Combining Texts

All the ideas for 'Introduction to 'Properties'', 'Ontology and Mathematical Truth' and 'Calculus Ratiocinator'

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13 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
4037 Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9967 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
9968 A model is 'fundamental' if it contains only concrete entities [Jubien]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
9965 There couldn't just be one number, such as 17 [Jubien]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
9966 The subject-matter of (pure) mathematics is abstract structure [Jubien]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9963 If we all intuited mathematical objects, platonism would be agreed [Jubien]
9962 How can pure abstract entities give models to serve as interpretations? [Jubien]
9964 Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
8. Modes of Existence / B. Properties / 6. Categorical Properties
4027 Properties are respects in which particular objects may be alike or differ [Mellor/Oliver]
8. Modes of Existence / B. Properties / 12. Denial of Properties
4029 Nominalists ask why we should postulate properties at all [Mellor/Oliver]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
9969 The empty set is the purest abstract object [Jubien]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
12742 A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz]
18. Thought / E. Abstraction / 5. Abstracta by Negation
4039 Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver]