An overview Lecture prepared for MODULE-13 (Western Logic) BY- MINAKSHI PRAMANICK Guest Lecturer, Dept. Of Philosophy.

EXISTENTIAL IMPORT OF CATEGORICAL PROPOSITION

An overview

Lecture prepared for MODULE-13 (Western Logic)BY-

MINAKSHI PRAMANICKGuest Lecturer, Dept. Of Philosophy

WHAT IS A JUDGEMENT?

JUDGMENT :Judgment is the mental operation of recognizing a relation of agreement or disagreement between two concepts or ideas. Thus in this judgment ‘Man is mortal’, a relation of agreement has been established between ‘man’ and ‘morality’; and in the judgment ‘No men are perfect’, a relation of disagreement has been established between ‘man’ and ‘perfection’.

JUDGEMENT AND PROPOSITION

PROPOSITION :A proposition is an expression of a judgment in language. Thus in the proposition ‘Men are mortal’, it expresses the relation of agreement between ‘men’ and ‘mortal’.

PROPOSITION AS PART OF AN ARGUMENT

CATEGORICAL PROPOSITION: In a deductive argument we present propositions that state the relations between one category and some other category . The propositions with which such arguments are formulated are therefore called “CATEGORICAL PROPOSITION”.

Categorical propositions are the fundamental elements, the building blocks of argument, in the classical account of deductive logic. Consider this argument-

EXAMPLE

No athletes are vegetarians.

All football players are athletes.

No football players are vegetarians.

This argument contains three propositions. Each of the premises is indeed categorical; that is, each premise affirms, or denies, that some class S is included in some other class P, in whole or in part.

THE FOUR KINDS OF CATEGORICAL PROPOSITIONS

UNIVERSAL AFFIRMATIVE PROPOSITION :In these we assert that the whole of subject class is included or contained in another class. For ex: “All politicians are liars.” They are also called A propositions. Any universal affirmative proposition can be symbolically represented as “All S are P.” ( S=subject , P=predicate )

UNIVERSAL NEGATIVE PROPOSITION :It asserts that the subject class is wholly excluded from the predicate class. For ex:“No politicians are liars”. Schematically categorical propositions of this kind can be written as “No S are P”.

PARTICULAR AFFIRMATIVE PROPOSITION :This proposition affirms that some member(s) of the subject class are member(s) of the predicate class. But it does not affirm this of subject class universally. For ex:”Some politicians are liars”. They are represented as I propositions. It is written schematically as “Some S are P”-which says that at least one member of the class designated by the subject term S is also a member of the class designated by the predicate term P.

PARTICULAR NEGATIVE PROPOSITION :It says that at least one member of the class designated by the subject term S is excluded from the whole of the class designated by the predicate term P. This denial is not universal. They are also called O propositions. For ex:”Some politicians are not liars”. It is written schematically as “Some S are not P”.

ARISTOTLE VS. BOOLE ON INTERPRETING CATEGORICAL PROPOSITIONS

In the interpretation of the ancient Greek Philosopher Aristotle, the truth of a universal proposition implies the truth of corresponding particular proposition.

In contrast, George Boole, a nineteenth-century English mathematician, argued that we can’t infer the truth of particular proposition from the truth of its corresponding universal proposition, because every particular proposition asserts the existence of its subject class; for e.g.:- If some politicians are liars, there must be at least one politician.

But universal proposition doesn’t assert the existence of it’s subject class, a universal proposition must be understood to assert only that, “If there is such a thing as a politician, then it is liar.”

Hence, the particular propositions (I&O) have EXISTENTIAL IMPORT and the universal propositions (A&E) have not.

According to the rules of validity of deductive argument, the conclusion cannot exceed the premises. So, if we infer the truth of particular proposition , which is a conclusion, from the truth of universal proposition , which is premise, then we make a fallacy, which is called the EXISTENTIAL FALLACY.

‘A’ PROPOSITION EXPRESSED BY VENN DIAGRAM

We label one circle S, for subject class, and the other circle P, for predicate class. The diagram for the A proposition, which asserts that all S are P, shows that portion of S which is outside of P is shaded out, indicating that there are no members of S that are not members of P. So the A proposition is diagrammed thus-

E PROPOSITION EXPRESSED BY VENN DIAGRAM

Here again S and P represent the subject and predicate terms. This kind of proposition denies the relation of inclusion between the two terms, and denies it universally. It tells us that no members of S are members of P.

The diagram for the E proposition will exhibit this mutual exclusion by having the overlapping portion of the two circles representing the classes S and P shaded out. So the E proposition is diagrammed thus-

I PROPOSITION EXPRESSED BY VENN DIAGRAM

The diagram for the I proposition indicates that there is at least one member of S that is also a member of P by placing an ‘x’ in the region in which the two circles overlap. So the I proposition is diagrammed thus-

O PROPOSITION EXPRESSED BY VENN DIAGRAM

The diagram for the O proposition indicates that there is at least one member of S that is not a member of P by placing an ‘x ‘in the region of S that is outside of P. So, the O proposition is diagrammed thus-

Venn diagram – A DECISION PROCEDURE

Let us now apply the Venn diagram test to an obviously invalid syllogism,-

All M are P All M are S Some S are P

Figure : III (3rd Figure ) Mood : AAI( DARAPTI )

According to Aristotelian Logic this argument is valid in Third figure. This argument has the valid mood DARAPTI, because, there was no concept of EXISTENTIAL IMPORT OF CATEGORICAL PROPOSITIONS.

But in the Boolean view this argument is invalid. Here, the conclusion of the argument is I proposition, which is a particular one, and it has Existential Import. But the two premises of this argument are A propositions which are universal propositions. They have no Existential Import. So, we can not infer, the truth of the conclusion from the truth of the premises.The argument violates the fundamental rule of Deductive Logic i.e., the conclusion should not go beyond the premises.

In this diagram, where S designates the Minor class , P the Major class and M the Middle class; the portions SPM,SPM,SPM have been shaded out by the premises. But the conclusion has not been diagrammed, because the parts SPM and SPM have not been crossed. Thus we see that diagramming both the premises of a syllogism of form AAI-3 does not suffice to diagram its conclusion, which proves that the conclusion says something more than is said by the premises, which shows that the premises do not imply the conclusion. An argument whose premises do not imply its conclusion is invalid. So our diagram proves that the given syllogism is invalid.

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