The Path of a Critical Thinker — Part 3

I’d like to clarify exactly what being a “critical thinker” means. A critical thinker is, at their core, a thinker who dares to question. A critical thinker is never entirely satisfied with anything less than absolute knowledge, and thus always holds their beliefs with an open hand, ready to discard them when evidence is presented that points to something better.

A critical thinker never stops questioning, never says, “well, I’ve seen all I need to see to convince me.” A critical thinker strives to understand logic, and base one’s life on reason and the pursuit of truth. A critical thinker is not free from bias, but recognizes the biases each one of us possesses, and wrestles to break free from their influence in order to draw well-reasoned conclusions and solutions to the pertinent issues and problems of the day.

• The Rules of Inference
I want to avoid turning this into an in-depth logic tutorial, but I need to stress the importance of understanding the basics of logic. It’s one thing to say that a valid argument “has proper form,” and another thing to know what “proper form” actually is.

A rule of inference is a rule by means of which the conclusion of an argument is derived from the premises. There are certain rules in logic that demonstrate the proper form a valid argument can assume. The letters used (p and q) in the descriptions below represent statements or components of a larger proposition. I have also decided against using symbols here for the sake of simplicity; thus, instead of “p ⊃ q” (for example), the premise is stated as “if p, then q.” Please keep in mind that this is merely an introduction, meant to guide the reader to further independent study. There is much more to learn:

Rules of Inference

1. Modus ponens
If p, then q.
p.
Therefore, q.

Example:
P1: If I sit out in the sun for too long, I will get a sunburn.
P2: I sat out in the sun for too long.
∴ I got a sunburn.
2. Modus tollens
If p, then q.
Not q.
Therefore, not p.

Example:
P1: If I sit out in the sun for too long, I will get a sunburn.
P2: I didn’t get a sunburn.
∴ I didn’t sit out in the sun for too long.
3. Hypothetical syllogism
If p, then q.
If q, then r.
Therefore, if p, then r.

Example:
P1: If I sit out in the sun for too long, then I will get a sunburn.
P2: If I get a sunburn, then I can’t go to Karate class tonight.
∴ If I sit out in the sun for too long, then I can’t go to Karate class tonight.
4. Disjunctive syllogism
p or q.
Not p.
Therefore, q.

Example:
P1: Jenni is either staying home tonight or she is going out with friends.
P2: Jenni didn’t go out with friends.
∴ Jenni stayed home tonight.
5. Constructive dilemma
If p, then q, and if r, then s.
p or r
Therefore, q or s.

Example:
P1: If Joe is at Karate class tonight, then he is happy.
P2: If Joe is working late tonight, then he is sad.
P3: Joe is either at Karate class tonight, or he’s working late tonight.
∴ Joe is either happy or sad tonight.

6. Simplification
p and q.
Therefore, p.

Example:
P1: I have an apple and a banana.
∴ I have an apple

7. Conjunction
p.
q.
Therefore, p and q.

Example:
P1: I have an apple.
P2: I have a banana.
∴ I have an apple and a banana.

8. Addition
p.
Therefore, p or q.

Example:
P1: I have an apple.
∴ I have an apple, or I have a banana.

• Inclusive Or vs. Exclusive Or

The rule of Addition is better understood when we know the distinction between the inclusive and exclusive use of the logical operator “or.”

“Exclusive or” means “either p or q is true, but both together are not true.”

Example: “Either the door is open or the door is shut.” The door can’t be both open and shut at the same time.

Another example of exclusive or: The server asks, “Would you like coffee or tea?”

But when the server asks, “Would you like cream or sugar?” there is an example of inclusive or. because you can get one or the other, or both.

(Yes, technically you can order both coffee and tea at the restaurant, but the “or” in that sentence is implied to be exclusive since most people only order one drink.)

“Inclusive or” means the statement “p or q” is true if just one of the two components is true. If I have an apple, then the statement “Either I have an apple or I have a banana” is logically true. The statement “I have either cream or sugar in my coffee” is true if I have either cream or sugar or both in my coffee. If I chose neither cream nor sugar, then the statement would be false.