Structure of Categorical Propositions MCQ Quiz in मल्याळम - Objective Question with Answer for Structure of Categorical Propositions - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Hence, among the above statements, statement B, C and D of categorial propositions contraposition is valid.

Hence, the correct answer is B, C and D only.

Additional Information

• A  categorical proposition is a simple proposition containing two terms, subject(S) and predicate (P), in which the predicate is either asserted or denied of the subject.
• Every categorical proposition can be reduced to one of four logical forms, named A, E, I and O.
• The 'A' proposition, is the universal affirmative usually translated as 'All S is P'.
• In the 'E' proposition, is the universal negative is usually 'No S is P'.
• The 'I' proposition, is the particular affirmative usually translated as 'Some S are P'.
• In the 'O' proposition, is the particular negative is usually translated as 'Some S are not P'

Key Points

• Contraposition is the inference in which the subject is interchanged with the complement of the predicate and the predicate is interchanged with the complement of the subject.
• In modern logic it is only valid for the A and O propositions. The valid contrapositive is logically equivalent to the original proposition.
• In traditional logic, the E proposition has a contrapositive by limitation which is the subaltern of the invalid E-contrapositive; i.e., the corresponding O proposition. The contrapositive by limitation is implied by the original but is not (usually) equivalent to it.

Proposition is a statement that provides the relation between two or more terms given in the statement. Any statement in logical reasoning is termed as a proposition.

A proposition is assumed to be true and then a conclusion is drawn from it. For example, “All dogs are tree” is assumed to be true as a proposition, but in actual fact, we all know that dogs and trees are entirely different entities or terms. There are four parts of the proposition that includes quantifier, subject, predicate, and copula.

• Quantifier: It consists of the terms like All, no, and some which specify a quantity. “All” and “no” are universal quantifier whereas “Some” is a particular quantifier.
• Subject: A person or thing about which something is being described.
• Predicate: Something that affirms or denies the subject.
• Copula: It tells the relation between subject and predicate.

A proposition that affirms or denies something without any condition is called categorical composition. Quality is an attribute of every statement/proposition which is determined by whether the proposition affirms or denied class inclusion.

For example,

All pillow is soft

All junk food is not good.

Categorical propositions can have one of the two qualities—affirmative or negative that can be understood through “Classification of the proposition”.

The square of opposition is a diagram used in categorical logic to depict the logical relationship that exists between particular propositions based on their form.

Key Points

Diagram of the Square of Opposition, where A E I O are the Proposition. 

Condition of the Sub-contrary. 

• I and O propositions are subcontrary.
• It is always between Particulars. 
• Both Statements can't be False at the same time but both can be True. 
• If One is False the other will be true definitely. 
• If One is True the other will be Doubtful. 

Therefore, If two propositions both cannot be false but both may be true, the relation between the two propositions is called Sub-contrary. 

Additional Information

• Rules of Contradictory:
  • A and O, E, and I propositions are contradictory. ​
  • If One is True the other will be false definitely.
  • If One is False the other will be True definitely. 
• Rules of Contrary:
  • A and E propositions are contrary. 
  • It's always Between Universal.​
  • Both statements cannot be true at the same time but both can be False. 
  • If One is True the other will be False definitely. 
  • If One is False the other will be  Doubtful. 

A categorical proposition is a proposition that relates two classes of objects. Categorical propositions contain a subject and a predicate term. 

The subject term comes first in a standard-form categorical proposition.

The predicate term comes second in a standard-form categorical proposition.

There are four types of categorical proposition:

Such a proposition asserts that there is at least one thing which is a member of the class designated by the subject term but not a member of the class designated by the predicate term. Since it affirms that the one or more crucial things are distinct from each and every member of the predicate class, a proposition of this form distributes its predicate term but not its subject term.

Hence, “Some birds are mammals” is a particular affirmative proposition and it distributes neither subject term nor predicate term is correct.

​ 

The Square of Opposition

When two categorical propositions are of different forms but share exactly the same subject and predicate terms, their truth is logically interdependent in a variety of interesting ways, all of which are conveniently represented in the traditional "square of opposition."

There are four ways in which propositions may be opposed as Contradictories, Contraries, Sub-contraries, Subalterns and Superalterns.

Contradictories- The standard form of a categorical proposition that has the same subject and predicate term but differs from each other in both quantity and quality. Two propositions if one is denial of the other if they can’t be true or can’t be both false.

For example –

All students are intelligent.

Some students are not intelligent.

Contraries- Two propositions are said to be contraries if they can’t both be true, and the truth of one entails the truth of other i.e. both can’t be true and both can’t be false. If either of these propositions is true, then the other must be false.

For example –

All students are intelligent.

No students are intelligent.

Subcontraries- If the particular propositions having the same subject and predicate terms but differing in quality, one affirming the other denying. Two propositions are said to be subcontraries if both of them together cannot be false although they may both be true.

For example –

Some students are intelligent.

Some students are not intelligent.

Subalternation- It is the opposition between a Universal proposition and its corresponding proposition. In the corresponding particular proposition, the universal proposition is called the superaltern and the particular proposition is called subaltern.  These propositions have the same subject and predicate terms and agree on quality. Both are affirming or both denying but differ in quantity.

For example –

No students are intelligent.

Some students are not intelligent. 

The correct answer is A, B and C only.
Key PointsProposition A states that no women are arrogant human beings, which can be rephrased as "All women are non-arrogant human beings" (by converting the negative statement to an equivalent positive statement).

Proposition B states that no arrogant human beings are women, which can be rephrased as "All non-women are non-arrogant human beings" (by converting the negative statement to an equivalent positive statement and reversing the subject and predicate).

Proposition C states that all women are non-arrogant human beings, which is equivalent to proposition A (by using the conversion rule mentioned above).

Proposition D states that all non-arrogant human beings are non-women, which is not equivalent to any of the other propositions. It is the contrapositive of the converse of proposition A.

Therefore, the logically equivalent propositions are A, B, and C
Additional InformationA logical argument is a process of creating a new statement from the existing statements. It comes to a conclusion from a set of premises by means of logical implications via logical inference.

According to the law of excluded middle, a proposition is either true or false.

Law of excluded middle:

• There are three fundamental law of thought
  • Law of non-contradiction: A proposition could be true and false simultaneously
  • Law of identity:  
  • Law of excluded middle: A proposition is either true or false
• The law of excluded middle states that a proposition is true or its negation is true.
• It means that a statement is either true or false.
• It excludes a middle ground between truth and falsity. 
• There is no middle ground between being true and being false.
• 

In logic, the categorical proposition asserts or denies that all or some of the members of one category are included in another. A proposition is assumed to be true and from which a conclusion can be drawn. The proposition consists of the following four parts :

1. Quantifier: All, no, and some. They specify a quantity. ‘All’ and ‘no’ are universal quantifiers and ‘some’ is a particular quantifier.
2. Subject (S): About which something is being said.
3. Predicate (P): Something that affirms or denies the subject.
4. Copula: Relation between subject and predicate.
   • Quantifier + Subject + Copula + Predicate

Quality: Categorical propositions can have one of the two qualities—affirmative or negative.

CLASSIFICATION: Propositions are basically of two types, namely universal and particular. Both of them can further be divided into two parts.

Hence, "All tigers are animals", is an example of Universal Affirmative.

Verbal testimony is a statement with certain criteria that is a means of genuine information. 

Key Points

Thus, A - IIII, B - IV, C - I, and D - II are correct matching.

A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.

Key Points Assertion A: In a valid categorical syllogism, the middle term must be distributed in at least one premise.

• Categorical syllogisms are sets of three categorical propositions.
• The first two are given and presumed to be true.
• These first two categorical propositions are called premises.
• The third categorical proposition is the conclusion.
• A categorical proposition is termed "valid" if the premises are sufficient to support to prove the conclusion true.
• The premises are always presumed to be true.

Hence Assertion is true.

Reason R: The conclusion of a valid argument cannot assert any more than is contained in the premises.

• An argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true.
• If all the premises are true, then the conclusion must be true.
• It is impossible that all the premises are true and the conclusion is false.

Hence it is true that the conclusion of a valid argument cannot assert any more than is contained in the premises.

Therefore, based on the above statement we can conclude that both A and R are true but R is NOT the correct explanation of A.

Key Points

Statement I: Mimāmsakas and Vedāntins agree with the Naiyāyikas that the syllogism consists of five members or propositions.

• Mimamsa, (Sanskrit: “Reflection” or “Critical Investigation”) is one of the six systems (darshans) of Indian philosophy.
• Mimamsa, probably the earliest of the six, is fundamental to Vedanta, another of the six systems, and has deeply influenced the formulation of Hindu law (see Indian law).
• Nyaya syllogism consists of five members or propositions where four propositions are considered as premises and the fifth one is the conclusion

The following is a typical Nyaya syllogism:

1. Socrates is mortal (Pratijna).
2. Because he is a man (hetu).
3. Whoever is a man is a mortal, e .g Pythagoras (Udaharana).
4. Socrates is a man who is invariably a mortal (upanaya).
5. Therefore Socrates is mortal (nigamana).

Hence, the statement I is incorrect.

Statement II: Mimāmsakas and Vedantins agree with the Naiyāyikas that the syllogism is necessary only for parārthānuma̅na or demonstrate inference and not for svārthānumāna or inference for oneself.

• The aim of Mimamsa is to give rules for the interpretation of the Vedas, the earliest scriptures of Hinduism, and to provide a philosophical justification for the observance of Vedic rituals.
• Because Mimamsa is concerned with the earlier parts of the Vedas (called the Karmakanda), it is also referred to as Purva-Mimamsa (“Prior Study”) or Karma-Mimamsa (“Study of Actions”).
• Vedanta, which deals with the later portion of Vedic literature called the Upanishads, is called Uttara-Mimamsa (“Posterior Study”) or Jnana-Mimamsa (“Study of Knowledge”).

Hence, Statement I is incorrect but Statement II is correct.