Notes on the Nature of Categorical Proposition

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Logic is concerned with arguments. It distinguishes good arguments from the bad ones. An argument consists of propositions Out of which one is called the conclusion and others are called premises. Arguments are either deductive or inductive. Notion of proposition is crucial to the notion of argument. Proposition for its definition depends on the notion of term, because proposition is a relation between terms.

A term, on the other hand, is a word or a combination of words that can be use either as a subject or a predicate of a given proposition. Hence to understand the notion of proposition we have to understand the notion of term, its relation to words as well as the notion of copula that relates the subject with the predicate in a proposition.

A word consists of a letter or a combination of letters conveying some meaning. For example, ‘a’ and ‘I’ are words consisting of one letter, and “table”, “chair” “students”, “mean’ “lion” are words consisting of many letters. A combination of words, expressing a complete sense is called a sentence.

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A sentence belongs to a particular language. It consists of a single word or a combination of words in conformity with the grammatical rules. For example, “Fire!’ “Go”, “The rose is red” etc. are sentences. First two sentences are one worded sentences and the last one is a sentence consisting of a combination of words.

Any arbitrary combination of words cannot be called a sentence. For example, “Going is Ram” is not a sentence though it is combination of words. In this case grammatical rules are not followed and thus it does not convey any meaning. By rearranging the words in the above expression we can obtain the expression such as “Ram is going” or “Is Ram going?” These are grammatically correct sentences.

Grammatically, sentences are of different types namely, assertive or declarative sentence (e.g. The rose is red”); imperative sentence (e.g. “Do not tell a lie”); interrogative sentence (e.g. Has the servant come back?); optative sentence (e.g. “May you be happy”) and exclamatory sentences  (e.g. “What a beautiful scenery is this !”).

A logician is not interested in all these types of sentences because all these, except the declarative sentence, are not used to assert or deny anything. Logicians are interested only in declarative sentences as they express propositions that are either true or false. Intuitively we may say that what a declarative sentence states or expresses is a proposition.

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A categorical proposition consists of three constituents ‘or parts, namely ‘subject’, predicate’ and ‘copula’. Note that unless otherwise qualified whenever we talk of proposition we shall mean categorical proposition. A proposition always asserts or denies something about something. About whom the proposition states something is called the subject and what it says is called the predicate of the proposition. The word or words that establish the relationship between subject and predicate is called the copula.

In other words, the copula of a proposition is a word (e.g. am’, ‘is’, ‘are’) or combination of words (e.g. ‘am not’, ‘is not’, ‘are not’) expressing the relation between subject and predicate. For example, in the proposition ‘Crows are black’, the word “crows’ is our subject as this proposition is conveying information about crows. The word ‘black’ is the predicate as it says that ‘black’ is true of crows. The word “are” relates both subject and predicate and thus “are” is the copula. Proposition is a relation between subject and predicate. The word or the combination of words that can be used either as a subject or as a predicate of a given proposition is called a term.

In the above proposition “Crows are black”, the word ‘crows’ is used as subject and the word ‘black’ is used as predicate. So “crows” and black are terms. But the word ‘are’ is used neither as a subject nor as a predicate and thus is a term. Its role is to relate both subject and predicate in the above proposition. Hence, it is called copula. The subject term refers to objects about which we are talking and the predicate term refers to what we are talking about the subject. Diagrammatically, the subject, predicate and copula of the given proposition “Crows are black” can be viewed as follows.

Subject term

Copula

Predicate term

Crows

are

black

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Though the proposition contains three elements (subject, predicate and copula) yet all declarative sentences in our everyday use of language may not exhibit all these three elements. For example, “Ram eats” expresses a proposition, where all these above three elements are not explicitly stated.

Hence we have to convert the proposition “Ram eats” is such a way so that all these three items are specified explicitly. For this purpose, it is convenient to identify the copula first. Then we can say what precedes the copula is the subject term and what succeeds the copula is the predicate term. Thus it is necessary to reflect on the nature of copula.

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