Consider these two statements: 1. All ravens are black. 2. If something isn't black, then it's not a raven. Though these two statements appear to be saying somewhat different things, in fact, they are logically equivalent: Either they're both true, or else they're both false. We can't make exactly one of them true. And this is a fact about logic. Now let's see an example of a paradox: At a desert oasis, A and B both separately undertake plots to try to kill C. A poisons his canteen, and later B punches a hole in it. C dies of thirst. Who killed him? At the trial, A argues that she can't possibly be the killer, for C never drank the poison. B argues that it couldn't have been him either, for B only deprived C of poisoned water. Both of their arguments seem pretty good, but C was surely killed, and someone should be held accountable. But, whom? The above story is just a simple example, but it illustrates nicely that even very innocent-seeming propositions can sometimes lead us into trouble. Part of this course will be an opportunity to investigate some of the most mind-bending and perplexing paradoxes that have ever been discovered, and we will try our hardest to solve them together.
The logic part of the course will be similar to an accelerated math class. We will cover new material every day, and there will be problem sets every night. In terms of content, we will cover much of the same material that a college-level introduction to logic course would cover. We will start by formally defining the core concepts (propositions, truth/falsity) as well as the logical operators (conjunction, disjunction, negation, the conditional). We will use truth tables to examine how these operators affect the truth of sentences that contain them. We will work our way toward definitions of satisfiability, implication, and validity. In the second half of the course, we will introduce predicates and quantifiers into our system in order to study first-order logic in all of its depth and rigor.
During this course, you will learn:
• How to read and understand the formal logic that acts as the basis for many academic disciplines.
• How to construct a proof in that formal logic.
• How that formal logic may be used both to generate and to understand some of the most interesting problems in Philosophy.
Algebra II or beyond is recommended for success in this course
Online sections of Pre-College courses are offered in one of the following modalities: Asynchronous, Mostly asynchronous, or Blended. Please review full information regarding the experience here.