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Good Math by Mark C. Chu-Carroll

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What Is Logic, Really?

A logic is a system for mechanical reasoning. It’s a system that allows you to express an argument in a neutral symbolic form and then use that symbolic form to determine whether or not the argument is valid. What matters in logic isn’t meaning; instead it’s whether or not the steps of reasoning that make up the argument follow from one another. It’s a very powerful tool, specifically because it ignores meaning when it’s doing reasoning. Logic can’t be biased toward one side of an argument, because logic neither knows nor cares what the argument means!

To make that kind of unbiased reasoning work, a logic needs to be structured in a rigorous, formal way. That formality shows us that the reasoning (formally called inference ...

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