Syllogism

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Guides to Understanding Syllogism

Syllogism is a form of reasoning inferred from assumptions. To expound briefly, reasoning is an act conducted when two ideas are compared together by means of a third, which must agree with one of them. If this third idea agrees with the other two, those two, of course, agree with one another; if it agrees with only one, they, of course, disagree with one another.

Thus, syllogism is an inference from something that is assumed previously. The necessity of the conclusion lies in the relation existing between that which is assumed and the conclusion.

The assumptions entail the necessity of the conclusion. In other words: the statement made in the conclusion is already implied in that which was assumed previously. A typical syllogistic argument consists of three predominant propositionsOpens in new window — two premises (major premise and minor premise), and a conclusion each of which is applied twice.

In the rhetorical tradition, the syllogism, along with its counterpart, enthymemeOpens in new window, are the most important multiclause units delivering individual lines of arguments.

Being a three–part structure for inferential reasoning, the syllogism requires, in its ideal form, statements with linking verbs, three carefully positioned recurring terms, and distinct quantifiers, making claims of inclusion, exclusion, and partial overalap. With a focus on the quantifiers and the option of affirming or denying, the resulting statements could take four forms:

1. universal affirmative,
2. universal negative,
3. particular affirmative,
4. particular negative.

Combined into arrays of three statements, these four statement types yielded twenty–four possible syllogisms, and these twenty–four were in turn grouped into sets according to the grammatical position (subject or predicate) of the three critical terms.

Typical Concept and Examples

Employing Melanchthon’s examples in the Erotemata Dialectices popular in the sixteenth century, the famous Barbara represents a syllogism whose three statements were all universal affirmations:

Major premise

Every animal is a substance

Minor premise

Every man is an animal

Conclusion

Therefore every man is a substance

The syllogisms below are cued with a universal negation, a particular affirmative, and a particular negation:
Those who perjure themselves cannot be trusted.
Major premise

Those who perjure themselves cannot be trusted.

Minor premise

This man has perjured himself in the past.

Conclusion

This man is not to be trusted.

All humans are mortal.
Major premise

All humans are mortal.

Minor premise

Socrates is human.

Conclusion

Therefore, Socrates is mortal.

No law of nature is mutable.
Major premise

No law of nature is mutable

Minor premise

The law prohibiting adultery is a law of nature

Conclusion

Therefore the law prohibiting adultery is not mutable

Reasoning in ordinary arguments is rarely expressed in the stripped–down form of the correctly worded three–part syllogism. The form can, however, often be reconstructed from an arguer’s actual phrasing. For instance, suffragist Susan B. Anthony defended herself against arrest for attempted voting in 1872 with a speech that included the following passage:

Webster, Worcester, and Bouvier all define a citizen to be a person in the United States, entitled to vote and hold office.

1. The only question left to be settled now is: Are women persons? And I hardly believe any of our opponents will have the hardihood to say they are not. Being persons then, women are citizens; and no state has a right to make any law or to enforce any old law, that shall abridge their privileges or immunities.

— (Safire 1997, 637 [courtesy of — Rhetorical Style: The Uses of Language in Persuasion, by Jeanne Fahnestock])

However, the full three–part syllogism underlying this passage and delivering the definition argument could be paraphrased as follows:

Major premise

Citizens are persons in the United States entitled to vote and hold office.

Minor premise

Women are persons in the United States.

Conclusion

Therefore women are citizens entitled to vote and hold office.

Units of argument closer to canonical syllogistic form can carry the appearance of airtight reasoning. They are then a device of emphasis. The following is derive from an editorial calling for the death penalty in the case of the convicted terrorist Zacarias Moussaoui.

1. The death sentence is properly reserved for the most heinous of crimes and least redeeming criminals.
2. But there are few cases more appropriate for this most severe penalty.
3. Here is a criminal (Moussaoui) who admitted to his crime, who expressed no remorse and who yearns to kill more.
4. Justice for the victims of his crime demands the maximum penalty the law allows.

The first sentence here is the major premise, the defining criteria for a death sentence as applicable to heinous crimes and unrepentant criminals.

The second and third sentences constitute the minor premise, the identification of Moussaoui and his crimes as fitting the criteria.

The final sentence concludes that he therefore deserves the death penalty. Departing from good form, however, this final sentence substitutes the new notion of justice for the victims for the strict reiteration that would read, “Therefore his heinous crime and unredeeming criminal nature deserve the death penalty.”

Important Hint!

The major premise of a syllogism makes a general statement that the writer believes to be true. The minor premise presents a specific example of the belief that is stated in the major premise. If the reasoning is sound, the conclusion should follow from the two premises.

A situation that calls for a syllogistic reasoning is where a person is arguing opposite another. The syllogism has its origins in the debate. Thus, it serves to convince the opponent that the statement made in the conclusion is true. The person who draws up the syllogism seeks arguments with which to convince his opponent that a certain proposition is true. This proposition, which will function as the syllogism’s conclusion, is therefore the starting-point when one constructs the syllogism.

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