Proposition and Logical Deduction in eLitmus
Proposition is one of the important part in Elitmus pH test, in verbal section contains more than three questions are asked from proposition part. Proposition is easiest one in verbal section. In this post you find more details about Proposition and logical deduction questions and important rules for handling those questions.
Proposition
In Logic, any categorical statement is termed as the Proposition.
A Proposition is a statement that asserts that either a part of, or the whole of, one set of objects - the set identified by the subject term in the sentence expressing that statement - either is included in, or is excluded from, another set - the set identified by the predicate term in that sentence.
The standard form of a proposition is:
Quantifier + Subject + Copula + Predicate
Thus, the proposition consists of four parts:
1) Quantifier: The words 'all', 'no' and 'some' are called quantifiers because they specify a quantity 'All' and 'no' are universal quantifiers because they refer to every object in a certain set, while the quantifier 'some' is a particular quantifier because it refers to at least one existing object in a certain set.
2) Subject (denoted by 'S'): The subject is that about which something is said.
3) Predicate (denoted by 'P'): The predicate is the part of the proposition denoting that which is affirmed or denied about the subject.
4) Copula: The copula is that part of the proposition which denotes the relation between the subject and the predicate.
Four-Fold Classification of Propositions:
A proposition is said to have a universal quantity if it begins with a universal quantifier and a particular quantity if it begins with a particular quantifier. Besides, propositions which assert something about the inclusion of the whole or a part of one set in the other are said to have affirmative quality, while those which deny the inclusion of the whole or a part of one set in the other are said to have a negative quality. Also, a term is distributed in a proposition if it refers to all members of the set of objects denoted by that term. Otherwise, it is said to be undistributed. Based on the above facts, propositions can be classified into four types:
1) Universal Affirmative Proposition (denoted by A): It distributes only the subject i.e. the predicate is not interchangeable with the subject while maintaining the validity of the proposition.
2) Universal Negative Proposition (denoted by E): It distributes both the subject and the predicate i.e. an entire class of predicate term is denied to the entire class of the subject term, as in the proposition.
3) Particular Affirmative Proposition (denoted by I): It distributes neither the subject nor the predicate.
4) Particular Negative Proposition (denoted by O): It distributes only the predicate. e.g., Some animals are not wild. Here, the subject term 'animals' is used only for a part of its class and hence is undistributed while the predicate term 'wild' is denied in entirety to the subject term and hence is distributed. These facts can be summarized as follows:
Statement Form
|
Quantity
|
Quality
|
Distributed
|
(A): All S is P.
|
Universal
|
Affirmative
|
S only
|
(E): No S is P.
|
Universal
|
Negative
|
Both S and P
|
(I): Some S is P.
|
Particular
|
Affirmative
|
Neither S nor P
|
(O): Some S is not P
|
Particular
|
Negative
|
P only
|
Logical Deduction:
The phenomenon of deriving a conclusion from a single proposition or a set of given propositions, is known as logical deduction. The given propositions are also referred to as the premises.
Two Inferential Processes of Deduction:
I.Immediate Deductive Inference:
Here, conclusion is deduced from one of the given propositions, by any of the three ways -conversion, obversion and contraposition.
1) Conversion: The Conversion proceeds with interchanging the subject term and the predicate term i.e. the subject term of the premise becomes the predicate term of the conclusion and the predicate term of the premise becomes the subject of the conclusion.
The given proposition is called converted, whereas the conclusion drawn from it is called its converse.
Table of Valid Conversions
Converted
|
Converse
|
A: All S is P
Ex. All pins are tops. |
I: Some P is S
Some tops are pins. |
E: No S is P.
Ex. No fish is whale. |
E: No P is S.
No whale is fish. |
I: Some S is P.
Ex. Some boys are poets. |
I: Some P is S.
Some poets are boys. |
O: Some S is not P.
|
No valid conversion
|
Note that in a conversion, the quality remains the same and the quantity may change.
2) Obversion: In obversion, we change the quality of the proposition and replace the predicate term by its complement.
Table of Valid Obversions
Obverted
|
Obverse
|
A: All birds are mammals.
|
E: No birds are non-mammals.
|
E: No poets are singers.
|
A: All poets are non-singers.
|
I: Some nurses are doctors.
|
O: Some nurses are not non-doctors.
|
O: some politicians are not statesmen.
|
I: Some politicians are non-statesmen
|
Contraposition: To obtain the contra positive of a statement, we first replace the subject and predicate terms in the proposition and then exchange both these terms with their complements.
Table of Valid Contrapositions
Proposition
|
Contra positive
|
A: All birds are mammals.
|
A: All non-mammals are non-birds.
|
I: Some birds are mammals.
|
I: Some non-mammals are non-birds.
|
Note: The valid converse, obverse or contra positive of a given proposition always logically follows from the proposition.
II. Mediate Deductive Inference (SYLLOGISM): First introduced by Aristotle, a Syllogism is a deductive argument in which conclusion has to be drawn from two propositions referred to as the premises.
Example:
1. All lotus are flowers.
2. All flowers are beautiful.
3. All lotus are beautiful.
Clearly, the propositions 1 and 2 are the premises and the proposition 3, which follows from the first two propositions, is called the conclusion.
Term: In Logic, a term is a word or a combination of words, which by itself can be used as a subject or predicate of a proposition.
Syllogism is concerned with three terms:
1. Major Term: It is the predicate of the conclusion and is denoted by P (first letter of 'Predicate').
2. Minor Term: It is the subject of the conclusion and is denoted by S (first letter of 'Subject').
3. Middle Term: It is the term common to both the premises and is denoted by M (first letter of 'Middle').
Category: English, Preposition
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