A. Foundations of Knowing
A.2 Logic and Formal Reasoning
Course description
Begin with the syllogism, then move to propositional and predicate logic proper. forall x is the main text: free, well-exercised, and supplied with solutions, with Barwise and Etchemendy's Language, Proof and Logic as an alternative treatment of the same ground. Cover basic set theory and relations alongside it, since both feed directly into B.1's proof unit; study the two together, not logic first and proof later. Practice spotting fallacies in real arguments; memorizing their Latin names is optional. Two traditions outside the usual syllabus deserve real time: the Mohist canons developed an independent logical vocabulary around disputation (bian), built for settling disagreements rather than for pure deduction; and the Nyaya five-membered inference schema requires an example step inside what looks like a deductive argument, which raises the question of how deduction and induction actually relate in a way Western syllogistic tends to skip. Aristotle's Organon is worth a glance for grounding, but a modern text teaches the material faster.
Checkpoints
Each checkpoint is tagged with the stage of the cycle it tests.| Stage | Checkpoint | Attempts |
|---|---|---|
formalism | Translate twenty natural-language arguments into predicate logic and test them with truth tables or natural deduction, using the forall x exercise sets and checking your answers against the solutions. | Post the first attempt |
skepticism | Construct a valid argument with a false conclusion and explain why validity alone never guarantees truth. | Post the first attempt |
abstraction | Explain why the Nyaya inference schema includes an example step, and what that requirement implies about the boundary between deduction and induction. | Post the first attempt |
intuition | Find and name the fallacy in five arguments taken from recent opinion columns, without consulting a checklist while you do it. | Post the first attempt |