Formal Fallacies

Question 1

What is a fallacy?

Answer 1

• A fallacy is an argument that uses poor reasoning.
• An argument can be fallacious whether or not its conclusion is true.
• A fallacy can be either formal or informal.

Question 2

What is a ‘formal fallacy’?

Answer 2

• A formal fallacy is a pattern of reasoning that is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid.
• A formal fallacy is contrasted with an informal fallacy, which may have a valid logical form and yet be unsound because one or more premises are false.

Question 3

Appeal to probability

Answer 3

A statement that takes something for granted because it would probably be the case (or might be the case).

Question 4

Argument from fallacy

Answer 4

Assumes that if an argument for some conclusion is fallacious, then the conclusion itself is false.

Question 5

Base rate fallacy

Answer 5

Making a probability judgement based on conditional probabilities, without taking into account the effect of prior probabilities

Question 6

Conjunction fallacy

Answer 6

Assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them.

Question 7

Masked man fallacy (illicit substitution of identicals)

Answer 7

The substitution of identical designators in a true statement can lead to a false one.

Question 8

What is a ‘Propositional Fallacy’?

Answer 8

• 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 that occur in it (most commonly: , , , , ).
• These 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.

Question 9

Affirming a disjunct

Answer 9

Concluded that one disjunct of a logical disjunction must be false because the other disjunct is true.

Eg: 1. A or B; 2. A; therefore not B.

Question 10

Affirming the consequent

Answer 10

The antecedent in an indicative conditional is claimed to be true because the consequent is true.

Eg: 1. if A, then B; 2. B, therefore A.

Question 11

Denying the antecedent

Answer 11

The consequent in an indicative conditional is claimed to be false because the antecedent is false.

Eg. 1. if A, then B; 2. not A, therefore not B.

Question 12

“Fallacious arguments usually have the deceptive appearance of being good arguments.”

Answer 12

• Recognizing fallacies in everyday arguments may be difficult since arguments are often embedded in rhetorical patterns that obscure the logical connections between statements.
• Informal fallacies may also exploit the emotional, intellectual, or psychological weaknesses of the audience. Having the capability to recognize fallacies in arguments is one way to reduce the likelihood of such occurrences.

Question 13

Syllogism

Answer 13

A kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

Syllogistic arguments are usually represented in a three-line form.

Question 14

1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.

Aristotle defined each of these three types of statements as what?

Answer 14

Defined by Aristotle, from the combination of:

(1) a general statement (the major premise), and
(2) a specific statement (the minor premise),
(3) a conclusion is deduced.

Eg. Knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal.

Question 15

Affirmative conclusion from a negative premise (illicit negative)

Answer 15

A formal fallacy committed when a categorical syllogism has a positive conclusion, but one or two negative premises.

Eg:

1. No fish are dogs, and
2. No dogs can fly,
3. Therefore all fish can fly.

The only thing that can be properly inferred from these premises is that some things that are not fish cannot fly, provided that dogs exist.

Question 16

What is the ‘fallacy of exclusive premises’

Answer 16

A syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.

Example of an EOO-4 invalid syllogism:

E Proposition: No mammals are fish.
O Proposition: Some fish are not whales.
O Proposition: Therefore, some whales are not mammals.

Question 17

What is ‘fallacy of four terms’?

Answer 17

The formal fallacy that occurs when a syllogism has four (or more) terms rather than the requisite three. This form of argument is thus invalid.

Question 18

Categorical syllogisms always have three terms:

Major premise: All fish have fins.
Minor premise: All goldfish are fish.
Conclusion: All goldfish have fins.

What are the three here?

Answer 18

The three terms are: “goldfish”, “fish”, and “fins”.

Question 19

Using four terms invalidates the syllogism:

Major premise: All fish have fins.
Minor premise: All goldfish are fish.
Conclusion: All humans have fins.

What are the 4 terms? Why does it invalidate the syllogism?

Answer 19

• 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.

Question 20

What is ‘Illicit major fallacy’?

Answer 20

Categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion.

This fallacy has the following argument form:

1. All A are B
2. No C are A
3. Therefore, no C are B

Question 21

Illicit major fallacy example:

1. All dogs are mammals
2. No cats are dogs
3. Therefore, no cats are mammals

What is the major term?

Answer 21

In this argument, the major term is “mammals”.

This is distributed in the conclusion (the last statement) because we are making a claim about a property of all mammals: that they are not cats. However, it is not distributed in the major premise (the first statement) where we are only talking about a property of some mammals: Only some mammals are dogs.

The error is in assuming that the converse of the first statement (that all mammals are dogs) is also true.

Question 22

Show a valid form of Illicit major fallacy

Answer 22

1. All A are B
2. No B are C
3. Therefore, no C are A

Question 23

What is ‘Illicit minor fallacy’?

Answer 23

Categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion.

This fallacy has the following argument form:

1. All A are B.
2. All A are C.
3. Therefore, all C are B.

Question 24

Illicit minor fallacy example:

1. All cats are felines.
2. All cats are mammals.
3. Therefore, all mammals are felines.

What is the minor term?

Answer 24

The minor term here is mammal.

This is not distributed in the minor premise “All cats are mammals,” because this premise is only defining a property of possibly some mammals (i.e., that they’re cats.) However, in the conclusion “All mammals are felines,” mammal is distributed (it is talking about all mammals being felines).

It is shown to be false by any mammal that is not a feline; for example, a dog.

Example:

Pie is good.
Pie is unhealthy.
Thus, all good things are unhealthy.