Formal Logic

Question 1

Name the 5 types of connectives?

Answer 1

1. If… then… = “If you pass the test, then I’ll give you a cookie”
2. … and … = “It’s cold and it’s raining.”
3. Not-… = “It’s not the case that today is Friday“
4. … or … = “This lane is for buses or bicyles”
5. … if and only if .. = “I will go to the party if there are good snacks”

Question 2

What are important principles for formal logic?

Answer 2

1. Principle of Bivalence and Law of Excluded middle, as before: There are only two truth values, and every proposition has exactly one of them.
2. Connectives are “Truth Functional”
   - The truth value of any compound/molecule proposition is completely determined
   by the truth values of the components/atoms together with the connective(s)
   that join them.
   - Consequence: if we know the truth value of P and the truth value of Q, we can
   automatically figure out the truth value of any connective
   - Compare: if we know the truth value of P and the truth value of Q, we don’t
   automatically know the truth value of “P because Q” – so “… because…” is not
   truth functional

Question 3

How do brackets affect arguments?

Answer 3

Compare: P = Joel is a Philosopher, Q = Joel is employed by UCC, R = Joel is a musician
(P Q) v R ≈ “Either Joel is a Philosopher and he’s employed by UCC, or he’s a musician.”
P (Q v R) ≈ “Joel is a Philosopher, and either he’s employed by UCC or he’s a musician”

Question 4

What value do truth tables have?

Answer 4

• We can use the truth tables to examine how a complex proposition behaves for every possible combination of the truth values of its components… and discover interesting things

Question 4

How can you use truth tables to prove logical equivalence?

Answer 4

• Two complex propositions are “logically equivalent” when they have the same truth value for every possible combination of truth values of their simple components
• Procedure: Complete the truth table for each complex proposition, and then compare.
• The pattern of truth values under the “main connective” of each proposition is the same  the two propositions are logically equivalent.

Question 5

How do you use truth tables to prove validity?

Answer 5

Process: Construct the truth tables, and inspect the relevant rows
Question: is it possible for an argument to have true premises and a false conclusion at the same time?7
Affirming the Antecedent: no
Denying the Antecedent: Yes
Chain argument: No