Combining Texts

All the ideas for 'Material Constitution', 'Gentzen's Analysis of First-Order Proofs' and 'Foundations of Geometry'

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12 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is based on transitions between sentences [Prawitz]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman]
Constitution is not identity, because it is an asymmetric dependence relation [Wasserman]
There are three main objections to seeing constitution as different from identity [Wasserman]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman]
9. Objects / F. Identity among Objects / 3. Relative Identity
Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman]