Logic
Logic
The term “logic” came from the Greek word logos, which is sometimes translated as “sentence” “discourse”, “reason”, “rule”, and “ratio”
Briefly speaking, we might define logic as the study of the principles of correct reasoning or the study of the principles of reasoning, especially of the structure of propositions as distinguished from their content and of method and validity in deductive reasoning.
Proposition: In logic, any categorical statement is termed as the proposition.
The standard form of proposition is consists of four parts
- Quantifier
- Subject
- Copula
- Predicate
Example: 1
All \[\to \] books \[\to \] are \[\to \] pens
\[\downarrow \] \[\downarrow \] \[\downarrow \] \[\downarrow \]
Quantifier \[\to \] subject \[\to \] copula \[\to \] predicate
Example: 2
Some \[\to \] dog \[\to \] are \[\to \] cats
\[\downarrow \] \[\downarrow \] \[\downarrow \] \[\downarrow \]
Quantifier \[\to \] subject \[\to \] copula \[\to \] predicate
Quantifier: The words which specify the quantity like ‘all’, ‘no’ and some.
Universal quantifier: The words ‘All and No’ are called universal quantifiers because they refer to every object in a certain set.
Particular quantifier: The word ‘Some’ is known as particular quantifier because it refers to at least one existing object in a certain set.
Subject (denoted by ‘S’): The subject is that about which something is said.
Predicate (denoted by ‘P’): It is the part of the proposition denoting that which is affirmed or denied about the subject.
Copula: It is the part of the proposition which denotes the relation between the subject and the predicate.
Note: We should keep in mind that the quantifiers (‘all’, ‘no’, ‘some’) are implied in all categorical propositions even though they are not explicitly stated. If these quantifiers are not explicitly used in the formulation of the propositions it is aid to be in non-standard form.
Quality: The kind of affirmation made by the proposition
Affirmative: asserts a quality to a class
Negative: denies a quality to a class
When we put the quality and quantity of categorical proposition together we see that there are four and only four possible arrangements:
- Universal Affirmative
- Particular Affirmative
- Universal Negative
- Particular Negative
Distribution: The quantity associated with either the subject or predicate term of a categorical proposition.
Four-Fold Classification of Propositions
A proposition, which begins with a universal quantifier, is said to have universal quantity. And a proposition, which begins with a particular quantifier, is said to have particular quantity. Besides, a proposition which asserts a quality to a class is called affirmative quality and a proposition which denies a quality to a class is called negative quality. Also, a term is distributed
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