**
**## Introduction

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.

## Instructions

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.

## Definitions

### Major Premise

The first premise in a categorical syllogism

### Minor Premise

The second premise in a categorical syllogism

### Major Term

The category mentioned in both the major premise and the conclusion. The
second term in the conclusion.

### Minor Term

The category mentioned in both the minor premise and the conclusion. The
first term in the conclusion.

### Middle Term

The category mentioned in both premises but not the conclusion. It is what
links major term and minor term together in the syllogism.

### Mood

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.

### Figure

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.

Position of Middle Term
Figure |
Major Premise |
Minor Premise |

First |
Subject |
Predicate |

Second |
Predicate |
Predicate |

Third |
Subject |
Subject |

Fourth |
Predicate |
Subject |

### Fallacy

A mistake in reasoning which makes an argument invalid.

### Distribution

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.

### Fallacy of the Undistributed Middle

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.

### Fallacy of Illicit Process of the Major Term

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.

### Fallacy of Illicit Process of the Minor Term

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.

### Fallacy of Exclusive Premises

When both premises are negative (E or O), there is no connection between
them, and nothing follows from them. This makes the argument invalid.

### Fallacy of Drawing an Affirmative Conclusion from a Negative Premise

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.

### Existential Fallacy

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.

## History

I originally wrote "Silly Syllogisms" as a Microsoft BASIC program in 1990,
back when I was teaching an Introduction to Philosophy course at RPI. I made it
available for the Amiga and Macintosh versions of Microsoft BASIC. When I got my
Amiga 3000 in 1992, Microsoft BASIC would not work on it. So I neglected the
program for years. After learning JavaScript in 2001, I realized I could do a
JavaScript version of "Silly Syllogisms" and put it on the web. So I pulled out
Irving M. Copi's *Introduction to Logic* and wrote a new JavaScript
version. This new version is not based on any code from the original BASIC
version of "Silly Syllogisms."