Logic

Properties as Axioms or Theorems

To close out this series that started with postulates and theorems in geometry, let’s look at different kinds of facts elsewhere in math. What is commonly called a postulate in geometry is typically an axiom in other fields (or in more modern geometry); but what about those things we call properties (in, say, algebra)?

Subtleties in a Logic Puzzle

(Archive Question of the Week) Logic puzzles can exercise our ability to reason carefully. Interestingly, the use of formal logic in doing so can actually get in our way, because such puzzles often have subtleties in their wording that are hard to capture in formal logic. Examining our thinking carefully can help us see wrong …

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Empty Sets and Vacuous Truth

I’m going to start this post with a simple question about the empty set, and gradually dive deeper. There will be connections here to previous discussions of conditional statements in logic.