Using questions to introduce a topic
Peer instruction questions can also be used to introduce students to a topic or problem for the first time, rather than testing them on something they have just learned. You might illustrate a problem or introduce a topic by asking a sequence of leading questions that allows students to discover the problem or topic for themselves.
Here, for example, is a sequence of questions used in a logic lecture to introduce the topic of vagueness:
Suppose we have the following colour strip, shading from red to yellow. Each proposition ri means "patch i looks red to me'.
1. What would be a reasonable assignment to r1 and r10?
A. r1 = T, r10 = F
B. r1 = F, r10 = T
C. r1 = T, r10 = T
D. r1 = F, r10 = T
2. Which of the following represents the claim that adjacent patches (like r1 and r2, r4 and r5) are indistinguishable in colour?
A. For some patch x, rx ⊃ rx+1
B. For every patch x, rx ⊃ ry for all y > x
C. For every patch x, rx ⊃ rx+1
D. For some patch i, rx & ~rx+1
So if adjacent patches in this strip are indistinguishable, we would have the following situation:
3. Is this assignment of truth values possible, assuming that ⊃ is the truth-functional, material conditional of classical propositional logic? That is, is there any consistent way assigning Ts and Fs to the remaining propositions, assuming the standard truth-table for ⊃?
A. No, it is impossible.
B. Yes, it is possible.
The sorites argument has the following form:
r1 ⊃ r2
r2 ⊃ r3
r8 ⊃ r9
r9 ⊃ r10
We have just seen that according to classical propositional logic, there is no way of making all the premises of this argument true and the conclusion false. What follows about the validity of the argument, according to classical propositional logic?
A. The argument is valid in classical propositional logic.
B. The argument is invalid in classical propositional logic.
C. It is neither valid nor invalid in classical propositional logic.
D. Nothing follows about the validity or invalidity of the argument from the given information.