Theories
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what is a set
collection of any entities
fundamental concepts of set
set membership relation E
irreflexivity of set
no set is a member of itself
anti-symmetry of set
if X E Y, then Y is not E X
6 parts of a theory for Aristotle
• Dom (set of actual entities) • Enn (concepts) • fun (-damental concepts) • def (-initions) • princ(-iples) • Thms (Theorems)
Theorems
formed by axioms, postulates & definitions
qualities of propositions in domain
universal, necessary & self-evident
three components new theory
ontology ennology nomology
Ontology
descriptions of the entities T is about
ennology
fundamental & defined concepts of T, may include which concepts represent which features –> relation to observable/ measurable factors
nomology
postulates about how the domain-members behave & relate
Few differences between classical & modern account of theory
• new theory does require connection to observation/ measurable factors (Enn(T) ) • post(T) do not have to be true, can have false theories • do not need to have explicit axioms for theory T to be applicable • Post(T) instead of princ (Theta)
Difference principle
D(T1,T2) = denn (T1+T2) + dpost (T1+ T2) + Dont (T1+ T2) (ennology, postulates, ontology) If D(T1,T2) = 0, then T1=T2