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.

(S is a Subject, P is a Predicate)

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 by Patrick Hurley or Aristotelian Logic by W. Parry.

Exercises

Hier you can check your knowledge about the syllogism. There are different types of exercises. Have fun while doing them.

Exercise 1

Indicate whether the following arguments are valid or invalid. If the syllogism is invalid indicate which rule of logic was violated. For the solutions, mark the following paragraph (which is seemingly empty) with your mouse.

Hint: you can first think about: what is the middle term of the syllogism. Then what kind of statment is the first permise is that: A, I, E or O, and what kind of statment is the conclusion.
Second you can check if the middle term is distributed at least once. If it is not, you do not need to proceed further, the syllogism is invalid.
Third, if there are any distributed terms in the conclusion, check to see if those very terms are distributed in the premises.
Finally check the rest of the rules. If no rules are violated, the syllogism is valid.

1.

Nothing easy is worthwhile.
Nothing good is easy.
Therefore, nothing good is worthwhile.

Perfect!!
This syllogism is invalid. No conclusion can be drawn from two negative premises.

2.

All married people know about marriage problems.
No priests are married people.
Therefore, no priests know about marriage problems.

Correct!!
This syllogism is invalid because “Know about marriage problems” is distributed in the conclusion, but is undistributed in the first premise.

3.

Mathematicians know what mathematics is.
No philosopher is a mathematician.
Therefore, no philosopher knows what mathematics is.

Invalid, Easy one, right??
“Knows what mathematics is” is distributed in the conclusion, but is undistributed in the first premise.

4.

All patriots are voters.
Some citizens are not voters.
Therefore, some citizens are not patriots.

Worked it out??
This syllogism is valid. The logic is valid, even though the conclusion may be false. For the first premise might be false. In other words, one may have false premises and a false conclusion, while the logic remains valid. It is also possible to have true premises and a true conclusion but false logic (the conclusion simply does not follow from the premises).

5.

All scientific knowledge is a work of reason.
All scientific knowledge is true.
Therefore, all that is true is a work of reason.

Found the answer??
This syllogism is invalid. “All that is true” is distributed in the conclusion, but is undistributed in the second premise.

6.

No oak trees bear fruit.
No maple trees bear fruit.
Therefore, no oak trees are maples.

Well done!!
This syllogism is invalid. One cannot conclude anything from two negative premises. The role of the Middle Term is to join the Major and Minor Terms. The Middle Term cannot do this if both premises are negative.

7.

All human action is conditioned by circumstances.
All human action involves morality.
Therefore, all that involves morality is conditioned by circumstances (moral relativism).

What is your result??
Yes, this syllogism is invalid. Any term which is distributed in the conclusion must also be distributed in the premises (“All that involves morality” is distributed in the conclusion, but not in the second premise).

8.

All that is good is pleasant.
All eating is pleasant.
Therefore, all eating is good.

Strike!!
This syllogism is also invalid. Undistributed Middle Term.

9.

No man is perfect
Some men are presidents.
Therefore, some presidents are not perfect.
Another light question, don't you think?
This syllogism is valid.

10.

All educated people have worked hard.
Some students are not educated.
Therefore, some students have not worked hard.

That's right!!
This syllogism is invalid because The term “not worked hard” is distributed in the conclusion, but it is undistributed in the first premise.

Exercise 2

In the following syllogistic arguments the conclusion is missing. Study the two reasons very carefully and complete the syllogism with the conclusion that logically follows. For the solutions, mark the following paragraph (which is seemingly empty) with your mouse.

Hint: Look carefully at the arguments. What is the subject, what is the predicat of the syllogism?

1. All fragile things are breakable things.
Some glasses are fragile things.
Therefore,...

Well done!
Some glasses are breakable things.

2. All mammals are warm-blooded animals.
All whales are mammals.
Therefore,...

Good job!
All Whales are warm-blooded animals.

3. All flowers are pretty objects.
All pansies are flowers.
Therefore,...

It was not so difficult, right?
All pansies are pretty objects.

4. All A are B
Some C are not B.
Therefore,...

Worked it out?
Some C are not A.

Exercise 3

You are supposed to rewrite the following arguments as standard-form syllogisms and name the mood of each argument. For the more advanced Learner name the figure of the syllogism. Decide if this syllogism is valid or invalid.

Example:
All mental decisions are things describable by science, but no things describable by science are uncaused happenings; it follows that no mental decisions are uncaused happenings.

Answer:
No things describable by science are uncaused happenings.
All mental decisions are things describable by science.
No mental decisions are uncaused happenings.

This is an EAE-1 syllogism and this syllogism is valid

Now is your turn.

1. Some human is not Athenian, but all Athenians are Greek; it follows that some human is not Greek.

All Athenians are Greek.
Some human is not Athenian.
Therefore, some human is not Greek.

This is an AOO-1 syllogism and this sylogism is valid.

2.

All liars are wicked, but not all liars are self deceived; it follows that all wicked are self deceived.

All liars are self deceived.
All liars are wicked.
All wicked are self deceived.

This is an AAA-3 syllogism and this syllogism is also valid.

3.

Some divine being is human, but no human is omniscient; it follows that some divine being is not omniscient.

No human is omniscient.
Some divine being is human.
Some divine being is not omniscient.

This is an EIO-1 syllogism and this syllogism is also valid.

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/

http://www.mentesenblanco-razonamientoabstracto.com/silogismos-ejercicio1-en.html