173 ;;Quote: classification is for describing uniformities of collections of instances

173 ;;Quote: in classification want to identify membership in a class (top-down hierarchy) and understand relations between classes (bottom-up)

173 ;;Quote: during application design need a bottom-up construction of classification because the domain is uncharted

174 ;;Quote: natural phenomena are approximations to Plato's ideal forms; ideal forms exist in artificial worlds such as math and computer science

174 ;;Quote: real numbers are unrepresentable ideals which are approximated in a computer

177 ;;Quote: inheritance is important for management of change, especially long-term

178 ;;Quote: algebraic structures in math include semigroups, groups, rings, fields, and universal algebras

178+;;Quote: an algebra in math characterizes behavior like types in computer science

179 ;;Quote: reduction in lambda calculus is like eliminating differentiation in the differential calculus

179 ;;Quote: relational algebra expresses queries as operations on a relation; relational calculi as predicates that tuples must satisfy

179 ;;Quote: calculi are concrete (syntactic) algebras while algebras are abstract (semantic) calculi

180 ;;Quote: what properties must types have to be an acceptable type system for object-oriented programming

180 ;;Quote: a programmer sees types as partitioning values into classes with common attributes and operations

180+;;Quote: polymorphism allows overlapping value sets which cover the universal value set

180 ;;Quote: object-orientation treats types as behavior specifications that can be composed, modified, and inherited

180 ;;Quote: a type system is a set of rules for associating a type with every meaningful subexpression

180+;;Quote: type-checking sees types as syntactic constraints that guarantees compatibility of composite expressions

180 ;;Quote: program verification sees types as behavioral invariants that instances of the type must satisfy

180 ;;Quote: system programmers sees types as protection of bit strings from unintended interpretation

180 ;;Quote: implementers see types as a specification of storage mapping for values

180 ;;Quote: object-oriented definitions can not handle natural kinds (i.e., primitive notions); natural kinds are not completely defined by a set of operations and attributes

181 ;;Quote: understanding notion of classification leads to fundamental issues in math and philosophy

181 ;;Quote: classification view of systems depends on a global perspective; communication view is localized and observable, like Plato's cave dwellers

181 ;;Quote: reality is closer to one true religion because there exists a global reality that subsumes all local views

181+;;Quote: should there be multiple religions (i.e., views of a system) or only one?

182 ;;Quote: Newtonian physics assumes the existence of a real universe; relativity and quantum mechanics are based on observability