# Comprehension extension and their inverse relationship

### Elements of Logic 18

Posts about Inverse Relationship written by Maria. SOME women confess their conflicting views about motherhood, marriage and working members of a category that also carry the same 'extension' is COMPREHENSION. Properties (functions) LOGICAL RULE: THERE IS A REVERSE RELATIONSHIP BETWEEN COMPREHENSION AND EXTENSION - Greater. anyone offering a serious appraisal of their validity, the question arises whether (comprehension, extension, and their inverse relationship), pp (the.

## The TERM in Logic

Mediate terms are formed indirectly, that is, through the mediation of other ideas. God, soul, spirit, universe D. According to the nature of referents: Concrete, Abstract, Logical, and Null 1. A term is concrete if its referent is tangible or can be perceived by the senses. Concrete term also refers to that which indicates a quality or characteristic as inherent in a subject.

A term is abstract if its referent is intangible or can be understood only by the mind and cannot be perceived by the senses. Abstract term also refers to the quality or characteristic considered independently from the subject in which it inheres. A term is logical if it was formulated to serve as linguistic device to aid learning. A term is null or empty if it has no actual or real referents but is only imaginary.

According to definiteness of meaning: Univocal, Equivocal, and Analogous 1.

A term is univocal if it exhibits exactly identical sense and meaning in different incidents. For example, we say Canines are dogs and Dalmatians are dogs. Theterm dogs is univocal, unless we give a different meaning in any of the term dogs in the statements.

Peter is a man. A term is equivocal when it indicates entirely different meanings in different occurrences. In the statements, Stars are heavenly bodies and Nicolas Cage and Brad Pitt are stars, the term stars is equivocal for the meaning of the term stars in the first statement is different from that of the second. An equivocal term thus is not one but two terms. A term is analogous when it shows partly identical and partly distinct meanings in different occurrences.

In the phrases head of a man and head of a family, the terms head in some sense are similar but nonetheless different in some aspects. Compatible terms are terms that can coexist in a subject, that is, there is no logical obstacle for them to be present in a subject at the same time.

Incompatible terms are terms that cannot coexist in a subject for they rule out each other. The following are kinds of incompatible terms: Contradictories are so mutually exclusive that there is no middle ground or third possibility between them. When some said that her girlfriend is not black, it is not safe to conclude that he must be white, for he may be brown or yellow.

White and black therefore are contrary not contradictory terms. In their meaning, they imply reference to one another. Yet, it has different meanings for it is used in different ways in the propositions. The various functions of a term in the proposition is called the supposition of term. Medieval philosophers developed supposition theory in the late twelfth century to identify the specific usage and meaning of a term in various propositional contexts.

Latin logicians called the different uses of the term its suppositiones, from sup ponere, 'to stand for'. The people assembled themselves together in the chapel. The people voted in the election. Both of these statements have the collective term people as their subject. The terms people however differ in supposition. In a sentence with plural or collective subject e. Such is the case in the first statement.

When the predicate applies to members of the subjecttaken as a group, the supposition is collective suppositio collectiva. Real and Logical Supposition When the term is used to refer to the object as it is in the real order, the supposition is real suppositio realis.

When used to denote the object as it is in the conceptual order, the term has logical or formal supposition suppositio logica. Personal and material supposition A term has personal supposition when it is employed to talk about the object or person it represents, for example, dog in Ed is feeding the dog.

When a word is taken to signify simply its inscription or utterance, it is in its material supposition suppositio materialis. Dog has three letters. Genus- a universal idea which expresses a part of the essence of a thing, that part which is common with other species in the same class. A lake is a body of water. Specific Difference- a universal idea which expresses a part of the essence of a thing, that part which differentiates it from that of other species.

A lake is water surrounded by land. Species- a universal idea that expresses the complete essence of a thing. Adding the specific difference to the genus constitutes it. A lake is a body of water surrounded by land, Man is a rational anima, A syrup is a medication dissolved in concentrated sugar solution 4.

Property — a universal idea that expresses an attribute that belongs to the thing by natural necessity. A lake is a body of fresh water. A syrup is sweet 5. Logical Accident — a universal idea that is not a part of the essence of a thing but something that belongs to the thing not by natural necessity but by contingency.

The lake is large, calm, and picturesque. Definition Definition is the process of laying down the meaning of a term or an idea by giving its predicaments and predicables. It is the process of specifying the idea being signified by the term through the manifestation of its conceptual features or nature. Man is a rational animal. Kinds of Definition Nominal Definition or Stipulative definition. The type of definition in which meaning are taken from the term itself.

It is done by: Pointing out the object meant or by giving examples. The meaning of the term is recreated using memory or by undergoing simple apprehension or by enumerating objects that falls under its categories Example: The meaning of the term is taken from the derivation or origin of the term.

It is therefore the study of the mind Definition by Synonym. The meaning of the term is given by giving a familiar term that has similar meaning Example: Liliputan- small Real Definition. The type of definition in which the meaning or essence or nature of the term is externally manifested.

This is done through: Genus and Specific deference. The genus which is the essential feature of a thing which it possesses in common with other things in a group is presented together with the essential feature of a thing which makes it unique from other members of the group in order to point out to a particular specie.

Man is a rational Animal or an embodied spirit Ethics is a philosophical study of the morality of human acts b. A definition that presents and explains the process or the origin of a thing. An analysis is the process of breaking down the parts of a whole and establishing the relationships of the parts to other parts and to the whole c.

It is the process of presenting the features and the physical characteristics of a thing.

A hospital is a building with relatively adequate facilities to treat the and care for the sick 5. Division Division is the systematic enumeration of the component parts of a whole. Physical Division- the enumeration of the quantitative parts of a quantitative whole. Man has head, arms, body, legs etc. Logical Division- the breaking up of a logical whole into its logical parts. Man is white, yellow, brown, or black.

Metaphysical Division- the breaking up of a thing to its essential constituents into genus and specific difference. Classification Classification is the systematic arrangement of major divisions and subdivisions. Classification starts from the less general to a more general grouping of things. It is considered the reverse of division. It is the process of putting together things of similar characteristics.

A product of Judgment Propositions are statements written or spoken that externally communicate mental sentence. When propositions express assertions of the relationship or disagreements of two ideas they are known as categorical propositions. When they express relationships between two or more propositions, which assert the nature and validity of their connections they are known as hypothetical proposition.

A proposition has three elements; subject, predicate and copula. The subject and the predicate are the two terms or ideas that are being related. Thus, they are called the matter of the proposition. The copula is the unifying principle that gives the structure of the proposition thus it is called the form for it specifies the actual relation between the subject and the predicate. Propositions and sentences, like words and terms are different from each other.

All propositions are sentences but not all sentences are propositions because some sentences do not express judgment. Properties of Categorical Propositions The two properties of categorical propositions are quality and quantity.

Quality refers to the affirmation or denial of the relationship of the two terms or ideas. The quality of a proposition is seen in the copula. If the copula expresses that the two ideas are identical then the quality is said to be affirmative. If the copula expresses that the two ideas are not identical or if the subject denies the predicate then the quality of the proposition is negative.

Quantity refers to the extension of the subject term of the proposition. The quantity of the subject term determines the quantity of the whole proposition but not the quantity of its predicate. Three types of Quantities 1. Particular- when the subject term involves only part of the whole extension of the term. Some nurses are patient.

Universal- when the subject term involves all the extension of the term. All nurses are care-givers. Singular- when the subject term involves the only extension or a specific extension of the term. Wilden is the dean of the medical college.

Note; For our purpose, any singular extension is analogous or equal to universal extension Types of Categorical Propositions Quantity and quality are found together in categorical propositions. Variations in these two properties determine the four types of categorical propositions. All Nurses are required to take the licensure exam. All nurses are not required to take the licensure exam.

Some nurses are required to take the licensure exam. Some nurses are not required to take the licensure exam. Thus, A and I propositions are affirmative while E and O propositions are negative.

The following illustration will help clarify the distinctions among the four types of propositions.

Mod-08 Lec-40 Calculus of Variations

To determine the quantity of the predicate, one must determine the quality of the proposition. Generally, A and I propositions have particular predicates and E and O propositions have universal predicates. All men are mortals— A proposition with a particular predicate 2. Some men are mortals- I proposition with a particular predicate 3. All men are rational animals—A proposition with a singular predicate 4. One of the patients is a diabetic-I proposition with a singular predicate 5.

All men are not immortal-E proposition with universal predicate 6. Some men are not immortal- O proposition with universal predicate Hypothetical Proposition Hypothetical propositions are propositions that state conditions, causation or opposition between two judgments, set of ideas or statements.

Types of Hypothetical Propositions 1. A conditional proposition is a hypothetical proposition, which expresses a necessary relation between the antecedent or the cause and the consequence or the effect. If man is a material being then he is mortal Study and you will learn Whenever it rains the ground is wet. Conditional propositions are true if both the clauses are true and there is sequence between them, that is, the consequence necessarily flows from the antecedent.

Thus on condition that the if clause is true and there is a valid sequence it follows that the then clause will also be true. A Disjunctive proposition is a hypothetical proposition introduced by either …or and expresses opposition between the two elements. Thus it provides alternatives that may be mutually exclusive to each other.

Type of Disjunctive Propositions 1. Contradictory disjunctive-when the alternatives presented are limited to only two. Only one can be true and only one can be false.

### Inverse Relationship | Surprised by Logic

Both cannot be true and both cannot be false at the same time. Either you are alive or dead 2. One is either healthy or sick. It is either true or false.