Maharashtra Board Class 12 Logic Chapter 3 Predicate Logic PDF Download

Predicate Logic

Frege's discovery of qualification, the deepest single technical advance ever made in logic.

Read the following argument.

All scientists are intelligent.

All intelligents are creative.

Therefore all scientists are creative.

Is this argument valid?

Test validity of this argument by using the method of truth table, shorter truth table, direct deductive proof. C.P and, I.P.

What answer do you get?

3.1 Need for Predicate Logic

The logic we have studied so far is known as propositional logic. The methods that we have studied in propositional logic like, Truth table, Shorter truth table, Direct deductive proof, C.P. and I.P. cannot decide or prove validity of all arguments. These methods can be used only for those arguments whose validity depends upon the ways in which simple statements are truth-functionally combined into compound statements. The branch of logic which deals with such type of arguments is called Propositional logic.

In Propositional logic a proposition is taken as one unit. It does not involve analysis of the proposition. It does not take into consideration how terms in the propositions are related. However there are certain types of arguments whose validity depends upon the inner logical structure of the non-compound statements it contains. Methods of propositional logic are not adequate in testing validity of such arguments. Let us take an example.

All singers are creative.

Mahesh is a singer.

Therefore, Mahesh is creative.

In propositional logic by using propositional constants one can symbolize the above argument as follows:

S

M / ∴ C

It is obvious that the above given argument is valid but it cannot be proved to be valid by the methods of propositional logic. The method of truth table on the contrary shows that the argument is invalid. All the three statements involved in the argument are non-compound statements. The inner logical structure of these statements and the relation between the terms involved in the statements is important in deciding the validity of this argument. The relation between the class of singer and the class of creative people is stated in the first premise. It states that the class of singers is included in the class of creative people i.e. whoever is a singer is also creative. The second premise states that the individual Mahesh belongs to the class of singer and therefore in the conclusion it is validly inferred that Mahesh also belongs to the class of creative people. When the argument is symbolized in propositional logic as stated above the inner logical structure of the statements and the relation between the terms involved is not revealed. It is therefore necessary to symbolize the argument in such a way that the inner logical structure of the statements is revealed and then one can prove validity of such arguments. The branch of logic which deals with such types of arguments is known as Predicate logic or Predicate calculus.

Like propositional logic, in predicate logic a proposition is not taken as one unit. The propositions are analyzed and symbolized to reveal, how the terms in the propositions are related with each other. However, Predicate logic is not totally different from propositional logic. The methods and notations of propositional logic are used in predicate logic so far as they are applicable to the non-compound statements with which it deals. If a formula is valid in propositional logic, the corresponding formula in predicate logic will also be valid. Though predicate logic includes propositional logic and is based on it, predicate logic goes beyond propositional logic since it reveals the logical structure of the propositions and the relation between the different terms of the proposition.

Can you recognize and state how the following non compound propositions differ from each other? How can we classify them?

Everything is beautiful.

Ashish is smart.

All birds have wings.

Some children are brilliant.

Nilesh is not tall.

No farmer is rich.

Nothing is permanent.

Some things change.

Some mobile phones are not expensive.

Some things are not attractive.

Teacher's Note

Predicate logic helps us understand deep arguments like "All teachers are guides, Ravi is a teacher, so Ravi is a guide." This is used in schools and law courts to check if thinking is correct.

Exam Trick

Remember: Propositional logic treats statements as whole units. Predicate logic breaks them down into parts. Just like when you read a book, sometimes you need to look at the whole story, sometimes at each sentence separately.

Points to Remember

Propositional logic takes statements as one complete unit.

Predicate logic analyzes the inner parts of statements.

Both types of logic are important in mathematics and philosophy.

Predicate logic can prove arguments that propositional logic cannot.

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