What is a fallacy?
- 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.
What is a ‘formal fallacy’?
- 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.
Appeal to probability
A statement that takes something for granted because it would probably be the case (or might be the case).
Argument from fallacy
Assumes that if an argument for some conclusion is fallacious, then the conclusion itself is false.
Base rate fallacy
Making a probability judgement based on conditional probabilities, without taking into account the effect of prior probabilities
Conjunction fallacy
Assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them.
Masked man fallacy (illicit substitution of identicals)
The substitution of identical designators in a true statement can lead to a false one.
What is a ‘Propositional Fallacy’?
- 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.
Affirming a disjunct
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.
Affirming the consequent
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.
Denying the antecedent
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.
“Fallacious arguments usually have the deceptive appearance of being good arguments.”
- 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.
Syllogism
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.
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
Aristotle defined each of these three types of statements as what?
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.
Affirmative conclusion from a negative premise (illicit negative)
A formal fallacy committed when a categorical syllogism has a positive conclusion, but one or two negative premises.
Eg:
- No fish are dogs, and
- No dogs can fly,
- 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.
What is the ‘fallacy of exclusive premises’
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.
What is ‘fallacy of four terms’?
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.
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?
The three terms are: “goldfish”, “fish”, and “fins”.
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?
- 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.
What is ‘Illicit major fallacy’?
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:
- All A are B
- No C are A
- Therefore, no C are B
Illicit major fallacy example:
- All dogs are mammals
- No cats are dogs
- Therefore, no cats are mammals
What is the major term?
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.
Show a valid form of Illicit major fallacy
- All A are B
- No B are C
- Therefore, no C are A
What is ‘Illicit minor fallacy’?
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:
- All A are B.
- All A are C.
- Therefore, all C are B.
Illicit minor fallacy example:
- All cats are felines.
- All cats are mammals.
- Therefore, all mammals are felines.
What is the minor term?
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.
