Combining Texts

All the ideas for 'The Laws of Thought', 'Foundations of Geometry' and 'works'

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13 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
Do not multiply entities beyond necessity [William of Ockham]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
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]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
Species and genera are individual concepts which naturally signify many individuals [William of Ockham]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham]
29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels
Even an angel must have some location [William of Ockham, by Pasnau]