Chapter:3 Syllogism

Chapter:3 Syllogism

WESTERN/ARISTOTLEIN SYLLOGISM

Meaning

• Syllogism in a very simple term is a 'conclusion drawn by using method of interference'.
• Arguments which consist of three propositions (statements), that are so related; when the premises are posited as true, the conclusion must also be true.
• It can also be defined as an ‘argument’ in which one proposition (the conclusion) is inferred (or drawn up) from two others (the premises) of a certain form.
• A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
• Deductive method of reasoning
• Discussed in syllogistic logic
• In Aristotle’s Prior Analytics, syllogism is defined as “a discourse in which, certain things having been supposed, something different from the things’ supposed results of necessity because these things are so.”

Structure of Categorical Syllogism

A categorical syllogism consists of three parts:

1. the major premise,
2. the minor premise, and

3. the conclusion. 

   Example: -

• Major premise: All humans are mortal.
• Minor premise: Socrates is a human

• Conclusion: Therefore, Socrates is mortal.

   

TYPES OF CATEGORICAL SYLLOGISM: 

Rules of syllogism and fallacies (Syllogistic Fallacies):

1. In a valid standard form categorical syllogism, there must be exactly three terms, each of which is used in same sense throughout the argument. A fallacy of four terms/fallacy of equivocation occurs when a term is used in a different way within the course of an argument.

Example: -

• Knowledge is power. Power tends to corrupt.
• Therefore, knowledge tends to corrupt.
• (This commits the fallacy of equivocation/four terms, because the word "power" is being used in different senses in the first two premises and indeed arguably has no precise meaning at all in the second premise.)

2. In a valid standard form categorical syllogism, middle term must be distributed in at least one premise. The fallacy of the undistributed middle term occurs when this doesn't happen.

Example: -

All Russians(S) were revolutionist (P). 

All anarchists(S) were revolutionist (S).

Therefore, all anarchists (S) were Russian (P).

(This commits the fallacy of undistributed middle, because the middle term (Russians) is not distributed in at least one of the premises.)

3. In a valid standard form categorical syllogism, if any term is distributed in the conclusion, it must be distributed in the premises. The fallacy of “illicit process of major term “or “illicit process of minor term "makes the argument fallacious when this doesn’t happen. The fallacy of illicit major occurs when the major term is distributed (As subject) in the conclusion, but not in the (major) premise. The fallacy of illicit minor occurs when the minor term is distributed in the conclusion, but not in the (minor) premise.

Example: -

All Protestants are Christians. 

No Catholics are Protestants.

Therefore, no Catholics are Christians.

(The term ‘Christian ‘is distributed in the conclusion, but not in the major premise as subject. Thus, this commits ‘fallacy of illicit major ‘)

Example:

All cats are felines. 

All cats are mammals.

Therefore, all mammals are felines.

(The minor term here is mammal, which is not distributed in the minor premise (as Subject). However, in the conclusion mammal is distributed. Thus, this commits “fallacy of illicit minor “.)

4. In a valid standard form categorical syllogism, there can’t have both premises negative. The fallacy of exclusive premises occurs when a syllogism has two premises that are negative.

Example: -

• No cats are dogs.
• Some dogs are not pets. 
• Therefore, some pets are not cats.
• (Two negative premises cannot give a logical foundation for a conclusion, as they will invariably be independent statements that cannot be directly related, thus the name 'Exclusive Premises'.)

5. In a valid standard form categorical syllogism, the conclusion of a syllogism must be negative, if either premise is negative. Drawing Affirmative conclusion from a negative premise (illicit negative) is a fallacy that is committed when a syllogism has a positive conclusion and one or two negative premises. Similarly, drawing negative conclusion from an affirmative premise (illicit negative) is a fallacy that is committed when a syllogism has a positive conclusion and one or two negative premises.

Example:

• No fish are dogs. 
• No dogs can fly.

• Therefore, all fish can fly. (Illicit negative)

   

• All colonels are officers.
• All officers are soldiers.
• Therefore, no colonels are soldiers. (Illicit positive)

6.  In a valid standard form categorical syllogism, no particular conclusion may be drawn from two universal premises. An existential fallacy occurs whenever a particular conclusion appears with two universal premises. Or, in a valid categorical syllogism, if the two premises are universal, then the conclusion must be universal, as well.

Example: -

• All mammals are animals.
• All tigers are mammals.
• Therefore, some tigers are mammals.
• (In both examples, the fallacy is committed because we have two universal premises but a particular conclusion)

Nyaya Syllogism/Anumana

Nyaya philosophy is one of the six orthodox or astika schools of Hindu philosophy which deals particularly to the science of logic. It was propounded by Aksapada Gautama (Gotama) in 3rd or 2nd century BCE. In Nyaysutra, Gautama has suggested four means of obtaining valid knowledge: perception, inference (anumana), comparison and verbal testimony.

Nyaya syllogism introduces a concept of five-part syllogism. They are: -

1. Pratigya (statement required to be proved)
2. Hetu (reason)
3. Udaharan( example)
4. Upanaya (application)
5. Nigmana (conclusion)

Example: -

This hill is fiery. (Pratigya)

 Because it is smoky. (Hetu)

Anything which is smoky is fiery. ( Udharan) 

So, it is hill. (Upanaya)

Therefore, this hill is fiery. (Nigmana)

Fallacies in Nyaya Syllogism

The validity of the knowledge is also tested by use of the method of finding logical error or fallacies. If provides five different types of logical fallacies. 

• Sabayi- bihichara (the inconclusiveness- the conclusion drawn up are more than one)
• Birudha(contradictory)the statement opposes the one that is supposed to be established)
• Prakaran Sama (controversial) the statement provokes or alters the very question that is meant to be settled.
• Sadhya sama (counter questioned) the logic itself is unproved
• Kalatita (mistimed) the logic is adduced when the time in which it might hold good does not apply.

ANUMANA/NYAYA SYLLOGISM v. WESTERN SYLLOGISM: visit premium version…