by Fergus Duniho
This script is a syllogisms tutor. It will train you in recognizing valid categorical syllogisms, as well as in identifying the mood and figure of a syllogism and the various formal fallacies that can make a syllogism invalid. A syllogism is an argument with two premises and a conclusion. A categorical syllogism is one whose premises and conclusion are all categorical statements. A categorical statement is a statement about the relationship between categories, and there are four basic relationships two categories can have. One category can be a subset of the other or not, and they can intersect or not. The four types of categorical statements that represent these four relationships are normally designated as A, E, I, and O.
|A||All S is P||One category is a subset of another|
|E||No S is P||The two categories do not intersect|
|I||Some S is P||The two categories intersect|
|O||Some S is not P||One category is not a subset of another|
A valid syllogism is one whose conclusion logically follows from its premises. To emphasize the difference between a valid argument and a sound argument, all premises and conclusions are randomly generated, such that many will be false. The validity of an argument does not depend upon whether its premises or conclusions are true. It merely depends on the formal relation between the premises and conclusion. Valid syllogisms can have false premises or false conclusions. An argument is sound when it is valid and has true premises. Validity is only part of what it takes to make an argument sound. Very few of the randomly generated syllogisms will be sound, but a fair number will be valid.
For each syllogism, fill in the fields for mood, figure, validity, and fallacies. When you're finished, press "Check Answers" to find out what the correct answers are. Press "New Syllogism" to do a new syllogism.
The first premise in a categorical syllogism
The second premise in a categorical syllogism
The category mentioned in both the major premise and the conclusion. The second term in the conclusion.
The category mentioned in both the minor premise and the conclusion. The first term in the conclusion.
The category mentioned in both premises but not the conclusion. It is what links major term and minor term together in the syllogism.
The mood of a categorical syllogism is a matter of what kind of categorical statement each statement is, and it is represented by a three letter acronym. The first letter represents the form of the first premise; the second represents the form of the second premise; and the third represents the form of the conclusion. The letters used are A, E, I, and O, as described above.
The figure of a categorical syllogism is the position of its major, minor, and middle terms. There are four figures. The major and minor terms have standard positions in the conclusion, which are the same for all figures. Each figure is ditinguished by the placement of the middle term.
|Figure||Major Premise||Minor Premise|
A mistake in reasoning which makes an argument invalid.
A category is distributed in a statement when the statement refers to every members of the category. The first term is distributed in A statements; the second is distributed in O statements; both are distributed in E statements; and none are distributed in I statements.
When neither premise refers to every member of the middle term, the middle term fails to connect the two premises, and nothing can follow from them. This makes the argument invalid.
When the conclusion is about every member of the major term, the major premise must also be about every member of the major term. The argument is otherwise invalid.
When the conclusion is about every member of the minor term, the minor premise must also be about every member of the minor term. The argument is otherwise invalid.
When both premises are negative (E or O), there is no connection between them, and nothing follows from them. This makes the argument invalid.
When either premise is negative (E or O), only a negative conclusion can follow. When there is an affirmative conclusion (A or I) with a negative premise, the argument is invalid.
The existential statements (I and O) imply the existence of their subject, but the universal statements (A and E) do not. It is true, for example, that all Vulcans are frogs, because there are no Vulcans, making this statement vacuously true. Since Vulcans aren't real, the set of all Vulcans is the empty set. The empty set is a subset of every set. In saying that all Vulcans are frogs, I am merely saying that the empty set is a subset of the set of frogs, which is true, and I am not asserting that any Vulcans exist, which would be false. Since universal statements do not imply the existence of anything, all that follows from two universal statements is another universal statement. If a conclusion is existential but both premises are universal, the syllogism is invalid.