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An enthymeme is a syllogism (a three-part deductive argument) with an unstated assumption which must be true for the
premises to lead to the conclusion. In an enthymeme, part of the argument is missing because it is assumed.
First example: Socrates is mortal because he's human.
The complete syllogism would be the classic:
All humans are mortal. (major premise - assumed)
Socrates is human. (minor premise - stated)
Therefore, Socrates is mortal. (conclusion - stated)
Second example: "The glove doesn't fit, so you must acquit."
The complete syllogism would be:
If the glove doesn't fit the defendant, you must acquit the defendant. (major premise - assumed)
The glove doesn't fit the defendant. (minor premise - stated)
Therefore, you must acquit the defendant. (conclusion - stated)
Stating the argument in this extended form suggests that the argument is incomplete. For example, one might be more likely to
ask if the glove might have shrunk or ask about the meaning of the expression the glove: What do you mean the glove?. The
presence of the definite article the suggests that there is a definite descriptor phrase with the same meaning in this context.
Examples of such phrases could be
The glove found at the scene of the crime
The glove used by the assailant.
For some definite descriptor phrases, the major premise of the above syllogism is clearly suspect.
(This argument is based on one used by Johnnie Cochran in his defense of O. J. Simpson.)
Hidden premises are often an effective way to obscure a questionable or fallacious premise in reasoning. Typically fallacies of
presumption (fallacies based on mistaken assumptions, such as ad hominem or two wrongs make a right) are attracted to
Use in humor
Enthymeme can be a humorous technique when the hidden premise is something surprising due to the context, its
offensiveness or its absurdity.
"Senator, I served with Jack Kennedy. I knew Jack Kennedy. Jack Kennedy was a friend of mine. Senator, you're no
Jack Kennedy." —Lloyd Bentsen to Dan Quayle, 1988. (The hidden premises might be, Jack Kennedy was a great man,
and you are not a great man.)
"There is no law against composing music when one has no ideas whatsoever. The music of Wagner, therefore, is
perfectly legal." —Mark Twain. (The hidden premise is that Richard Wagner's music has no ideas.)
"Now, I don't know or have never met my candidate; and for that reason I am more apt to say something good of him
than anyone else." —Will Rogers. (The hidden premise is that only people who don't know or haven't met the
candidate say good things about him.)
Use in advertising
Advertisers rarely draw out the links between the images they show and the product they wish to sell. The
beautiful women, draped across the dashing red sports car... there is no logical connection between the
two, but the advertiser would like to imply a premise that there is. If the advertiser came out and said "Buy
this car and you will have more sexual satisfaction" it might be easier to reject as a premise.
To use another example, advertisers often show examples of people enjoying their product. They never
actually say "... and, you should do what these people do," it is an implied major premise.
Logical fallacy - Definition
A logical fallacy is an error in logical argument which is independent of the truth of the premises. It is a flaw in the structure of an argument as opposed to an error in its
premises. When there is a fallacy in an argument it is said to be invalid. The presence of a logical fallacy in an argument does not necessarily imply anything about the argument's
premises or its conclusion. Both may actually be true, but the argument is still invalid because the conclusion does not follow from the premises using the inference principles of
the argument. By extension, an argument can have a logical fallacy even if the argument is not a purely logical one; for instance an argument that incorrectly applies principles of
probability or causality can be said to have a logical fallacy.
Recognizing fallacies in practical arguments may be difficult since arguments are often structured using rhetorical patterns that obscure the logical connections between
assertions. As we illustrate with various examples, fallacies may also exploit the emotions or intellectual or psychological weaknesses of the interlocutor. Having the capability of
recognizing logical fallacies in arguments will hopefully reduce the likelihood of such an occurrence.
A different approach to understanding and classifying fallacies is provided by argumentation theory; see for instance the van Eemeren, Grootendorst reference below. In this
approach, an argument is regarded as an interactive protocol between individuals which attempts to resolve a disputed proposition. The protocol is regulated by certain rules of
interaction and violations of these rules are fallacies. Many of the fallacies in the list below are best understood as being fallacies in this sense.
Examples of fallacious arguments
In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of a nonexistent
Some acts of killing human beings are legal in this state.
Some acts of killing human beings are illegal in this state.
Therefore some acts of killing human beings are both legal and illegal in this state.
This is fallacious. Indeed, there is no logical principle which states
For some x, P(x).
For some y, Q(y).
Then for some z, P(z) and Q(z).
The easiest way to show the above inference is invalid is by using Venn diagrams. In logical parlance, the inference is invalid,
since under at least one interpretation of the predicates it is not validity preserving.
Unfortunately, few fallacious arguments are as clear cut as the above example suggests. A great many arguments involve
causality, which is certainly not part of formal logic. Others involve psychological ploys such as use of power relationships
between proposer and interlocutor, appeals to patriotism and morality, appeals to ego etc., to establish necessary intermediate
(explicit or implicit) premises for an argument. Indeed, fallacies very often lay in unstated assumptions or implied premises in
arguments that are not always obvious at first glance. One way to obscure a premise is through enthymeme.
We now give a few examples illustrating common errors in reasoning. Note that providing a critique of an argument has no
relation to the validity of the conclusion. The conclusion could very well be valid, while the argument itself is unsound. See
argument from fallacy.
In the following, we view an argument as a dialogue between a proposer and an interlocutor.
Example 1
James argues:
Application of the death penalty is killing a human being.
Killing a human being is wrong.
Therefore, application of the death penalty is wrong.
This argument claims to prove the death penalty is wrong. This particular argument has the form of a categorical syllogism. Any
argument must have premises as well as a conclusion. In this case we need to ask what the premises are, that is the set of
assumptions the proposer of the argument can expect the interlocutor to grant. The first assumption is almost true by
definition: the death penalty is the killing of a criminal who has been duly convicted under a process of law. The second
assumption is less clear as to its meaning. Since the assertion has no quantifiers of any kind, it could mean any one of the
Every act of killing a human being is wrong.
Most acts of killing a human being are wrong.
All acts of killing a human being are wrong, except those that are carried out for some legitimate purpose such as
deterring serious crime.
Some acts of killing a human being are wrong.
The third interpretation for example would be those of individuals who accept the Fifth Commandment under a common
interpretation in Judeo-Christian theology. In that interpretation, the above syllogism would then fail to have validated its
second premise. James may try to assume that his interlocutor believes every act of killing is wrong; if the interlocutor grants
this then the argument is valid. In this case, the interlocutor is essentially conceding the point to James. However, the
interlocutor is more likely to believe some acts of killing are not wrong, for instance those carried out in self defense or in
legitimate warfare; and in this case James is not much better off than he was before he formulated the argument, since he now
has to prove the assertion that the death penalty is not a legimate form of killing, which is a disguised form of the original thesis.
From the point of view the interlocutor, James commits the logical fallacy of begging the question.
Example 2
Barbara argues:
Andre is a good tennis player.
Therefore, Andre is 'good', that is to say a morally good person.
Here the problem is that the word good has different meanings, which is to say that it is an ambiguous word. In the premise,
Barbara says that Andre is good at some particular activity, in this case tennis. In the conclusion, she says that Andre is a morally
good person. These are clearly two different senses of the word "good". The premise might be true but the conclusion can still
be false: Andre might be the best tennis player in the world but a rotten person morally. Appropriately, since it plays on an
ambiguity, this sort of fallacy is called the fallacy of equivocation, that is, equating two incompatible terms or claims.
Example 3
A humorous variant of the fallacy of ambiguity is as follows. Ramesh argues:
Nothing is better than eternal happiness.
Eating a hamburger is better than nothing.
Therefore, eating a hamburger is better than eternal happiness.
This argument has the appearance of an inference which applies transitivity of the two-placed relation is better than, which in
this critique we grant is a valid property. The argument is an example of syntactic ambiguity. In fact, the first premise
semantically does not predicate an attribute of the subject, as would for instance the assertion
A potato is better than eternal happiness.
In fact it is semantically equivalent to the following universal quantification:
Everything fails to be better than eternal happiness.
So instantiating this fact with eating a hamburger, it logically follows that
Eating a hamburger fails to be better than eternal happiness.
Note that the premise A hamburger is better than nothing does not provide anything to this argument. This
fact really means something such as
Eating a hamburger is better than eating nothing at all.
Fallacies in the media and politics
Fallacies are used frequently by pundits in the media and politics. When one politician says to
another, "You don't have the moral authority to say X", this could be an example of the
argumentum ad hominem or personal attack fallacy; that is, attempting to disprove X, not by
addressing validity of X but by attacking the person who asserted X. Arguably, the politician is not
even attempting to make an argument against X, but is instead offering a moral rebuke against the
interlocutor. For instance, if X is the assertion:
The military uniform is a symbol of national strength and honor.
Then ostensibly, the politician is not trying to prove the contrary assertion. If this is the case,
then there is no logically fallacious argument, but merely a personal opinion about moral
worth. Thus identifying logical fallacies may be difficult and dependent upon context.
In the opposite direction is the fallacy of argument from authority. A classic example is the
Ipse dixit—"He himself said it" argument—used throughout the Middle Ages in reference to
Aristotle. A modern instance is "celebrity spokespersons" in advertisements: a product is
good and you should buy/use/support it because your favorite celebrity endorses it.
An appeal to authority is always a logical fallacy though it can be an appropriate form of
rational argument if, for example, it is an appeal to expert testimony. In this case, the expert
witness must be recognized as such and all parties must agree that the testimony is
appropriate to the circumstances. This form of argument is common in legal situations.
By definition, arguments with logical fallacies are invalid, but they can often be (re)written in
such a way that they fit a valid argument form. The challenge to the interlocutor is, of
course, to discover the false premise, that is the premise which makes the argument
A list of fallacies
The entries in the following list are neither exhaustive nor mutually exclusive, that is, several
distinct entries may refer to the same pattern. As noted in the introduction, these fallacies
describe erroneous or at least suspect patterns of argument in general, not necessarily
argument based on formal logic. Many of the fallacies listed are traditionally recognized and
discussed in works on critical thinking; others are more specialized.
Ad hominem (also called argumentum ad hominem or personal attack) Including:
ad hominem abusive (also called argumentum ad personam)
ad hominem circumstantial (also called ad hominem circumstantiae)
ad hominem tu quoque (also called you too argument)
Amphibology (also called amphiboly)
Appeal to authority (also called argumentum ad verecundiam or argument by authority)
Appeal to belief
Appeal to consequences (also called argumentum ad consequentiae)
Appeal to emotion including:
Appeal to fear (also called argumentum ad metum or argumentum in terrorem)
Appeal to flattery
Appeal to the majority (also called argumentum ad populum)
Appeal to pity (also called argumentum ad misericordiam)
Appeal to ridicule
Appeal to spite (also called argumentum ad odium)
Two wrongs make a right
Wishful thinking
Appeal to motive
Appeal to novelty (also called argumentum ad novitatem)
Appeal to probability
Appeal to tradition (also called argumentum ad antiquitatem or appeal to common
Argument from fallacy
Argument from ignorance (also called argumentum ad ignorantiam or argument by lack
of imagination)
Argument from silence (also called argumentum ex silentio)
Argumentum ad baculum (also called appeal to force)
Argumentum ad crumenam (also called appeal to wealth)
Argumentum ad lazarum (also called appeal to poverty)
Argumentum ad nauseam (also called argument from repetition)
Argumentum ad numerum
Base rate fallacy
Bandwagon fallacy (also called appeal to popularity, appeal to the people, or
argumentum ad populum)
Begging the question (also called petitio principii, circular argument or circular
Cartesian fallacy
Conjunction fallacy
Correlative based fallacies including:
Fallacy of many questions (also called complex question, loaded question or
plurium interrogationum)
False dilemma (also called false dichotomy or bifurcation)
Denying the correlative
Suppressed correlative
Dicto simpliciter, including:
Accident (also called a dicto simpliciter ad dictum secundum quid)
Converse accident (also called a dicto secundum quid ad dictum simpliciter)
False analogy
False premise
Fallacies of distribution:
Ecological fallacy
Faulty generalization including:
Biased sample
Hasty generalization (also called fallacy of insufficient statistics, fallacy of
insufficient sample, fallacy of the lonely fact, leaping to a conclusion, hasty
induction, secundum quid)
Overwhelming exception
Statistical special pleading
Gambler's fallacy/Inverse gambler's fallacy
Genetic fallacy
Guilt by association / Honor by association
Historian's fallacy
Homunculus fallacy
Ignoratio elenchi (also called irrelevant conclusion)
Inappropriate interpretations or applications of statistics including:
Biased sample
Correlation implies causation
Gambler's fallacy
Prosecutor's fallacy
Screening test fallacy
Invalid proof
Lump of labour fallacy (also called the fallacy of labour scarcity)
Meaningless statement
Middle ground (also called argumentum ad temperantiam)
Misleading vividness
Naturalistic fallacy
Negative proof
Non sequitur including:
Affirming the consequent
Denying the antecedent
No true Scotsman
Package deal fallacy
Pathetic fallacy
Perfect solution fallacy
Poisoning the well
Questionable cause including:
Correlation implies causation (also called cum hoc ergo propter hoc)
Fallacy of the single cause
Joint effect
Post hoc (also called post hoc ergo propter hoc)
Regression fallacy
Texas sharpshooter fallacy
Wrong direction
Red herring (also called irrelevant conclusion)
Reification (also called hypostatization)
Relativist fallacy (also called subjectivist fallacy)
Retrospective determinism (it happened so it was bound to)
Shifting the Burden of proof
Slippery slope
Special pleading
Straw man
Style over substance fallacy
Syllogistic fallacies, including:
Affirming a disjunct
Affirmative conclusion from a negative premise
Existential fallacy
Fallacy of exclusive premises
Fallacy of four terms (also called quaternio terminorum)
Fallacy of the undistributed middle
Illicit major
Illicit minor