Academic Tools for Logical Thinking:

Syllogisms 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.

Mode: EasyDifficult
Major Premise: Major Premise

The first premise in a categorical syllogism


Minor Premise: Minor Premise

The second premise in a categorical syllogism

Conclusion:

Make your selections from the dropdown boxes, tick the appropriate selections and click the 'Check Answers' button to see the results.
The conclusion that '' based on the premises is: Invalid Valid
Mood 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 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 distinguished by the placement of the middle term.

Position of Middle Term


Figure Major Premise Minor Premise
1 Subject Predicate
2 Predicate Predicate
3 Subject Subject
4 Predicate Subject

Figure 1 2 3 4
Major Premise M » P P » M M » P P » M
Minor Premise S » M S » M M » S M » S
Conclusion S » P S » P S » P S » P
:
Fallacies: Fallacy

A mistake in reasoning which makes an argument invalid.

Syllogism Results:
Fallacy of Fallacy of Undistributed Major Middle Term

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.

Undistributed 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.

Major Middle Term 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.

Position of Middle Term


Figure Major Premise Minor Premise
1 Subject Predicate
2 Predicate Predicate
3 Subject Subject
4 Predicate Subject

Figure 1 2 3 4
Major Premise M » P P » M M » P P » M
Minor Premise S » M S » M M » S M » S
Conclusion S » P S » P S » P S » P
Fallacy of Fallacy of Undistributed Minor Middle Term

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.

Undistributed 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.

Minor Middle Term 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.

Position of Middle Term


Figure Major Premise Minor Premise
1 Subject Predicate
2 Predicate Predicate
3 Subject Subject
4 Predicate Subject

Figure 1 2 3 4
Major Premise M » P P » M M » P P » M
Minor Premise S » M S » M M » S M » S
Conclusion S » P S » P S » P S » P
Fallacy of Illicit Process of the 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.

Major Term Major Term

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

Fallacy of Illicit Process of the 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.

Minor Term Minor Term

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

Fallacy of Exclusive Premises 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 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 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.

This is a training module for learning about syllogisms.

There are 2 modes to work with; 'Easy' and 'Difficult'. At the top right you can toggle between the 2 modes. In easy mode you will be able to see the info in the 'premises' field, the items in the dropdown box for 'Mood' will be color-coded (green background) to help you identify which syllogisms are valid, the conclusion for the 'Mood-Figure' combination will be visible, the tooltips (for the texts in blue color) will show and the 2 panels ('Overview of Valid Syllogisms' and 'Overview of Fallacies'; the cheatsheets) will be visible.

If you need help, hover the mouse over the 'blue' text (when in 'easy' mode) to get some instant assistance.

At the start (or when you click the
New Syllogism
button) the top field with 'Major Premise' and 'Minor Premise' will be randomly filled with 2 premises and a conclusion beneath.

It is up to you to analyze the premises and its conclusion and make the appropriate selections in the section below that.

  1. First decide whether the conclusion is valid or not and check the 'Invalid' or 'Valid' button.
  2. Second, select the 'Mood' and 'Figure' of the syllogism. If you are not familiar with these concepts, it is suggested to study this first as it can be quiet daunting. You can get some instant info using the tooltips or going to the cheatsheets ('Overview of Valid Syllogisms' and 'Overview of Fallacies'). A lot of excellent documentation is available on Wikipedia.
  3. Next, decide if the syllogism has any fallacies and if so, tick those. Again, instant info is available via the tooltips.
  4. Lastly, if you made all your selections, click the
    Check Answers
    button so see your results. If you correctly identified the validity, mood, figure, and all its fallacies, a score of 100% is awarded. For each item you miss or each incorrectly ticked fallacy points are deducted.
Valid Moods: A-A A-E or E-A A-I or I-A A-O or O-A E-I
Figure: 1 2 3 4
Existential Assumption: Yes (Solid) No (Dashed)
Conclusion: SaP SeP SiP SoP
© Pemani Productions 2018. All Rights Reserved.