Syllogisms

 WHAT IS A SYLLOGISM?
The term syllogism is applied to the distinctive form of argument that is the application of deductive reasoning. A syllogism includes two premises that are compared against each other in order to infer a conclusion.

The following is an example of a syllogism:

  • Major Premise:          No insect is warm-blooded.
  • Minor Premise:         The wasp is an insect.
  • Conclusion:              No wasp is warm-blooded.

In this syllogism members of a category do not possess a certain characteristic (major premise). An individual is in that category (minor premise). Therefore, that individual cannot possess the characteristic (conclusion).
WHAT IS A CATEGORICAL SYLLOGISM?
The example syllogism in the previous section is a categorical syllogism. In a categorical syllogism, the major premise will state something that will be taken as an absolute (categorical) starting point, and the minor premise will be examined against this absolute starting point in order to infer the conclusion.

Examples of categorical statements:

  • All raccoons are omnivores.
  • No insect is warm-blooded.
  • Some mammals are omnivores.
  • Some mammals are not omnivores.

WHEN IS A CATEGORICAL SYLLOGISM A FALLACY?

A categorical syllogism can be fallacious either because a premise is untrue or because the relationship between the major and minor premise does not support the conclusion.

  • Untrue premise leading to a fallacious conclusion:

Major premise:          All swimming vertebrates are fish.

Minor premise:          The whale is a swimming vertebrate.

Conclusion:              The whale is a fish.

In fact, not all swimming vertebrates are fish so the conclusion that the whale is a fish is unsound.

  • Relationship between major and minor premise does not support conclusion:

Major premise:          Some instructors lack a sense of humor.

Minor premise:          Kim is an instructor.

Conclusion:              Kim lacks a sense of humor.

Certainly somewhere in the world an instructor must lack a sense of humor, so let us agree that the major premise is true. Let us also agree that the Kim in the minor premise is an instructor. Still, the conclusion is unsound because it is impossible to determine whether Kim belongs to the group that lacks a sense of humor. A major premise that states that only some members of a group have a characteristic can never set the stage for concluding that any particular member of the group has that characteristic.

WHAT IS AN IF/THEN SYLLOGISM?
An alternative name for the if/then syllogism is the hypothetical syllogism, but you may find it handy to use the if/then label because the characteristic sign of such a syllogism is the ‘if/then’ in the major premise. Here are the two common forms:

  • Major premise: If A then B.
  • Minor premise: A is true.
  • Conclusion:       Therefore, B is true
  • Major premise: If the price of steel goes up then car production goes down.
  • Minor premise: The price of steel goes up.
  • Conclusion:       Therefore, car production goes down.
  • Major premise: If A then B.
  • Minor premise: B is not true.
  • Conclusion:       Therefore, A is not true
  • Major premise: If student scores rise then the state pays a bonus to the school district.
  • Minor premise: The state did not pay a bonus to the school district.
  • Conclusion:       Therefore, student scores did not rise.

When is an if/then syllogism a fallacy?

Remember that a syllogism may be fallacious if a premise is false. In the case of the either/or fallacy, the major premise must accurately capture a logical relationship—that is, the ‘if’ must actually be a condition for the ‘then’. An if/then syllogism also may be fallacious if the major premise oversimplifies matters by identifying only one condition when in fact several are necessary.

Example of a fallacious if/then syllogism:

  •             Major premise:          If her overall GPA is 2.0 then she will graduate.
  •             Minor premise:          Her overall GPA is 2.0.
  •             Conclusion:              Therefore, she will graduate.

What if the student’s major has a GPA requirement as well? For example, a department may require a 2.5 GPA for all courses taken for the major.