LANGUAGE

Ø Is an abstract system of word meaning and symbols of all aspects of culture. It includes speech, written character, numeral symbols, gestures and expression s of non-verbal communication.

There are some terms that do not have meaning and falls into two classes.

1. grammatical term
2. abstract term

All language begins as ordinary language under the process of immediate necessity of communication but not in all cases like:

• customary usage as how it spend
• grammatical terms
• dedension of case speed fall down

Ordinary Language Analysis

Ø Is the argument that any language which is adequate stands as the transmitter of nuisances as differences and style of meaning on which everyday conversation must be fluid.

CLASSIFICATION

Ø The distinction, identification and organization of two or more items, information and facts according to their similarities which are determined through comparison.

Ø It gives a closer view on the link between the objects being compared.

Definition according to Gottfried Wilhelm Von Leibniz:

Ø It is the differentiation of two or more objects which is not exactly a like: essential dissimilarity. Two objects are not “ever exactly alike”. Infact no two things are “ever exactly alike”.

Plato’s theories of Universals

1. Universalia in re (universal in things) – everything is a combination of form and matter.
2. Universalia anti rem (universal before things) – the link between the members of the class is that they are all imitations of an archetype which existed before the world was made.
3. Universalia post rem (universal after the things) – nothing general exist, only particular.

Four Different Types of similarities

1. Genetic similarity – having similar origins.

2.Structural similarity – having the same constituent parts.

3.Functional similarity – having similar behavior.

4.Apparent similarity – having similar external features

DEFINITION

Ø A definition maybe statement of him essential properties of a certain thin or a statement of equivalence between one expression that gives meaning of the first.

Definiendum – the thing that is being defined.

Definiens – the expression which defines the things.

Types of Definition

1. Lexical Definition – a dictionary definition that reports the meaning of the word as it is normally used.
2. Intensional Definition – a general term, the other set of features which are shared by everything to which it applies.
3. Extension Definition – the collection of individual things to which is correctly applied.
4. Contextual Definition – some words cannot be clearly defined on their own, but it is possible to offer schema for defining every sentence which they occur.
5. Stipulative Definition – His specification of a meaning adopted or assumed specifically for the purpose of argument or discussion in given context.
6. Ostensive Definition – gives the meaning of a term by pointing out the thing denoted by it, or pointing out of examples of the kind of the thing meant on by it.
7. Précising Definition – extend the dictionary definition for specific purposes.
8. Operational Definition – quantity is a specific process whereby it is measured.

AXIOMS and THEOREMS

Axioms – is a proposition that is not proved or demonstrated but consider self-evident or subject to necessary decision.

Theorem – a statement which has been proven or has been established in validity.

Historical Background

The early Greeks developed the LOGICO-DEDUCTIVE METHOD whereby conclusions (new knowledge) follow from premises (old knowledge)

COMMON NOTIONS by Euclid (very basic, self evident assertion)

1. Things which are equal to the same thing are also equal to one another.
2. If equals be added to equals, the wholes are equals
3. If equals be subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than part.

Axiomatic System – is any set of axioms from which some or all axioms can be used in conjunction to logically derived theorems.

Properties of Axiomatic System

1. Consistent – if it lacks of contradiction.
2. Complete – if for every statement, either itself of its negation or contradiction is derivable.
3. Independent – if it is not a theorem that can be derived from other axioms in the system.