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A logical fallacy is, fundamentally, an error in logic. This means that an argument that uses one certainly doesn't hold if you're using logic and reason as your source of decision making - although it doesn't stop people from using them or being swayed by them. People who want to sound smart tend to use the Latin (or some cases, Dog-Latin) names to refer to them. Others, who don't care about being too diplomatic when bringing them up, will just cry bullshit and carry on. There are two forms of a logical fallacy, formal and informal.
 Where fallacious thinking comes from
Logical fallacies come from human intuition. A logical fallacy is not necessarily a Bayesian fallacy, so given a particular circumstance, jumping to the conclusion will be more likely than not, and get baked into human thinking as a heuristic. When the heuristic is applied outside its reasonable bounds, it becomes a cognitive bias.
The problem is that this can lead to you being grievously wrong about reality. So you may form an opinion by a heuristic (System 1 thinking), but you need to show your working to make sure you haven't just said something silly (System 2 thinking).
This particularly applies to thinking about science, because scientific thinking is unintuitive for most people unless trained into it; and to arguing your points in general, because heuristics are full of glaring exceptions.
Formal fallacies are those fallacies that violate a particular rule of propositional calculus, such as modus ponens. These fallacies can be determined to be invalid simply by the inspection of the form or structure of the argument - at heart, a formal fallacy contains some sort of non sequitur. This doesn't necessarily mean that a conclusion is wrong, but it does mean that we will need a better reason or argument to derive the conclusion.
For example, given the syllogism of A -> B, B -> C, A therefore C, it doesn't matter what A, B and C actually are. If the statement is incorrect because of the content of A, B or C, it would be an informal fallacy, not a formal fallacy because the logic works out. The difference can often be difficult to spot because we may have trouble splitting the content of an argument from its form.
Consider the following proposition:
- Some men are doctors.
- Some doctors are tall.
- Therefore, some men are tall.
We immediately want to say "yes" in response to this, and take the proposition to be correct because this is what reality reflects. However, this is actually an inference beyond what the logical set up allows us to make. Saying that "some men are tall" given the first two premises is a formal logical fallacy. Why this is so can be more easily highlighted by replacing "tall" with a different property, such as "are women" to yield:
- Some men are doctors.
- Some doctors are women.
- Therefore, some men are women.
This doesn't change the logical structure of the argument, but the fallacy is easier to spot because the content changes it to a more obvious absurdity. Arguments regarding the gender binary notwithstanding, of course.
Formal fallacies are propositional, quantificational, syllogistical, modal, or fallacy fallacy.
Informal fallacies (also relevance fallacies) are arguments that, while not violating propositional calculus rules, are invalid because of the content of their argument. Informal fallacies are often characterised by the fact that there is a disconnect of some kind between their premises and conclusions. Inappropriate generalisations and argument from ignorance are forms of informal fallacies. These tend to be more numerous and slightly more interesting than formal fallacies.
Conditional fallacies may or may not be fallacious, conditional on whether or not one of their premises is accepted. An informal conditional fallacy follows the form:
P1: X is Y.
P2: Being Y causes something to be true / to be false / etc.
C1: X is true / false / etc.
This is not always fallacious. For example, a good argument from authority:
The problem only occurs when Y is something stupid. For example, a bad argument from authority:
Conditional fallacies are almost always informal fallacies. However, if comparing multiple systems of logic (which would imply different valid and invalid logical structures, and thus different formal fallacies) then it may be possible for a formal fallacy to be conditional.
Fallacious argument styles occur when one speaker uses certain tactics to attempt to prevent honest and useful discourse.
For example, a Gish Gallop involves spewing so many arguments out that the opponent cannot respond to them. Because the opponent failed to respond to every point, the Galloper can argue that they have won the debate. However, this is fallacious; even though not every point was responded to, this does not mean that the points which went unrebutted were true; instead, the tactic merely showed that the respondent needed more time.
 What isn't a fallacy
One common error when first learning about logical fallacies is to fail to realise that a fallacy can only be present if it is used as part of an argument: for example, "you are an idiot" is not an ad hominem fallacy because it is simply a blank statement: "you are an idiot, therefore you are wrong" is an ad hominem because a conclusion is being drawn. Further, "you are saying idiotic things, therefore you are an idiot" is a valid argument regardless of whether the premise (the opponent is saying idiotic things) is true. However, it is only a sound argument in the event the premise is true.
Just because an argument is valid does not mean the conclusion is true. A valid argument simply means that if the premises are true, the conclusion must be true as well. A sound argument is a valid argument with the additional requirement that the premises (and thus the conclusion) are true. For instance, consider the following argument.
- P1: All humans are cows.
- P2: All cows are plants.
- C1: All humans are plants.
Although the conclusion is false and the premises are false, this is still a valid argument because if the premises were true, the conclusion must be true as well. Since at least one premise is false, the argument is valid but not sound.
 Common examples
- Affirming the consequent — The formal fallacy: from A-> B and B to infer A. The inverse of the valid affirming the antecedent: from A -> B and A to infer B.
- Argument from ignorance — Basing the truth of a premise only on whether it has been proved to your satisfaction.
- Argument from incredulity — Literally "that's unbelievable = that's obviously not real". This kind of thinking would quickly put an end to virtually all quantum physics.
- Negative proof — Arguing that something must exist because there is no evidence it does not exist.
- One single proof — Dismissing all circumstantial evidence in favor of a single "smoking gun" that may not (and may not need to) exist.
- Argumentum ex culo — Various forms of making things up or lying.
- Ad hoc — Yanking shoddy explanations from where the sun don't shine in an attempt to make a hypothesis fit the data.
- Argument by assertion — The belief that if you say something enough times, it eventually becomes true and therefore you win the argument.
- Bullshit — Placing your argument above the truth.
- Equivocation — Deliberately substituting the meaning of a given word in one context for another context that is inappropriate in order to make your argument.
- Extended analogy - Arguing an opponent's analogy that A is like B in one particular way is a claim that A and B are directly comparable to one another.
- Fallacy fallacy - The meta-fallacious argument that your opponent (or someone arguing for a similar point) has used logical fallacies, therefore the argument is wrong.
- False analogy — Use of a flawed or self-refuting analogy.
- Generalisation from fictional evidence
- Great Beethoven fallacy
- Moving the goalposts — Changing evidential requirements in an argument once they have been met, "what I really meant was..."
- Red herring — A group of fallacies which bring up a fact which is irrelevant to the issue, in an attempt to distract the opponent and/or audience.
- Straw man — Distorting an opponent's position for greater rhetorical flexibility.
- Argumentum ad hominem — Attacking the opponent directly rather than addressing the opponent's idea.
- Argumentum ad cellarium — attacking the opponent directly by accusing him of still being in "mom's basement"
- Bulverism — Rather than proving that an argument in favour of an opinion is wrong, a person instead assumes that the opinion is wrong, and then goes on to explain why the other person held it.
- Poisoning the well — Attempting to refute an argument based on the perceived veracity of the presenter.
- Shill gambit - Attacking the opponent directly by accusing him of being bought, typically by a large corporation.
- Appeal to motive - Attacking the opponent's motive for so arguing, as a way of bringing dispute on the argument
- Tu quoque, where a criticism is falsely dismissed because its author is also guilty of the charge.
- Argumentum ad lapidem — Dismissing a statement as absurd without giving proof of its absurdity.
- Argumentum ad verecundiam — The Appeal to Authority; because someone famous/powerful/respected believes it, it must be true.
- Appeal to ancient wisdom — It's right because the Maya/Chinese/Hebrews said it thousands of years ago!
- Appeal to tradition — Just because it's always been that way doesn't mean it's the right way.
- Argumentum ad populum or bandwagon — Arguing for a point based on popularity rather than merit.
- Galileo gambit — If someone is going against the tide of popular thinking, they must be right because the likes of Galileo were right, while in reality, Galileo was right because he had evidence (see also Argumentum ad martyrdom).
- Balance fallacy — Giving equal weighting to both sides of an argument, even if one really doesn't deserve the time.
- Begging the question — Assuming the conclusion as part of the premise (similar to circular reasoning, see also Solferino fallacy).
- Confusing correlation for causation — The number of pirates on the seas has gone down, this correlates with global temperatures rising. So, do pirates cause global cooling?
- Composition and division — A pair of fallacies confusing what is true of a part with what is true of the whole.
- Association fallacy — Associating the values of one group with the values of another due to superficial or coincidental similarities.
- No True Scotsman — Excluding an inconveniently misbehaving member of a class to defend the class as a whole.
- Overgeneralisation — Taking a few specifics and making a general rule out of them, without the few specifics adequately representing the entire group.
- Spotlight fallacy — Assuming aspects of a group from aspects from a smaller observed part of the group.
- Denying the antecedent — If A implies B, and not-A, therefore not-B.
- False cause — Presuming that a real, or perceived, relationship between things, means that one is the cause of the other.
- Retrospective determinism - Claiming that a particular outcome was inevitable simply because it happened.
- False dilemma — Portraying two options as the only possibilities, with no middle ground (see Pascal's wager for an example).
- Appeal to moderation — Presuming that the answer to a problem always lies between two extremes.
- Fallacy of relative privation — A moral equivalence fallacy that says because B is worse than A, A is justified. Also known as the 'not as bad as' fallacy.
- Genetic fallacy — Judging something good or bad, on the basis of where it comes from, or from whom it comes. The genetic fallacy, despite its name, has nothing to do with the science of genetics.
- Argumentum ad Hitlerum — Saying something is bad because Hitler did it.
- Intuition pump — Deliberately abusing a thought experiment to prove a fallacious point.
- Illicit process — Incorrectly concluding for all of a set when the premises apply to only some of a set. Specificially, the illicit major and illicit minor.
- Loaded question — Asking a question, which has an assumption built into it, so that it can't be answered without appearing to agree to the assumption, or else appearing evasive by questioning the assumption. To be distinguished from a Leading question, which is not a fallacy, but is a way of suggesting the desired answer by how the question is phrased. "Are you still beating your wife?" is a loaded question, for it assumes that at one time you did beat your wife; while "You weren't beating your wife, were you?" is a leading question, for it suggests the simple answer no.
- My enemy's enemy — Supporting someone because you've a mutual enemy with them.
- Nirvana fallacy — Claiming that a realistic solution is useless because it is not as good as an idealized perfect solution.
- Non sequitur — Arguably the most fundamental logical fallacy, this is claiming A implies B when it doesn't.
- Pathetic fallacy — This is not a fallacy, but a metaphor, the term being due to John Ruskin, for the assigning animate qualities to inanimate objects: happy skies , babbling brook.
- Presupposition — Making an implicit assumption as part of an argument.
- Reification — Treating an abstraction as a real thing, e.g. treating the test score called "intelligence" as an innate part of a person.
- Reductio ad absurdum — Following a chain of thought to its absurd or contradictory conclusion. Sometimes worthwhile, but oftentimes fallacious.
- Argument from adverse consequences — Arguing against a point based on expected negative outcome.
- Argumentum ad baculum — A subset of arguing from adverse consequences, the negative outcomes are being actualised by the one making the argument. Also a form of the style over substance fallacy (see below).
- Slippery slope — If event A happens, it will lead downhill to further undesirable results. For example, "if we allow gays to get married, then we'll have to let men marry little kids".
- Continuum fallacy Asserting that a continuum of possibilities between two distinct states renders the states identical.
- Argument from adverse consequences — Arguing against a point based on expected negative outcome.
- Self-refuting idea — A claim that on closer inspection disagrees with itself.
- Slothful induction — Ignoring the strongest conclusion of an inductive argument to focus on a weaker one.
- Special pleading — Demanding that your point of view is subject to different standards than all other points of view without any justification beyond "it's the only real support I have for my argument".
- Style over substance fallacy — Using language or rhetoric (ethos or pathos) to enhance the appeal of an argument, but not its validity, or arguing the method of presentation affects the truth of a claim.
- Appeal to novelty — Arguing that a claim is valid because it is novel.
- Appeal to nature — Arguing that something is good because it is "natural" (see also Moralistic fallacy).
- Argumentum ad baculum — Also an argument from adverse consequences, this is attempting to intimidate an opponent (baculum is Latin for "stick").
- Argumentum ad nauseam — The belief that something becomes true if repeated often enough to make you vomit (see also Gish Gallop and Chewbacca Defense).
- Emotional appeal — Evaluating an argument based on its emotional consequences rather than logical ones (see also What's the harm fallacy).
- Suppressed correlative — Attempting to redefine two mutually exclusive options so that one encompasses the other.
 See also
- 5 Ways Common Sense Lies to You Every Day
- The Art of Being Right: 38 Ways to Win An Argument, Arthur Schopenhauer demonstrates how to use logical fallacies to beat your rhetorical opponent.
- Top 25 Creationist Fallacies - A well made 25 minute video.
 Fallacy collections
There are lots of fallacy collections in the Web. Some of them promote a particular agenda, but most fallacies listed in them are real and present in arguments everyday. Unfortunately, many are deprecated.
Here is a list of websites, ordered by usefulness:
- Fallacy Files 
- Your Logical Fallacy Is
- International Encyclopedia of Philosophy 
- Anti-Mormon Illogic 
- Wikipedia 
- George Boeree 
- Diana Mertz Hsieh 
- Sinclair Community College 
- Agnosticism - Atheism 
- Global Tester 
- Objectivism 
- Stephen Downes 
- Atheism Web 
- Round Earth 
- Evolution_V_Creation 
- Kulikovsky Online 
- Daniel Kies 
- Virtual School 
- Peter A. Angeles 
- Sine Wave 
- Carleton University 
- Nizkor Project 
- P5 
- Mathenomicon 
- Vanessa Hall 
- L. Van Warren 
- Skeptic's Dictionary 
- J. P. Craig 
- Informal Fallacies 
- Baloney Detection Kit 
- Autonomist 
- Art of Debate 
- Gordon, Hanks, & Zhu 
- Free Dictionary 
- Freemasonry 
- Taking Sides 
- Jeff Richardson 
- Chisnell.com 
- Agent Orange 
- Humanist Discussion Group 
- Biblical Nonsense 
- Bruce Thompson 
- Arthur Schopenhauer 
- A list of fallacious arguments
- 42 Fallacies for Free