Although the word is often used in wider senses, philosophers normally use the word "fallacy" to apply to certain arguments: an argument can be a fallacy, but a statement or a belief cannot. Sometimes, "fallacy" is defined as "invalid argument", but unfortunately this is both too broad and too narrow. It is too broad because not all invalid arguments can reasonably be called fallacies. It is too narrow because some of the forms of argument traditionally called fallacies are in fact valid arguments (see below on begging the question).
A proof is an argument that shows that something is true. Consequently, a proof must be a sound argument: it must have true premises, and it must be valid. Is that sufficient for an argument to be a proof? Most philosophers would say no. Showing that something is true is showing it to someone. A proof works by beginning with premises that are not only true but also obvious, or convincing, or of the sort that anyone would accept, or fit some such characterization. It then shows its conclusion to be true by showing that it follows from these premises. So, one criticism of a proof could be that nobody who did not already accept its conclusion would be likely to accept its premises. This
A refutation is a kind of proof. To refute an argument is to prove that it is invalid. To refute a proposition is to prove that it is not true. This is not at all the same thing as denying that an argument is valid or that a statement is true. Anyone can deny anything: I can deny, for instance, that the sun rises about every 24 hours or that 2 + 2 = 4. I'd be mistaken in both cases, but I can still do it. However, I don't know how to refute either of them: you can't refute something if it's true. (This has begun to get a little fuzzy in popular usage, where people sometimes use "refute" as if it just meant "say it isn't so").
Since refuting something is proving it isn't true, a refutation has to be an argument. If a refutation really is a refutation, then it must be a proof of the denial of what it refutes.
Against this background, the best way to define a fallacy is probably this: something that appears to be a proof but actually isn't. There are several ways an argument can fail to be a proof: it might be invalid, or it might have a false premise, or its premises might actually not be appropriate for proving its conclusion. What makes something a fallacy is not just that it's a failed proof, however: fallacies are arguments that appear to be proofs. Appearance is ultimately subjective, but there are certain patterns of argument that many people find persuasive even though they are deficient. These are the ones people
The oldest treatises we have on logic are Aristotle's Topics and On Sophistical Refutations. The second of these (which is really just a continuation of the first) is about what Aristotle called "sophistical" arguments, an expression we could translate tolerably well as "fallacies." Aristotle describes about thirteen patterns of fallacious argument, to each of which he gives a name. His terminology has been extraordinarily durable and has persisted into modern texts on fallacies with the names usually translated into Latin, which of course makes perfect sense since Aristotle spoke Greek. Actually, there's a good deal about these traditional classifications that does not translate well, and modern texts often work very hard to find a useful way of understanding something that fits much better in Aristotle's Greek (look up "fallacy of accent" for a good example). Since the traditional terminology is widely used in criticizing arguments (especially by philosophers), it's important to be familiar with it. Below is an extremely brief set of notes.
Equivocation is using the same word or expression with different meanings in different places. To be more precise, it's a fallacy when an argument relies on this going undetected. Textbooks tend to illustrate this fallacy with silly examples that nobody is ever likely to be fooled by: "Lawyers are experts on laws. Therefore, lawyers are experts on the laws of physics." In real life, equivocation is often more subtle and difficult to detect. Consider, for instance, arguments about abortion, which often center on the question, "What is a human being?" Is anything that is human and alive a human being? If so, then what about a human heart or kidney that has been removed from a cadaver for transplant into another person: is it alive, and is it human? A great many philosophical debates
Amphiboly is an ambiguity of syntax, that is, an ambiguity about how the grammar of a sentence is to be understood (as opposed to equivocation, which could be seen as an ambiguity of semantics, that is, an ambiguity about
An ad hominem argument ("against the person" in Latin) is an attack on the person who presented an argument instead of on the argument itself. The classic form of this fallacy treats a proposition, or a viewpoint, as somehow compromised just because of something disagreeable about the person who has stated it: "Smith's views on philosophy should not be taken seriously since he treats his children terribly, has failed in business seven times, is grossly unkempt, and is addicted to betel nuts." Or perhaps something like this:
Wittgenstein was a very unpleasant person to his students, and he was really quite brutal as a schoolteacher in Austria. Therefore, we shouldn't take his philosophical views seriously.
In many cases, ad hominem arguments take on a more unpleasant character by appealing to their audience's racial, religious, etc., prejudices. I'll let you imagine your own examples.
An argument from authority is arguing that a claim is true because a certain person with authority says it is. In some cases, there is nothing at all wrong with taking someone as an authority for something: if I tell you that I have a serious pain in my left foot, then that's a very good reason for thinking that the proposition "Smith has a serious pain in his left foot" is true. More generally, there are at least two classes of arguments from authorities that are not only quite respectable but also probably unavoidable. The first concerns testimony: we rely on other people's reports of what they have seen, heard, read, etc., and believe things just because people have said them. Of course, this is a limited kind of authority. I can be an authority about what I saw while looking out of my window last night, but hardly of what you saw looking out of your window last Thursday while I was unconscious. The second kind of case is expert opinion: we often believe things just because a doctor, or a mechanic, or a historian has told us so. If relying on the opinions of others in cases like this were always unreasonable, then we'd have a hard time extending our knowledge beyond the present experience of our own lifetimes.
When people criticize arguments as bad arguments from authority, they generally have in mind a case in which someone is supposing that whatever a certain person says is true: "Well, Quine says that reference is always indeterminate, and his word's good enough for me." As you might expect, whether an argument from an authority is a good one in philosophy is liable to become the subject of a philosophical argument itself. However, philosophers would probably agree at least on this: when it comes to philosophical arguments, there are no philosophical authorities.
Generalization is another term for inductive arguments: drawing a conclusion about all the members of a class on the basis of one or more instances. Such arguments are the lifeblood of empirical science and of a great deal of our everyday knowledge of the world. Philosophers have put considerable effort into understanding how generalizations work. Which generalizations are the hasty ones? There are some easy cases we can spot quickly: "All my friends use Microsoft Windows; therefore, all people use Microsoft Windows." "Everybody I know is a Republican; therefore, almost everyone is a Republican." Some are harder: "All the swans anyone I know about has ever seen are white; therefore, all swans are white." Stated in Europe in the seventeenth century, this would have been an extremely strong argument. However, as Europeans discovered when they got to Australia, there are black swans. Was it a "hasty generalizaton" for Europeans to conclude in 1600 that all swans are white?
The full name of this fallacy in Latin is post hoc, ergo propter hoc: "after this, therefore because of this." A common source of such arguments is medical foklore: "I had an awful case of hives and I took Dr. Feelgood's magic homeopathic remedy and they went away, so the stuff must work." However, there's a major philosophical issue lurking here. What more do you need to conclude that A causes B beyond the fact that B happens after A? Would it be enough that whenever something sufficiently like A happens, then a thing like B happens? Or is there something more to cause than that? David Hume rather famously argued that there isn't anything more to causality than this "constant conjunction." To stop a long argument before it gets started, I will just say that in philosophical contexts, whether a given argument really is an instance of this fallacy can be a subject of debate.
A straw man is a dummy argument: an argument that no one actually supports. The criticism "You're attacking a straw man" usually means, "The argument you're attacking isn't actually one that anyone defends." Generally, a straw man is an argument that is easy to attack (hence the name "straw man"). Thus, attacking a straw man is deceptive because it misrepresents someone else's position by turning it into something easily refuted. To put that another way, attacking a straw man comes close to a form of lying, since it amounts to saying, "Here's your argument, and here's how to refute it," when in fact this actually isn't your argument. Philosophers, of course, often disagree quite strongly about the way to interpret the arguments of other philosphers, and so there's another fertile ground for philosophical disagreement.
This fallacy is an invalid form of argument:
If you rely on the validity of this invalid form of argument to draw a conclusion, then you've committed the fallacy of affirming the consequent. Does anyone ever do that? "If God exists, then the world is wonderfully designed. But the world is wonderfully designed. Therefore, God exists." Stated in this way, we have what appears to be a fallacy. However, there is a related kind of argument known as argument to the best explanation: "Q; if it were the case that P, then Q would follow; therefore, P (since that would explain the fact that P)." This type of argument has much in common with the structure of scientific explanations, on some interpretations. In any particular case, whether it's a fallacy or a good argument is liable to depend on how it's interpreted, and that in turn is often a matter for philosophical debate.
This fallacy is an invalid form of argument:
If you actually find someone arguing in this way, then you've caught them in a fallacy. However, conditional sentences in English are often more than they seem. Sometimes, "If A then B" may have the force of "If A, then B because of A." It is not quite as implausible to argue thus: "A is the cause of B; but not A; therefore, not B."
Begging the question is assuming the conclusion of an argument as one of the premises. Logically speaking, this is not an invalid form of argument: if the premises are all true and the conclusion is one of the premises, then obviously the conclusion must be true. The problem with begging the question is rather that it is a bad form of proof. The purpose of a proof is to persuade you, on the basis of what you already accept, that something else is true. If one of the things I want to use in order to convince you that P is true is the proposition P itself, then I'm not going to get very far: why would you accept P, given that you don't already acceptP?
When someone charges someone else with begging the question, it is almost always a charge that an argument is a concealed or implicit case of begging the question. Here is an example:
Obviously, Smith is an idiot. After all, he's obviously as dumb as a bag of hammers.
However much this sounds like a real argument, its conclusion is little more than a restatement of its lone premise.
The term circular argument is sometimes used synonymously with "begging the question," but it is sometimes used for a more complex process: a sequence of arguments in which the first argument takes some proposition P as a premise in arguing for a conclusion and the second takes this conclusion as a premise in arguing for the original premise P:
In this argument, the premise P is used as a starting point in a series of arguments culminating in a proof of P itself. Arguably, this is an extended form of begging the question. Of course, when philosophy enters the picture, things are not quite so simple. If the circle is very big, might that make a difference? in epistemology, coherence theorists can be seen as holding just that view.
The terms "begging the question" and "circular argument" go back to Aristotle, and even he probably didn't invent them (he treats them as terms already familiar to his readership: see Prior Analytics II.15-17). The original expression for the phrase "begging the question" meant literally "asking for the initial proposition" and referred to a kind of debate in which one person undertook to defend a thesis by answering questions and the other person undertook to refute that thesis by asking questions and deriving a contradiction from the answers. In that game, "the initial proposition" is the thesis that the answerer has to defend and the questioner has to attack. If the thesis is P and the questioner were to ask as a question, "Do you agree that P?" then that would be "asking for the initial thing." This is a pointless move, since the whole aim of the debate is to disprove P. Now, in older English, to beg is to ask. The Latin quaestio means "search" (from which we get English "quest"); an archaic sense of "question" is "thing sought". And that is what "begging the question" means: "asking for the thing sought". I hope this makes sense of this rather bizarre expression. "Circular argument" also appears in Aristotle (see Prior Analytics II.5-7, Posterior Analytics I.3), and Aristotle argues that it amounts to just begging the question.