Combining Texts

All the ideas for 'Mathematics without Numbers', 'Events as property exemplifications' and 'Relations'

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16 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J]
If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim]
Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons]
Events are composed of an object with an attribute at a time [Kim, by Simons]
Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim]
Kim's theory results in too many events [Simons on Kim]
8. Modes of Existence / A. Relations / 1. Nature of Relations
We want the ontology of relations, not just a formal way of specifying them [Heil]
Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
Truthmaking is a clear example of an internal relation [Heil]
If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
If properties are powers, then causal relations are internal relations [Heil]