Combining Texts

All the ideas for 'In Defence of Three-Dimensionalism', 'Sets, Aggregates and Numbers' and 'Exigency to Exist in Essences'

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13 ideas

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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K]
Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K]
You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons]
9. Objects / E. Objects over Time / 5. Temporal Parts
Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The actual universe is the richest composite of what is possible [Leibniz]