Facts, judgments, or expert testimony can provide statements from which to reason {premise}. Arguments start with premises. Premises can be definitions, axioms, postulates, or previously proved theorems.
not contradictory
Premises must have no contradictions.
not dependent
Premises must be independent.
definition
Definition includes how to use word {operational definition, premise}, what words can substitute {synonym, premise}, class and distinction, pointing at object {ostensive definition, premise}, and conceiving example. Definition can eliminate ambiguity and clarify idea. Word has precise meaning {denotation, meaning}, as well as properties, associations, and feelings {connotation, meaning}. Theory can explain definition, which can influence attitudes and increase vocabulary.
axiom
Premises can be about general or fundamental objects or symbols, assumed to be true.
postulates
Premises can be general statements about mathematical or logical objects and symbols. Anything implied by an elementary and true proposition is true. Disjunction of proposition with itself implies proposition: (a | a) -> a. Propositions imply disjunction of themselves and other propositions: a -> (a | b). Disjunction of one proposition with another implies disjunction of other and first {commutation, postulate}: (a | b) -> (b | a). Disjunction of proposition with disjunction of two other propositions implies disjunction of second with disjunction of first and third {association, postulate}: (a | (b | c)) -> (b | (a | c)). Assertion that statement is true and that the statement implies second statement is true is equivalent to assertion that second statement is true {modus ponens, postulate}. a. a -> b. b. Assertion that proposition implies second proposition is equivalent to disjunction of inverse of first proposition and second proposition {implication, postulate}. (a -> b) = (-a | b). These postulates have no proof that they are independent or consistent.
Mathematical Sciences>Logic>Statements>Reasoning
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224