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Crux comments on Fallacymania: party game where you notice fallacies in arguments - Less Wrong
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What's the difference? I don't see a distinction between the phrases "faulty reasoning" and "mistake in thinking".
Reasoning is when you tell your arguments to another person. Thinking is when you make decisions for yourself.
I now see what you mean by fallacies being X (errors in argumentation) and cognitive biases Y (errors in thinking).
However, you're using an idiosyncratic definition of the word "reasoning", and I would advise you to update your understanding so you reduce the chance of confusing more people in the future. "Reasoning" in many cases refers to internal thinking, as you can see explained here.
Ok, thank you.