Main Menu Exercises

Before beginning, you may want to review some of these sections:

[Universal Statements] [Deduction] [Conditional Arguments]

["Only" in Conditional Arguments] [Conditional Chain Arguments]

Introduction to Universal Syllogisms

A universal syllogism is a syllogism composed of universal claims. The first claim, or major premise, describes all of one class or group, X, in terms of some other class or group, Y. The second claim, or minor premise, places a third class or group, Z, either within X or not within Y. The paradigms for a valid universal syllogism are as follows: 

All X are Y.

Z is X.


Therefore, Z is Y.
--or--

All X are Y.

No Z is Y.


Therefore, no Z is X.

These are the only two valid forms for a syllogism with a major premise in the form "All X are Y." In other words, such syllogisms are invalid if the minor premise is either "Z is Y" or "No Z is X."

Universal claims with a major premise of "No X is Y" will be treated in the section on Non-universal Syllogisms.

Like conditionals, syllogisms can be chained. (See Conditional Chain Arguments.) Consider the following claims:

  1. All great novels are great art.
  2. All great art is moving and meaningful.
  3. All things moving and meaningful are worth preserving.
Now consider what happens when the following minor premise is added:
Moby-Dick is a great novel.
Combined with premise #1 ("All great novels are great art"), this minor premise leads to the conclusion that "Moby-Dick is great art." Using that conclusion as the minor premise in conjunction with major premise #2 ("All great art is moving and meaningful"), we can conclude that "Moby-Dick is moving and meaningful." Finally, using that conclusion as the minor premise in conjunction with major premise #3, we can conclude that "Moby-Dick is worth preserving." As a paradigm, such a chain argument would look like this: 

All A are B.

All B are C.

All C are D.


Z is A.

Therefore, Z is B.

Therefore, Z is C.

Therefore, Z is D.
--or--

All novels are art.

All art is moving.

All moving is worth preserving.


Moby-Dick is novel.
Therefore, Moby-Dick is art.
Therefore, Moby-Dick is moving.
Therefore, Moby-Dick is worth preserving.

Words such as "only" can affect the meaning of a universal claim in the same way they affect conditionals. (See "Only" in Conditional Arguments.) Consider the claim, "Only the good die young." Which of the following is a restatement of that claim?

A. Every young person that dies is good.
--or--
B. Every good person that dies is young.
That is the sort of question you should ask yourself whenever attempting to understand a complex claim. "Only the good die young" means that "anybody (good or otherwise) can die old, but only good can die young," so, in this case, the answer is A. As a general rule, then, "All X is Y" is equivalent to "Only Y is X."

Other words and phrases that can function like "only" include "just," "none but," and "none except." Thus, all of the following are logical equivalent to "All those who die young are good."

Only the good die young.
Just the good die young.
None but the good dies young.
Nobody except the good dies young.

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