Logic

How does one _prove_ that an informal fallacy is a fallacy (instead of just waving a Latin name?)

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How do you show of any bad pattern of reasoning that it is indeed unreliable (whether or not that kind of reasoning is called a fallacy or is dignified with a Latin name)?

By coming up with some example arguments that rely on that kind of reasoning yet are evidently and uncontroversially terrible arguments. Such counterexamples reveal that kind of reasoning to be hopelessly unreliable.

Suppose that, when the wraps are off, someone's argument relies on the pattern if A, then B; B; therefore A. That's plainly an unreliable pattern -- just think of e.g. the instance "If Jo is a woman, Jo is human; Jo is human; therefore Jo is a woman"! So the original argument is fallacious.

Or suppose that, when the wraps are off, someone's argument moves from the premisses that Xs are not A and a Y is constituted of nothing but Xs to the conclusion that a Y is not A. Then that again is plainly an unreliable pattern -- just think of e.g. theinstance "H2O molecules aren't wet; a puddle of water is constituted of nothing but H2O molecules, so a puddle of water is not wet"!

The first bad pattern of reasoning exemplifies the so-called formal fallacy of "affirming the consequence"; the second one would be traditionally classed as a version of the informal fallacy of division. They are fallacies because they are unreliable inference patterns. And we can see them to be unreliable by coming up with obvious counterexamples to their reliability.

Peter's quite right, of course, but I think there's a bit more we can say. What makes a good pattern of reasoning good (logically good, that is) is whether it preserves truth, that is, whether it only leads from true premises to true conclusions and never from true premises to false conclusions. (If it starts with false premises, that's another matter altogether.) And the best way to tell whether an argument pattern will be truth-preserving is to do a truth-table analysis of it: Assume (that is, make believe) that the premises are true, then figure out what the truth values of the atomic propositions are, and, finally, figure out what the truth value of the conclusion is. If, whenever you assume that the premises are true, it turns out that the conclusion has to be true, then you know the argument is a logically good one; otherwise, it is a "fallacy", i.e., a logically bad argument. See any introductory logic text for the details (I understand that Peter has a very nice one :-)

There are a couple of wrinkles with this: First, some logically good arguments are pretty bad because their premises are, in fact, false. Those arguments are factually bad. The best kind of argument is one that is both logically good ("valid") and also factually good; if it's both, then it's said to be "sound".

Second, some well-known fallacies are logically good! The best example of this is "begging the question" or "circular arguments". They have the form "p; therefore, p". They may be logically good, but they are of no practical use in convincing anyone of the truth of p.

But two qualifications to William's comments. First, not all arguments are susceptible to truth-table analysis. (For example: every horse is an animal. Therefore, every horse's head is an animal's head.) Second, there are plenty of good arguments (inductive arguments, for short) whose premises don't strictly imply their conclusions, but that make their conclusions probable given the premises. At least sometimes, informal fallacies aspire to inductive rather than deductive goodness, and so showing that the conclusion doesn't strictly follow from the premises is beside the point.

Peter's point still applies however: we can show that such arguments are bad by showing that they have the same form as arguments that are patently bad. Here's a patently bad argument: most pets are mammals. Kiki is a mammal, and so (probably) Kiki is a pet. Any argument with this form is bad, even though the aim isn't to show that the conclusion strictly follow from the premises.

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