A propositional fallacy is an error in logic that concerns compound propositions. For a compound proposition to be true, the truth values of its constituent parts must satisfy the relevant logical connectives which occur in it (most commonly: <and>, <or>, <not>, <only if>, <if and only if>). The following fallacies involve inferences whose correctness is not guaranteed by the behavior of those logical connectives, and hence, which are not logically guaranteed to yield true conclusions.
Types of Propositional fallacies:
False dilemma (false dichotomy, fallacy of bifurcation, black-or-white fallacy) – two alternative statements are held to be the only possible options, when in reality there are more.
If-by-whiskey – an argument that supports both sides of an issue by using terms that are selectively emotionally sensitive.
Fallacy of many questions (complex question, fallacy of presupposition, loaded question, plurium interrogationum) – someone asks a question that presupposes something that has not been proven or accepted by all the people involved. This fallacy is often used rhetorically, so that the question limits direct replies to those that serve the questioner's agenda.
Ludic fallacy – the belief that the outcomes of non-regulated random occurrences can be encapsulated by a statistic; a failure to take into account unknown unknowns in determining the probability of events taking place.
Fallacy of the single cause (causal oversimplification) – it is assumed that there is one, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes.
False attribution – an advocate appeals to an irrelevant, unqualified, unidentified, biased or fabricated source in support of an argument.
False authority (single authority) – using an expert of dubious credentials and/or using only one opinion to sell a product or idea. Related to the appeal to authority fallacy.
Argument to moderation (false compromise, middle ground, fallacy of the mean) – assuming that the compromise between two positions is always correct.
Gambler's fallacy – the incorrect belief that separate, independent events can affect the likelihood of another random event. If a coin flip lands on heads 10 times in a row, the belief that it is "due to land on tails" is incorrect.
Hedging – using words with ambiguous meanings, then changing the meaning of them later.
Historian's fallacy – occurs when one assumes that decision makers of the past viewed events from the same perspective and having the same information as those subsequently analyzing the decision. (Not to be confused with presentism, which is a mode of historical analysis in which present-day ideas, such as moral standards, are projected into the past.)
Homunculus fallacy – where a "middle-man" is used for explanation, this sometimes leads to regressive middle-men. Explains without actually explaining the real nature of a function or a process. Instead, it explains the concept in terms of the concept itself, without first defining or explaining the original concept. Explaining thought as something produced by a little thinker, a sort of homunculus inside the head, merely explains it as another kind of thinking (as different but the same).
Inflation of conflict – The experts of a field of knowledge disagree on a certain point, so the scholars must know nothing, and therefore the legitimacy of their entire field is put to question.
Moral high ground fallacy – in which one assumes a "holier-than-thou" attitude in an attempt to make oneself look good to win an argument.
Moralistic fallacy – inferring factual conclusions from purely evaluative premises in violation of fact–value distinction. For instance, inferring is from ought is an instance of moralistic fallacy. Moralistic fallacy is the inverse of naturalistic fallacy defined below.
Moving the goalposts (raising the bar) – argument in which evidence presented in response to a specific claim is dismissed and some other (often greater) evidence is demanded.
Naturalistic fallacy fallacy (anti-naturalistic fallacy) – inferring impossibility to infer any instance of ought from is from the general invalidity of is-ought fallacy mentioned above. For instance, is does imply ought for any proposition , although the naturalistic fallacy fallacy would falsely declare such an inference invalid. Naturalistic fallacy fallacy is an instance of argument from fallacy.
Nirvana fallacy (perfect solution fallacy) – when solutions to problems are rejected because they are not perfect.
Onus probandi – from Latin "onus probandi incumbit ei qui dicit, non ei qui negat" the burden of proof is on the person who makes the claim, not on the person who denies (or questions the claim). It is a particular case of the "argumentum ad ignorantiam" fallacy, here the burden is shifted on the person defending against the assertion.
Post hoc ergo propter hoc Latin for "after this, therefore because of this" (faulty cause/effect, coincidental correlation, correlation without causation) – X happened then Y happened; therefore X caused Y. The Loch Ness Monster has been seen in this loch. Something tipped our boat over; it's obviously the Loch Ness Monster.
Prosecutor's fallacy – a low probability of false matches does not mean a low probability of some false match being found.
Psychologist's fallacy – an observer presupposes the objectivity of his own perspective when analyzing a behavioral event.
Red herring – a speaker attempts to distract an audience by deviating from the topic at hand by introducing a separate argument which the speaker believes will be easier to speak to.
Referential fallacy – assuming all words refer to existing things and that the meaning of words reside within the things they refer to, as opposed to words possibly referring no real object or that the meaning of words often comes from how we use them.
Regression fallacy – ascribes cause where none exists. The flaw is failing to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.
Reification (hypostatization) – a fallacy of ambiguity, when an abstraction (abstract belief or hypothetical construct) is treated as if it were a concrete, real event or physical entity. In other words, it is the error of treating as a "real thing" something which is not a real thing, but merely an idea.
Retrospective determinism – the argument that because some event has occurred, its occurrence must have been inevitable beforehand.
Shotgun argumentation – the arguer offers such a large number of arguments for their position that the opponent can't possibly respond to all of them. (See "Argument by verbosity" and "Gish Gallop", above.)
Special pleading – where a proponent of a position attempts to cite something as an exemption to a generally accepted rule or principle without justifying the exemption.
Wrong direction – cause and effect are reversed. The cause is said to be the effect and vice versa.
Personal attacks (Argumentum ad hominem) – the evasion of the actual topic by directing the attack at your opponent.
Faulty generalizations – reach a conclusion from weak premises. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions yet only weakly buttress the conclusions. A faulty generalization is thus produced.
No true Scotsman – when a generalization is made true only when a counterexample is ruled out on shaky grounds.
Cherry picking (suppressed evidence, incomplete evidence) – act of pointing at individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position.
Hasty generalization (fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, leaping to a conclusion, hasty induction, secundum quid, converse accident) – basing a broad conclusion on a small sample.
Misleading vividness – involves describing an occurrence in vivid detail, even if it is an exceptional occurrence, to convince someone that it is a problem.
Overwhelming exception – an accurate generalization that comes with qualifications which eliminate so many cases that what remains is much less impressive than the initial statement might have led one to assume.
Pathetic fallacy – when an inanimate object is declared to have characteristics of animate objects.
Thought-terminating cliché – a commonly used phrase, sometimes passing as folk wisdom, used to quell cognitive dissonance, conceal lack of thought-entertainment, move onto other topics etc. but in any case, end the debate with a cliche—not a point.
Inductive fallacy – A more general name to some fallacies, such as hasty generalization. It happens when a conclusion is made of premises which lightly supports it.
A red herring fallacy is an error in logic where a proposition is, or is intended to be, misleading in order to make irrelevant or false inferences. In the general case any logical inference based on fake arguments, intended to replace the lack of real arguments or to replace implicitly the subject of the discussion.
Red herring – argument given in response to another argument, which is irrelevant and draws attention away from the subject of argument. See also irrelevant conclusion.
Ad hominem – attacking the arguer instead of the argument.
Poisoning the well – a type of ad hominem where adverse information about a target is presented with the intention of discrediting everything that the target person says.
Abusive fallacy – a subtype of "ad hominem" when it turns into verbal abuse of the opponent rather than arguing about the originally proposed argument.
Argumentum ad baculum (appeal to the stick, appeal to force, appeal to threat) – an argument made through coercion or threats of force to support position.
Argumentum ad populum (appeal to widespread belief, bandwagon argument, appeal to the majority, appeal to the people) – where a proposition is claimed to be true or good solely because many people believe it to be so.
Appeal to equality – where an assertion is deemed true or false based on an assumed pretense of equality.
Association fallacy (guilt by association) – arguing that because two things share a property they are the same.
Appeal to consequences (argumentum ad consequentiam) – the conclusion is supported by a premise that asserts positive or negative consequences from some course of action in an attempt to distract from the initial discussion.
Appeal to emotion – where an argument is made due to the manipulation of emotions, rather than the use of valid reasoning. 
Appeal to fear – a specific type of appeal to emotion where an argument is made by increasing fear and prejudice towards the opposing side
Appeal to flattery – a specific type of appeal to emotion where an argument is made due to the use of flattery to gather support.
Appeal to pity (argumentum ad misericordiam) – an argument attempts to induce pity to sway opponents.
Appeal to ridicule – an argument is made by presenting the opponent's argument in a way that makes it appear ridiculous.
Appeal to spite – a specific type of appeal to emotion where an argument is made through exploiting people's bitterness or spite towards an opposing party.
Wishful thinking – a specific type of appeal to emotion where a decision is made according to what might be pleasing to imagine, rather than according to evidence or reason.
Appeal to motive – where a premise is dismissed by calling into question the motives of its proposer.
Appeal to novelty (argumentum ad novitam/antiquitam) – where a proposal is claimed to be superior or better solely because it is new or modern.
Appeal to tradition (argumentum ad antiquitam) – a conclusion supported solely because it has long been held to be true.
Appeal to nature – wherein judgment is based solely on whether the subject of judgment is 'natural' or 'unnatural'. For example (hypothetical): "Cannabis is healthy because it is natural."
Appeal to wealth (argumentum ad crumenam) – supporting a conclusion because the arguer is wealthy (or refuting because the arguer is poor). (Sometimes taken together with the appeal to poverty as a general appeal to the arguer's financial situation.)
Argument from silence (argumentum ex silentio) – a conclusion based on silence or lack of contrary evidence.
Bulverism (Psychogenetic Fallacy) – inferring why an argument is being used, associating it to some psychological reason, then assuming it is invalid as a result. It is wrong to assume that if the origin of an idea comes from a biased mind, then the idea itself must also be a false.
Naturalistic fallacy (is–ought fallacy, naturalistic fallacy) – claims about what ought to be on the basis of statements about what is.
Reductio ad Hitlerum (playing the Nazi card) – comparing an opponent or their argument to Hitler or Nazism in an attempt to associate a position with one that is universally reviled. (See also – Godwin's law)
Straw man – an argument based on misrepresentation of an opponent's position.
Tu quoque ("you too", appeal to hypocrisy, I'm rubber and you're glue) – the argument states that a certain position is false or wrong and/or should be disregarded because its proponent fails to act consistently in accordance with that position.
Broken window fallacy – an argument which disregards lost opportunity costs (typically non-obvious, difficult to determine or otherwise hidden) associated with destroying property of others, or other ways of externalizing costs onto others. For example, an argument that states breaking a window generates income for a window fitter, but disregards the fact that the money spent on the new window cannot now be spent on new shoes.
Definist fallacy – involves the confusion between two notions by defining one in terms of the other.
Naturalistic fallacy – attempts to prove a claim about ethics by appealing to a definition of the term "good" in terms of either one or more claims about natural properties (sometimes also taken to mean the appeal to nature) or God's will.
Slippery slope (thin edge of the wedge, camel's nose) – asserting that a relatively small first step inevitably leads to a chain of related events culminating in some significant impact/event that should not happen, thus the first step should not happen. While this fallacy is a popular one, it is, in its essence, an appeal to probability fallacy. (e.g. if person x does y then z would (probably) occur, leading to q, leading to w, leading to e.) This is also related to the Reductio ad absurdum.
The following is a sample of books for further reading, selected for a combination of content, ease of access via the internet, and to provide an indication of published sources that interested readers may review. The titles of some books are self-explanatory. Good books on critical thinking commonly contain sections on fallacies, and some may be listed below.