Combining Texts

All the ideas for 'fragments/reports', 'Gentzen's Analysis of First-Order Proofs' and 'Foundations of Geometry'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

13831

Logic is based on transitions between sentences [Prawitz]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

13825

Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

13823

In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]

6. Mathematics / A. Nature of Mathematics / 2. Geometry

13472

Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

9546	Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]

18742

Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]

18217

Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]