There are many ways to classify informal logical fallacies. I prefer listing the conditions for a good or cogent argument and then classifying logical fallacies according to the failure to meet these conditions.
Every argument makes some assumptions. A cogent argument makes only warranted assumptions, i.e., its assumptions are not questionable or false. Fallacies of assumption make up one type of logical fallacy. One of the most common fallacies of assumption is called begging the question. Here the arguer assumes what he claims to be proving. Most arguments for psi commit this fallacy. For example, many believers in psi point to the ganzfeld experiments as proof of paranormal activity. They note that a .25 success rate is predicted by chance but Honorton had some success rates of .34. One defender of psi claims that the odds of getting 34% correct in these experiments was a million billion to one. That may be true but one is begging the question to ascribe the amazing statistic to paranormal powers. It could be evidence of psychic activity but there might be some other explanation as well. The amazing statistic doesn't prove what caused it. The fact that the experimenter is trying to find proof of psi isn't relevant. If someone else did the same experiment but claimed to be trying to find proof that angels, dark matter, or aliens were communicating directly to some minds, that would not be relevant to what was actually the cause of the amazing statistic. The experimenters are simply assuming that any amazing stat they get is due to something paranormal.
Not all fallacies of assumption are fatal. Some cogent arguments might make one or two questionable or false assumptions, but still have enough good evidence to support their conclusions. Some, like the gambler's fallacy, are fatal, however. The gambler's fallacy is the false assumption that the odds for something with a fixed probability increase or decrease depending on recent occurrences. If black has come up four times in a row, some people will bet on red because they think it more likely that red will come up than black on the next roll. It isn't. The odds never change for red or black. (They're always a little under 50/50 because of the two green numbers, 0 and 00.)
Another quality of a cogent argument is that the premises are relevant to supporting their conclusions. Providing irrelevant reasons for your conclusion need not be fatal, however, provided you have sufficient relevant evidence to support your conclusion. However, if all the reasons you give to support your conclusion are irrelevant then your reasoning is said to be a non sequitur. For example, poor women can't afford abortions, so the government should pay for them is a non sequitur. It is true that a poor woman can't afford an abortion but it doesn't follow from that fact that the government or anyone else should pay for it. Poor men can't afford a new car, but it doesn't follow from that that the government ought to provide them with a new car. The poverty of women or men would become relevant if first it were established that everybody has a right to an abortion or a new car and that the government must make sure they get anything they have a right to, if they request it.
The divine fallacy or the argument from incredulity is a type of argument to ignorance. If others can't disprove a claim, that is irrelevant to its truth. Arguments from ignorance put forth the irrelevant fact that something can't be done or proved, so some other claim must be true. The truth of any claim depends on the evidence in support of it; claims that the evidence doesn't prove a claim is true is irrelevant to whether some other claim is true. Here are a few examples of the divine fallacy. I can't figure this out, so a god must have done it. Or, This is amazing; therefore, a god did it. Or, I can't think of any other explanation; therefore, a god did it. Or, This is just too weird; so, a god is behind it.
One of the more common fallacies of relevance is the ad hominem, an attack on the one making the argument rather than an attack on the argument. One of the most frequent types of ad hominem attack is to attack the person's motives rather than his evidence or his reasoning. For example, when an opponent refuses to agree with some point that is essential to your argument, you call him an "antitheist" or "obtuse." Personal characteristics or motives are irrelevant to whether a person's premises adequately support her conclusions. Good people sometimes make bad arguments and bad people sometimes make good arguments. People with good motives can make bad arguments and people with evil motives can make good arguments.
Other examples of irrelevant reasoning are the ad populum fallacy, the irrelevant appeal to tradition, and the irrelevant appeal to authority. The popularity or longevity of a belief is irrelevant to its truth. The integrity and expertise or authority of those holding a belief are irrelevant to its truth.
A third quality of a cogent argument is sometimes called the completeness requirement: A cogent argument should include all the relevant evidence. In real life, it is often impossible to know all the relevant evidence, so we should strive not to omit any relevant evidence that we are aware of and we should try to discover as much relevant evidence as the argument deserves. We need to be much more diligent about satisfying the completeness requirement when dealing with, say, a criminal trial than when dealing with a decision as to what car to buy or what color pencil should be used for a school project. There is a natural tendency, however, to be selective in our search for evidence. The confirmation bias may drive us to seek only evidence that supports what we already believe or want to believe.
Selective thinking is the basis for most beliefs in the psychic powers of so-called mind readers and mediums. It is also the basis for many, if not most, occult and pseudoscientific beliefs. Selective thinking is essential to the arguments of defenders of untested and unproven remedies. Suppressing or omitting relevant evidence is obviously not fatal to the persuasiveness of an argument, but it is fatal to its cogency. The regressive fallacy is an example of a fallacy of omission. The regressive fallacy is the failure to take into account natural and inevitable fluctuations when ascribing causes to events. The false dilemma (or false dichotomy), whereby one restricts consideration of reasonable alternatives, is also a fallacy of omission. Sometimes this fallacy is called the black or white fallacy or the either-or fallacy: one poses what looks like a true dilemma--I must pick one or the other--when, in fact, there are other viable alternatives.
While at TAM5, the James Randi Educational Foundation's annual reasonfest, I was approached by André Kole, who introduced himself as a magician and longtime friend of Randi's. I was there as part of workshop on critical thinking. Kole asked me if I would read a short pamphlet he'd written and give him my opinion of his arguments. I looked at the title of his pamphlet and told him I'd read it but I could see that the main problem is that he's arguing a false dichotomy. The title of his tract is Jesus: Magician or God? (Kole is a "Christian magician" who does "faith-based illusions."*) I told him without reading his tract that there were other possibilities like madman, fraud, and myth. My own view is that the character described in the four gospels accepted as "authentic" by most Christians is a mythical character. A man named Jesus existed but the stories about his miracles are either exaggerations or distortions of actual, non-miraculous events or confabulations that incorporated myths from other traditions (like the Mithraic tradition). He may have been a faith healer like Benny Hinn or Peter Popov.
I read the tract and told Kole that he did a good job in arguing that Jesus was not a magician, but that it didn't follow that just because he wasn't a magician he was therefore a god. I really had no interest in arguing with Kole about the Bible or the alleged miracles, but he asked me what I thought of his argument and I told him. If he wants to prove Jesus was a god, he has to do more than prove that he wasn't a magician.
Kole was not satisfied with my appraisal and asked me to explain how the Bible could be so accurate about some range of prophecies he rattled off that I'd never heard of. His view is that the Bible makes many claims that he doesn't believe can be explained except by accepting that they came from a god. This is begging the question and a variant of the divine fallacy: since I can't see any other way of explaining this, a god must have done it.
A fourth quality of a cogent argument is fairness. A cogent argument doesn't distort evidence nor does it exaggerate or undervalue the strength of specific data. The straw man fallacy violates the principle of fairness. In a straw man argument, one attacks a distorted version of another person's argument. Anyone using a straw man argument is refuting a position of his own creation, not the position of someone else. The refutation, however, may appear to be a good one to someone unfamiliar with the original argument.
One of the most frequent fallacies of reasoning occurs by giving improper weight to evidence. While all relevant evidence to a conclusion should be considered, each piece of evidence is not equal in significance to every other piece. One should not elevate a relatively minor piece of evidence to the status of linchpin in an argument, nor should one treat stronger evidence that is contrary to your view as if it were minor. Each piece of evidence has to be properly weighted and then the overall weight of the evidence must be evaluated.
A fifth quality of cogent reasoning is clarity. Some fallacies are due to ambiguity, such as the fallacy of equivocation: shifting the meaning of a key expression in an argument. For example, the following argument uses 'accident' first in the sense of 'not created' and then in the sense of 'chance event.'
Since you don't believe you were created by a god then you must believe you are just an accident. Therefore, all your thoughts and actions are accidents, including your disbelief in any god.
Finally, a cogent argument provides a sufficient amount of evidence to support its conclusion to whatever degree of probability is asserted. Failure to provide sufficient evidence is to commit the fallacy of hasty conclusion. One type of hasty conclusion that occurs quite frequently in the production of superstitious beliefs and beliefs in the paranormal is the post hoc fallacy, the notion that because one thing happened after another the first must have caused the second. You need more evidence to prove precognition than that your aunt Sady died the night after you had a dream about her dying. Another causal fallacy argues from the fact that two variables are correlated, they are causally related. You need more evidence than a strong correlation to provide adequate evidence for causality. Correlation doesn't prove causality, as the saying goes.
A clear sign that you arguing for the wrong position is when you provide nothing but truthful, relevant evidence, omit nothing relevant from consideration, and still don't have enough evidence to prove your point.
Some fallacies may be classified in more than one way, e.g., the pragmatic fallacy, which at times seems to be due to vagueness and at times due to insufficient evidence. The pragmatic fallacy is committed when one argues that something is true because it works, where 'works' means something like "I'm satisfied with it," "I feel better," "I find it beneficial, meaningful, or significant," or "It explains things for me." For example, many people claim that astrology works, acupuncture works, chiropractic works, homeopathy works, numerology works, palmistry works, therapeutic touch works. What 'works' means here is vague and ambiguous. You could also criticize such arguments for not supplying enough evidence that they work in the sense of being accurately predictive or medically efficacious. You could also criticize such arguments for posing a false dichotomy by ignoring other plausible explanations for the effects observed. Finally, you could also criticize such arguments for their selective use of evidence and ignoring all the anecdotes where the given therapy did not work in any sense of the word or where the prediction could have been satisfied by a gazillion scenarios.