valid+True)

Question 2

Annotating Derivations

Answer 2

A) Each step in the derivation is annotated with the steps
1) with the previous steps it depends on and
2) with the basic argument form it invoques.

Question 3

Derivation and Validity (2)

Answer 3

A) Combining valid Argument Forms (or Derivation from them) produces new valid arguments (∵ truth-preserving)
B) The derivation is only valid if it uses valid inference steps through the sequence.

Question 4

Ideal Derivation (3)

Answer 4

A) Discovers and removes redundant premises
B) Discovers and fills gaps or hidden premises
C) I-Steps only depend in previous steps (not circular)

Question 5

Enthymemes

Answer 5

A) An argument with suppressed premises
B) Potentially dangerous, since one can add premises ad infinitum to try to make them correct.
EX:
Mary is a widow, [widows are women], Mary is a women

Question 6

Reductio Ad Absurdum

Answer 6

A) Momentarily assume a step with the rest of premises to show absurdity (contradiction).
B) In annotating it always indent the assumed steps until contradiction and clarify its a supposition in the first assumed step.