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### Propositions

• 1. Proposition We have learned that proposition is the verbal expression of a judgment. It is a statement in which something is affirmed or denied. There are three general types of propositions: categorical propositions, hypothetical propositions, and modal propositions. Categorical Proposition is one which gives a direct assertion of agreement or disagreement between the subject and the predicate term. Hypothetical Proposition is a kind of proposition that does not declare an unconditional affirmation or denial, but expresses a relation of dependence such as an opposition or a likeness between two clauses. Modal Propositions is a kind of proposition which does not just only affirm or deny the predicate of the subject but also states the manner or mode of in which the predicate is identified. It does not simply declare that the predicate belongs to the subject but how the predicate belongs, or does not belong to the subject. However, the focus of this lesson is more about categorical propositions rather than the other two mentioned. Element and Structure of a Categorical Proposition A categorical proposition contains three elements namely: subject term, predicate term, and copula. The subject term is the object affirmed or denied in the proposition. The predicate term is the quality or attribute affirmed or denied by the subject. The copula is the element that links the subject to the predicate. It is the linking verb in grammar like the “am”, “is”, and “are”. The negated word “not” is part of the copula. Examples: All men are rational No monkeys are birds Some dancers are singers Some basketball players are not tall Quality and Quantity of Propositions The quality of a proposition consists in the nature of the proposition as either affirmative or negative. The proposition is affirmative if there is agreement between the subject term and the predicate term. The proposition is negative if there is disagreement between the subject term and the predicate term. The first and third proposition in the above given example are affirmative, while the second and the fourth proposition are negative. The quality of the proposition consists in the nature of the proposition as either universal or particular. It refers to the denotation or number of individuals or referents to whom the subject term applies. Thus, a proposition is universal, if
• 2. the subject term is universal. If the subject term is particular, the proposition is particular. In the example given above, the first and second propositions are universal, while the third and fourth examples are particular. In the proposition there are concrete indicators that will tell us the quantity of the proposition. They are called the quantifiers. Universal Quantifiers. All, every, any, whatever, wherever, anything, everything, no, none, nothing, never, and others that are similar to these. Particular Quantifiers. Some, most, several, many, few, at least one, not all, majority and others. Combining the quality and quantity of propositions, we come up with four types of categorical propositions. Four Types of Propositions 1. Universal Affirmative Propositions or “A” Proposition 2. Universal Negative Propositions or “E” Proposition 3. Particular Affirmative Proposition or “I” Proposition 4. Particular Negative Proposition or “O” Proposition Standard Forms A: All S is P E: No S is P I: Some S is P O: Some S is not P A mnemonic device for the four types of proposition is to remember Affirmo and Nego. Following the standard form above, a model statement can be represented as Quantifier + Subject Term + Copula + Predicate Term Distribution of a Term A distributed term is a term of a categorical proposition that is used to refer to every member of a class. If the term is not being used to refer to each and every member of the class then the term is undistributed. Consider the following: A: All birds are winged creature E: No Birds are wingless creature I: Some birds are black things O: Some birds are not black things
• 3. The chart below represents the distribution of the above statements Proposition Subject Predicate A Refers to all birds Does not refer every member, e.g. bats, flying fish E Refers to all birds by indicating that they are not part of the predicate class Refers to every winged creature by indicating that they are not part of the subject class I Refers only to some birds Refers only to some black things, that is, those which are birds O Refers only to some birds, not all of them Refers to all members of the class, that is, not one of them is in the class referred to as “some bird” Only Universal propositions, either affirmative or negative, distribute their subject terms. Particular propositions, both affirmative and negative, do NOT distribute their subject terms Thus the quantity of any categorical proposition determines whether its subject is distributed! Only Negative propositions, either universal or particular, distribute their predicate terms Affirmative propositions, either universal and particular, do NOT distribute their predicate terms Thus the quality of any categorical proposition determines whether its predicate is distributed! So, here is the key to determining the how categorical propositions distribute their Subjects and Predicate terms: Universal Quantity distributes the Subject term Negative Quality distributes the Predicate term! Quantity, Quality, and Distribution Table Following the discussion on the form, quantity, quality and distribution, the table below summarizes the topic. Proposition Standard Form Quantity Quality Distribution Subject Predicate A All S is P Universal Affirmative Distributed Undistributed E No S is P Universal Negative Distributed Distributed I Some S is P Particular Affirmative Undistributed Undistributed O Some S is not P Particular Negative Undistributed Distributed
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