Combining Texts

All the ideas for 'Necessary Existents', 'Reflections on Knowledge, Truth and Ideas' and 'Sets, Aggregates and Numbers'

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10 ideas

2. Reason / D. Definition / 1. Definitions
'Nominal' definitions just list distinguishing characteristics [Leibniz]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive [Leibniz]
18. Thought / C. Content / 2. Ideas
True ideas represent what is possible; false ideas represent contradictions [Leibniz]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
26. Natural Theory / C. Causation / 2. Types of cause
In the schools the Four Causes are just lumped together in a very obscure way [Leibniz]