:))

Classification

-distinction, identification, and organization of more items, information’s, and facts according to the (ultimate) similarities which are determined through comparison.

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

“CLASSIFICATION” according to Gottfried Willhelm Von Leibniz it is the definition of two or more objects and that these two or more objects are “not exactly alike” In fact no two things are “ever exactly alike,” that if there were two objects which are so alike, they would be the same object. There is always an “essential dissimilarity” even in pair or apparent identical objects.

PLATO’S THEORIES OF UNIVERSALS

1. Universalia In re (Universals in the things)

-         everything is a combination of form and matter

2. Universalia Ante  rem (Universals before the things)

-         the link between the members of a class is that they are all imitations of an archetype which existed before the world was made.

3. Universalia Past rem (universals after the things)

-         nothing general exist, only particular

Four things to consider in Classification

Four different types of similarity in descending order of usefulness for purpose  of identification:

1. Genetic Similarity – having similar identifications
2. Structural Similarity- having the same constituents
3. Functional Similarity- having similar behavior
4. Apparent Similarity- having similar external features
   
   
   DEFINITION
   
   
            May be a statement of the essential properties of a certain thing, or a statement of the essential properties of equivalence between or expression and another, usually more complex  expression that gives meaning of the first.
   A thing being defined is called (from latin) a “definiendum”; the expression which defines it is called “definiens”
   
   
   Lexical Definition- a dictionary definition which reports the meaning of the word as if its normally used.
   
   
   .Extensional Definition- of general term is just the collection of individual things to which it correctly applied.
   
   
   . Intensional Definition- of a general term, on the other hand is the set of features which are shared by everything  to which it is applies.
   .Contextual Definition- some ords cannot be defined on their own, but it is possible to offer a schema for defining of every sentence which they occur.
   
   
   . Stipulative Definition-  is a specification of  a meaning adopted or assumed specifically for the purposes of argument or discussion on a given context
    Ostensive Definition- Gives the meaning of a term by pointing out of the thing denoted by it, or pointing of example of the kind of thing meant by it.
   
   
        Precising Definition- Is a definition which extends the dictionary definition of a term fo specific purpose by including additional criteria that narrow down the set of things meeting the definition.
   
   
        Operational Definition- of quantity is a specific process whereby it is answered.
   
   
   AXIOMS and THEOREMS
   Axiom (postulate) is a proposition that is not proved or demonstrated but considered self-evident or subject to necessary decision.
   Theorem- is a statement which has been proven or has been established its validity.
   Historical Background
          The Early Greeks developed the LOGICO-DEDUCTIVE METHOD whereby conclusions (new knowledge) follow from premises (old knowledge)
         Euclid established common nations (very basic self- evident assertions)
   
   
   1. Things which are equal to the something are also equal to one another.
   2. If equals be added to equals, the wholes are equal.
   3. If equals be subtracted from equals the remainers are equal.
   4. Things which coincide with one another are equal to another.
   5. The whole is greater than part.
   
   
   Axiomatic System- any set of axioms from which some or all axioms can be used in conjunction to logically derived theorem.
   
   
                    Characteristics of Axiomatic System
   1.      Independent-  if it is not a theorem that can be derived from other axioms in the system.
   2.      Complete- If for every statement, either, itself or its negation is derivable.
   3.      Consistent- if it lacks contradiction.
      Many theorems are of the form of an indicative conditional: If A, then B,
               In this case A is called hypothesis  (antecedent) of theorem and B the conclusion (consequent)
   
   
   
   
   Relation of Theorem to Proof:
               Theorem are true precisely in the sense that the possess proofs.
   Pythagorean Theorem :  370 proofs.