Syllogism

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Syllogism

/ˈsɪləˌdʒɪzəm/

Definition

A syllogism is a logical argument composed of three parts: the major premise, the minor premise, and the conclusion inferred from the premises. I will help you to understand the syllogism you just need to follow this article step by step.

Steps

First Step

First thing that you have to know is the basic structure of syllogism. As you already know the syllogism consists of three propositions :

1. major premise
   
2. minor premise and
   
3. conclusion
   

in which there appear a total of exactly three categorical terms, each of which is used exactly twice. Each of the premises has one term in common with the conclusion: the major term in the major premise, which forms the predicate of the conclusion, and the minor term in the minor premise, which forms the subject of the conclusion. The categorical term in common in the premises is called the "middle term". For instance:

Major premise: No geese are felines.
Minor premise: Some birds are geese.
Conclusion: Therefore, Some birds are not felines.

In this example you can see that "felines" is the major term and predicate of the conclusion, "bird" is the minor term and subject of the conclusion, and "geese" is the middle term.

Second Step

It is easier when you try to think of each term as representing a category. For instance "plant" is a category composed of everything that can be described as a plant.

Third Step

You can notice that each part is expressed as "Some/all/no S is/are [not] P," and have four possible variation. The universal affirmative (symbolized as A) is expressed as "all S is/are P,". The universal negative (symbolized as E) is expressed as "no S is/are P,". The particular affirmative (symbolized as I) is expressed as "some S is/are P,". The particular negative (symbolized as O) is expressed as "some S is/are not P,". This you can see in the table below:

A |All |S |are |P |universal affirmatives |All humans are mortal.
E |No |S |are |P |universal negatives |No humans are perfect.
I |Some |S |are |P |particular affirmatives |Some humans are healthy.
O |Some |S |are not |P |particular negatives |Some humans are not clever.

Fourth Step

The fourth step is to determine the figure of the syllogism. Depending on whether the middle term serves as subject or predicate in the premises, a syllogism may be classified as one of four possible figures.

Fifth Step

For the next step you have to decide if the syllogism is valid. A valid Argument is an argument whose premises are true and then the conclusion has to be true. If a syllogism is valid it is not possible for its premises to be true while its conclusion is false. An example of valid argument can be: There are over seventy students in this classroom; therefore, there are over ten students in this classroom.

Attention

You have to be aware that the fallacy of illicit minor and illicit major can occur. A formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion is called illicit major. The example of this fallacy is in the form All A are B; no C are A. Therefore, no C are B. For instance, "All cats are animals"; "no dogs are cats"; therefore, "no dogs are animals": this syllogism is invalid because the major term "animals" is undistributed in the major premise, but distributed in the conclusion.

Categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion committed the fallacy of the illicit minor. An example of this is in the form All A are B; all A are C. Therefore, all C are B. For instance, "All cats are mammals"; "all cats are animals"; therefore, "all animals are mammals": this syllogism is invalid because the minor term "animals" is undistributed in the minor premise (because not all animals are cats), but distributed in the conclusion.

Tip

If I awake your interest about the syllogism, and you want to know more details, you can click on this link: syllogism or read A concise introduction to logic Patrick Hurley or Aristotelian Logic by W. Parry.

References and links

Hurley, P.,J. (2012). A concise introduction to logic. Wadsworth

Parry, W.,T. (1991). Aristotelian Logic. State University of New York Press

http://plato.stanford.edu/entries/aristotle-logic/