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> For example, using "appeal to authority", it is logically true that just because a group of Fields Medalists think your proof is wrong, does not necessarily m

> For example, using "appeal to authority", it is logically true that just because a group of Fields Medalists think your proof is wrong, does not necessarily mean that your proof is wrong. But in practice, there is a very high chance you are in the wrong. The proof is wrong not because the status of those Field Medalists but instead because of the content of their argument. That's all that the appeal to authority is saying. I'd agree that it's a mistake to relate the existence of a logical fallacies to the probability of a statement being correct. Instead, it only gives information about whether the reasoning of the statement is on solid ground.

threatofrain 6y ago
But what kind of reasoning is on solid ground when we’re talking about logic... outside of math? Saying logic here is almost lying to ourselves because we’re not expecting anyone to create logical chains of reasoning. Do mathematicians even use logic as a reasoning tool, as opposed to a proving tool?
- bitshiftfaced 6y ago
  Isn't that exactly the question that informal logical fallacies seek to address? I don't think you can just throw away the word "logic" like that. We try to make arguments using deduction and inference, so there is a logical structure behind them. It's just that it isn't as well-defined and doesn't have the mathematical rigor of formal logic.
  - threatofrain 6y ago
    Logic a fundamentally different process of intellectual productivity, which is why mathematicians don’t see proving and reasoning as the same thing. Formal methods weren't even widespread until late in mathematical history, yet somehow we had mathematical productivity. Mathematicians can scarcely describe their own thinking process, and proving is often the last step to mathematical reasoning. Talking about logical fallacy in ordinary conversation is backward.

threatofrain 6y ago

But what kind of reasoning is on solid ground when we’re talking about logic... outside of math? Saying logic here is almost lying to ourselves because we’re not expecting anyone to create logical chains of reasoning. Do mathematicians even use logic as a reasoning tool, as opposed to a proving tool?

bitshiftfaced 6y ago
Isn't that exactly the question that informal logical fallacies seek to address? I don't think you can just throw away the word "logic" like that. We try to make arguments using deduction and inference, so there is a logical structure behind them. It's just that it isn't as well-defined and doesn't have the mathematical rigor of formal logic.
- threatofrain 6y ago
  Logic a fundamentally different process of intellectual productivity, which is why mathematicians don’t see proving and reasoning as the same thing. Formal methods weren't even widespread until late in mathematical history, yet somehow we had mathematical productivity. Mathematicians can scarcely describe their own thinking process, and proving is often the last step to mathematical reasoning. Talking about logical fallacy in ordinary conversation is backward.