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Let's stop tripping over the term "logic," shall we? IF it gets cold when it rains, AND it is raining, THEREFORE it will be cold. That's "logic." Technically it's "Boolean algebra" but FFS, it's also "logic." "Algebra" doesn't mean "symbols." It means "solve for the unknown." "Solving for the unknown" is a daily activity for people who think. Not only that, but the argument isn't "let's stop teaching reasoning" it's "let's stop teaching ALGEBRA" which, by your logic, we don't need. And, simply put, you're wrong. There aren't that many more ways I can illustrate the wrongness of your thinking because it requires a basic understanding of symbolic logic and I'm guessing you suck at algebra.
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