Lecture 7 - Theories Flashcards
What is a set?
Set is a collection of entities
Sets are pluralities taken as unities, as wholes, having a definite number of
members.
Identity criterion for sets
Sets are identical iff they share all their members
Subset
X ⊆Y iff all members of X are members of Y.
Proper subset
X ⊂Y iff all members of X are members of Y but Y contains at least one
member (in picture: w) that X does not contain — w ̸∈ X, w ∈ Y.
Extension of a concept
set of all and only things falling under the concept
Three main categories in apodeictic theory
entities, concepts and propositions
Entities
Domain: set that collects actual entities that exist
Theory is about this
Concepts
ENN: concepts employed by theory
Fund: primitive, have no definition, proper subset of ENN
Joined set of concepts is ultimately defined
Principles
Definitions: descriptions
Principles: which are propositions that employ the concepts in Enn(Θ), and which have no demonstrations
Theorems: propositions deducted from ENN, can be demonstrated on basis of principles
Principles: axioma’s, postulates and (definitions)
Requirement for principles
The propositions in Princ(Θ) are universal, necessary, and self-evident truths
Give set-theoretical relations between components of apodeictic theory
see notebook
What does apodeictic theory miss?
Empirical/observational evidence
Difference apodeictic theory and modern theory
conceps represent phenomena
Requirements for modern theory
- Ontology: description of the entities that Th is about, collected in its domain.
- Ennology: fundamental and defined concepts of Th, which may include a specification of which concepts represent which features of the domain members.
- Nomology: Postulates about how the domain-members behave and relate
Difference measure
Theory consists of object + concepts + propositions
numbers of these can be counted
Identity-Criterion for theories:
Th1 = Th2 iff D(Th1,Th2) = 0
