10 rules of categorical syllogism

Answer 1

An argument must meet all of the following conditions to be valid. Failing to meet one or more conditions shows an argument to be invalid.
1) The middle term must be distributed at least once.
2) If a term is distributed in the conclusion, then it must be distributed in its premise.
3) If one of the premises is negative, then the conclusion must be negative, and if the conclusion is negative, then one of the premises must be negative.
4) There must not be two negative premises.

Only the combination of true premises with a false conclusion in a valid argument is impossible. The validity of an argument is determined by its logical form rather than by its content. If an argument having a certain form is valid then all arguments having the same form are equally valid no matter how different the content may be. Likewise if an argument having a certain form is invalid then all other arguments with the same form will be invalid. A sound argument is a valid argument with all true premises.

Source(s):http://homepage.usask.ca/~wiebeb/Syllogism.html

Answer 2

The constituents of categorical syllogism are Matter and Form.

A. Matter: Proximate

Major Term -is a term with greater extension

-is the predicate of the conclusion

-is found in the major premise

Minor Term -is a term with lesser extension

-is the subject of the conclusion

-is found in the minor premise

Middle Term -is the term which compares the major and the minor term.

B. Matter: Remote

Major Premise -is the first premise, and it contains the universal principle.

Minor Premise -is the second premise, and it carries the application of the universal principle.

Conclusion -is the main claim of the argument.

B. Form: External and Internal

External form -is the expressional structure of the syllogism.

Internal form -is the constituent principle of the nature and unity of the syllogism.

Answer 3

The general rules regarding terms are: * (1) Only three terms may appear in the syllogism, each of which is used in the same sense throughout the argument. * (2) Neither the major nor minor term may be a universal in the conclusion, if it was only a particular term in the premises. * (3) The middle term may not appear in the conclusion. * (4) The middle term must be distributed at least once in the premises, that is, used as a universal The general rules of quantity and quality are: * (5) If both premises are affirmative, the conclusion must also be affirmative. * (6) Both premises may not be negative; one at least must be affirmative. * (7) If either premise is negative, the conclusion must be negative; if one of the premises is a particular proposition, the conclusion must be a particular proposition. * (8) No conclusion can be drawn from two particular premises; one at least must be a universal proposition.

Answer 4

1)The middle term must be distributed at least once in the premises.

Example (middle term is bolded)

VALID:

All animals (distributed) are living things (undistributed).

All cats (distributed) are animals (undistributed).

Therefore all cats are living things.

INVALID

All living things (distributed) are animals(undistributed).

All cats (distributed) are animals (undistributed).

Therefore all cats are living things.

2) A distributed term in the conclusion must have been distributed at least once in the premises.

VALID:

All animals (distributed) are living things (undistributed).

All cats (distributed) are animals (undistributed).

Therefore all cats (distributed) are living things.

INVALID

All cats (distributed) are animals (undistributed).

All animals (distributed) are living things (undistributed).

Therefore all living things (distributed) are cats (undistributed).

3) A syllogism with a negative premise must have a negative conclusion.

VALID:

All animals are living.

No pencils are animals.

Therefore no pencils are living.

INVALID

All animals are living.

No pencils are animals.

Therefore all pencils are living.

4) A syllogism with a particular premise must have a particular conclusion.

VALID:

Some turtles are pets.

All turtles are animals.

Therefore some animals are pets.

INVALID

Some turtles are pets.

All turtles are animals.

Therefore all animals are pets.

5) You cannot draw a conclusion if there are 2 negative premises.

Ex:

No cows eat bears.

No bears can fly.

Therefore: ?

You can explore these examples and others with the syllogistic machine at http://thefirstscience.org/syllogistic-machine/

Answer 5

The Ten Particular Rules of the Categorical Syllogism

1. Three Terms (TT): There must be three and only three terms in a categorical syllogism, each of which is used in exactly the same sense in the entire argument. Each of these terms is used twice but not in the same proposition.

2. Out of Place Middle Term (OPM): The middle term (M) must not appear in the conclusion. The Acronym OP stands for "Out of Place". If the middle term is found in the conclusion where it is not supposed to be, then it is out of place.

3. Overextended Major Term (OP): The major term (P) may not be universal in the conclusion if it is only particular in the premise. When that conclusion asserts more than what is indicated in the premises, and then we have a case of overextending. In other words, the quantity of the major term is wider in the conclusion than in the premise.

4. The Overextended Minor term (OS): The minor term (S) may not be universal in the conclusion if it is only particular in the premise. If the quantity of the minor term is wider in the conclusion than in the premise, then it is overextended or bloated.

5. Undistributed Middle Term (UM): The middle term (M) must be distributed or universal at least once in the premises. If in both premises are the quantity of the middle term is particular, it is unable to function as a medium of comparison. It is paralytic so to speak.

6. Affirmative Premises Affirmative Conclusion (APAC): If both premises are affirmative, the conclusion must also be affirmative. If the premises asserts that there is something, there is no way can be conclusion assert the there is nothing. Otherwise, it is Judas Kiss, a betrayal of the premises

7. Double Negative (DN): No valid conclusion can be drawn from two negative premises; at least either premise must be affirmative.

8. Negative Premise Negative Conclusion (NPNC): If either premise is negative, the conclusion must be negative.

9. Particular Premise Particular Conclusion (PPPC): If either premise is particular, the conclusion must be particular.

10. Double Particular (DP): No valid conclusion can be drawn from two particular premises.

Hope it will help you guys.! :)

Answer 6

The three parts of a categorical syllogism are the major premise, the minor premise and the conclusion. For example, all mammals have hair (major premise), all whales are mammals (minor premise), therefore, all whales have hair (conclusion).