Formal fallacies are arguments that follow an invalid argument form. Even if the premises are true, the argument form does not establish the necessary truth of the conclusion. The conclusion may turn out to be true, but it's truth is not established by the argument. The argument is considered ‘unsound’ e.g. All dogs are mammals. Cats are not dogs. Therefore, cats are not mammals. All formal fallacies are specific types of non sequiturs.
A
affirming a disjunct
To conclude that one disjunct of a logical disjunction must be false because the other disjunct is true: A or B; A; therefore not B.The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because ‘or’ is defined inclusively rather than exclusively. It is a fallacy of equivocation between the operations OR and XOR.
e.g. Max is a mammal or Max is a cat. Max is a mammal. Therefore, Max is not a cat.
affirmative conclusion from a negative premise (illicit negative)
When a categorical syllogism has a positive conclusion, but at least one negative premise.
e.g. Max was not born in England and not born in Scotland. Therefore he was born in Wales.
e.g. No fish are dogs, and no dogs can fly, therefore all fish can fly.
affirming the consequent (illicit conversion)
The antecedent in an indicative conditional (a conditional sentence whose grammatical form restricts it to discussing what could be true), is claimed to be true because the consequent is true.
e.g. If A, then B. B, therefore A.
e.g. If the lamp were broken, then the room would be dark. The room is dark, so the lamp is broken.
There are other possible antecedents that might cause the room to be dark (say the lamp is unplugged).
appeal to probability or appeal to possibility (possibiliter ergo probabiliter — possibly, therefore probably.)
A statement that takes something for granted because it would probably be the case (or might be the case).
e.g. Something can go wrong (premise). Therefore, something will go wrong (invalid conclusion).
e.g. If I do not bring my umbrella (premise) It will rain. (invalid conclusion).
argument from fallacy (also known as the fallacy fallacy, argumentum ad logicam)
Assumption that if an argument for some conclusion is fallacious, then the conclusion is false. A fallacious argument can still have a consequent that happens to be true.
It is a special case of denying the antecedent where the antecedent is an entire fallacious argument rather than a false proposition.
e.g. A: All cats are animals. Tom is an animal. Therefore, Tom is a cat.
B: A is invalid, therefore, Tom is not a cat.
B
An example of the base rate fallacy is the false positive paradox. This paradox describes situations where there are more false positive test results than true positives. For example, 50 of 1,000 people test positive for an infection, but only 10 have the infection, meaning 40 tests were false positives. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population. When the prevalence, the proportion of those who have a given condition, is lower than the test's false positive rate, even tests that have a very low chance of giving a false positive in an individual case will give more false than true positives overall.
C
conjunction fallacy
The assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them.
e.g. Linda is 31 years old, single, outspoken, and very bright. As a student she majored in philosophy, was deeply concerned with issues of discrimination and social justice, and participated in anti-nuclear demonstrations.
Which is more probable? A: Linda is a bank teller. B: Linda is a bank teller and is active in the feminist movement.
People tend to answer ‘B’ but the probability of two events occurring together is always less than or equal to the probability of either one occurring alone.
D
denying the antecedent
The antecedent in an indicative conditional is claimed to be true because the consequent is true.
e.g. If A, then B. B, therefore A.
E
ecological fallacy
A formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the group to which those individuals belong.
e.g. If the mean score of a group is larger than zero, this does not imply that a random individual of that group is more likely to have a positive score than a negative one. As long as there are more negative scores than positive scores an individual is more likely to have a negative score.
enthymeme
An argument in which one premise is not explicitly stated.
There are four types:
Syllogism with an unstated premise. e.g. Socrates is mortal because he's human. The unstated premise is that all humans are mortal.
Syllogism based on signs. Signs are things that are so closely related that the presence or absence of one indicates the presence or absence of the other. e.g. He is ill. He has a cough, therefore he is ill. Here having a cough is a sign of illness.
Syllogism where the audience supplies a premise. e.g. Drunk driving hurts innocent people. Therefore, drunk driving is wrong. The audience supplies the premise that hurting innocent people is wrong.
Visual enthymemes. Pictures can also function as enthymemes because they require the audience to help construct their meaning. Internet memes are a good example of this, their meaning being inherited through the input and adaptations of the collective group of users.
exclusive premises, fallacy of
A categorical syllogism that is invalid because both of its premises are negative.
e.g. No cats are dogs. Some dogs are not pets. Therefore, some pets are not cats.
existential fallacy (existential instantiation)
Any argument whose conclusion implies that a class has at least one member, but whose premisses do not so imply. Usually, this involves arguing from a universal premiss or premisses to a particular conclusion.
e.g. All unicorns are animals. Therefore, some animals are unicorns.
F
four terms, fallacy of (quaternio terminorum)
A categorical syllogism that has four (or more) terms rather than the requisite three. e.g. Minor premise: All fish have fins. Minor premise: All goldfish are fish. Conclusion: All humans have fins.
The premises do not connect ‘humans’ with ‘fins’, so the reasoning is invalid. Notice that there are four terms: ‘fish’, ‘fins’, ‘goldfish’ and ‘humans’. Two premises are not enough to connect four different terms, since in order to establish connection, there must be one term common to both premises.
G
H
I
illicit contraposition
A formal fallacy where switching the subject and predicate terms of a categorical proposition, then negating each, results in an invalid argument form.
This is only a fallacy for type ‘E’ and type ‘I’ forms, or forms using the words ‘no’ and ‘some’, respectively. (See Categorical proposition. Logical Forms:
No S are P. Therefore, no non-P are non-S.
Some S are P. Therefore, some non-P are non-S.
e.g. No Catholics are Jews. Therefore, no non-Jews are non-Catholics.
illicit major
A categorical syllogism that is invalid because its major term is not distributed in the major premise but distributed in the conclusion.
e.g. All A are B. No C are A. Therefore, no C are B
e.g. All dogs are mammals. No cats are dogs. So, no cats are mammals.
illicit minor categorical-syllogism
A categorical syllogism that is invalid because its minor term is not distributed in the minor premise but distributed in the conclusion.
e.g. All cats are felines. All cats are mammals. Therefore, all mammals are felines.
The minor term here is mammal, which is not distributed in the minor premise ‘All cats are mammals’, because this premise is only defining a property of possibly some mammals.
J
K
L
M
masked man (illicit substitution of identicals)
The substitution of identical designators in a true statement can lead to a false one e.g. Premise 1: Lois Lane thinks Superman can fly. Premise 2: Lois Lane thinks Clark Kent cannot fly. Conclusion: Therefore Superman and Clark Kent are not the same person.
N
negative conclusion from affirmative premises
When a categorical proposition has a negative conclusion but both premises are affirmative.
e.g. All A is B. All B is C. Therefore, some C is not A.
This is valid only if A is a proper subset of B and/or B is a proper subset of C. It reaches a faulty conclusion in the case that A = B = C.
O
P
propositional fallacies
An error in the logic of 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. They are, most commonly, <and>, <or>, <not>, <only if>, <if and only if>. Propositional fallacies are inferences whose correctness is not guaranteed by the behavior of those logical connectives, and are not logically guaranteed to yield true conclusions.
Types of propositional fallacies: affirming a disjunct — concluded that one disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A; therefore not B. affirming the consequent — the antecedent in an indicative conditional is claimed to be true because the consequent is true; if A, then B; B, therefore A. denying the antecedent — the consequent in an indicative conditional is claimed to be false because the antecedent is false; if A, then B; not A, therefore not B.
quantifier shift
A logical fallacy in which the quantifiers of a statement are erroneously transposed. The change in the logical nature of the statement may not be obvious when it is stated in a natural language like English.
e.g. Every person has a woman that is their mother. Therefore, there is a woman that is the mother of every person.
It is fallacious to conclude that there is one woman who is the mother of all people.
However, if the major premise (‘every person has a woman that is their mother’) is assumed to be true, then it is valid to conclude that there is some woman who is any given person's mother.
R
S
implication: This is a relation between propositions — sentences that are true or false. Implicature: This is a relation between the fact that someone makes a statement and a proposition.
For example, suppose that I state that today is Sunday and it's raining. This statement logically implies (in the sense of 1 above) that it's raining. In contrast, the fact that I made the statement implicates (in the sense of 2 above) that I believe that it's raining. The statement taken by itself implies nothing about what I believe, but the fact that I made the statement implicates that I believe it. In other words, I didn't say that I believe it's raining, but from the fact that I said it's raining you can infer that I believe it.
syllogistic fallacies
Logical fallacies that occur in syllogisms.
Types of syllogistic fallacies:
affirmative conclusion from a negative premise (illicit negative) - when a categorical syllogism has a positive conclusion, but at least one negative premise.
fallacy of exclusive premises – a categorical syllogism that is invalid because both of its premises are negative. fallacy of four terms (quaternio terminorum) – a categorical syllogism that has four terms. illicit major – a categorical syllogism that is invalid because its major term is not distributed in the major premise but distributed in the conclusion. illicit minor – a categorical syllogism that is invalid because its minor term is not distributed in the minor premise but distributed in the conclusion. negative conclusion from affirmative premises – when a categorical syllogism has a negative conclusion but affirmative premises. fallacy of the undistributed middle – the middle term in a categorical syllogism is not distributed
undistributed middle, fallacy of (Lat. non distributio medii)
The middle term (the common term in both premises) in a categorical syllogism is not distributed in either the minor premise or the major premise.
e.g. All Z is B. All Y is B. Therefore, all Y is Z
Note: the distributed terms are in bold.
