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Hi, I'm a biology student who often uses biology as a framework for understanding thought. I've come to a really tough crossroads of thought. What differentiates cognitive biases from logical fallacies?

The difference between the cognitive biases and the logical fallacies is that the biases can be taken to be common built-in tendencies to error of individual judgements , whereas the fallacies, both formal and non-formal (so-called "informal", badly named because "informal" actually means "casual" or "unofficial" or "relaxed") are types of argument . The point is that the biases can be said to have causes, and are hence of psychological but not logical interest, whereas the fallacies do not have causes (though the making of a fallacy on a particular occasion may have) and the reverse is true. There is more to be said, of course, because a psychologist might take an interest in the fallacies.

I would really like to know what logic is. The Stanford Encyclopedia of Philosophy has TOO MANY articles on logic for someone like me. Let me list most of them: action logic, algebraic propositional logic, classical logic, combinatory logic, combining logic, connexive logic, deontic logic, dependence logic, dialogical logic, dynamic epistemic logic, epistemic logic, free logic, fuzzy logic, hybrid logic, independence friendly logic, inductive logic, infinitary logic, informal logic, intensional logic, intuitionistic logic, justification logic, linear logic, logic of belief revision, logic of conditionals, logical consequence, logical pluralism, logical truth., many-valued logic, modal logic, non-monotonic logic, normative status of logic, paraconsistent logic, propositional dynamic logic, provability logic, relevance logic, second-order and higher-order logic, substructural logic, temporal logic. I have started reading some of these articles, but I still didn't find an answer for my basic question. In...

There are "forms" of thinking and reasoning and arguing that do something very specific. They guarantee that if the premises of your thinking and reasoning and arguing are true, then so is your conclusion. These "argument forms", as we can call them, are said to be "valid". Logic is the study of these forms, and the methods used to distinguish them from invalid forms. An example? Well, what about De Morgan's theorems, one of which states not-(p AND q) is the same thing as (not-p OR not-q). This is valid, and it is worth studying, even for its intrinsic interest. And if you do study it, what you are studying is logic, or a part of it.

Is there a way to prove that logic works? It seems that the only two methods for doing this would be to use a logical proof –which would be incorporating an assumed answer into the question– or to use some system other than logic –thus proving that sometimes logic does not work.

Aristotle gives a nice account of why we must have something "definite in our thinking" and not contradictions in Metaphysics IV. In order to say of something that it is or can be both F and not-F, he writes, we must have successfully identified that thing as the thing that is or can be both F and not-F. But we are in no position to do that if the something both is and is not the something we are talking about, or trying to talk about! So we do not have to abandon the piece of logic, the principle of non-contradiction, in one form, at least, which states that opposite things cannot significantly be said of the same thing. Here, at least, it seems that logic does not break down on the basis of the interesting argument that you gave.