Proofs and Sentential Logic

Question 1

When is an argument valid?

Answer 1

When it is impossible for premise to be true and the conclusion false
(conclusion necessarily follows from its premises)

Question 2

Soundness

Answer 2

An argument is sound if each of its premise is true

Question 3

Deduction

Answer 3

A deduction is an argumentation such that each step in the chain of reasoning is known to be valid

Question 4

Proof

Answer 4

A deduction from premises known to be true

Question 5

commutativity of conjunction

Answer 5

phi and psi / psi and phi
(A ^ B) / (B ^ A)

Question 6

Associativity of conjunction

Answer 6

(A ^ b) ^ C / A ^ (B ^ C)

Question 7

Idempotence of conjunction

Answer 7

(A ^ A) / A

Question 8

Interpret (A -> B)
(conditional)

Answer 8

It is not the case that A is true and B is false

Question 9

Exhaustion

Answer 9

Every sentence has at least one of the values True or False. Equivalently: Every sentence is either True or False

Question 10

Exclusion

Answer 10

Every sentence has at most one of the values True or False. Equivalently: No sentence is both True and False

Question 11

Exhaustion and Exclusion

Answer 11

Two postulates that guarantee that every sentence has exactly one truth-value

Question 12

Truth-functional schema (or form)

Answer 12

A schema is a truth-functional schema if and only if it contains only
- truth-functional operators
- placeholders whose side conditions specifies that sentences satisfying the Exhaustion and Exclusion postulates are substituted in for them

Question 13

1. Aristotle is a logician
2. All logicians have super-powers
   ________________________________________
3. Aristotle has super-powers

Answer 13

• not a valid argument form
• contains no truth-functional operator
• formally valid
  (SOME truth-functional invalid arguments are formally invalid, but some are nonetheless formally valid)