### All the ideas for Peter B. Lewis, David Hilbert and Hastings Rashdall

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36 ideas

###### 3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
 15716 If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
###### 5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
 18844 You would cripple mathematics if you denied Excluded Middle [Hilbert]
###### 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
 17963 The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
 17966 Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
###### 6. Mathematics / A. Nature of Mathematics / 1. Mathematics
 8717 Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
 12456 I aim to establish certainty for mathematical methods [Hilbert]
 12461 We believe all mathematical problems are solvable [Hilbert]
###### 6. Mathematics / A. Nature of Mathematics / 2. Geometry
 13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
###### 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
 9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
 12462 Only the finite can bring certainty to the infinite [Hilbert]
 12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
###### 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
 12455 The idea of an infinite totality is an illusion [Hilbert]
###### 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
 12457 There is no continuum in reality to realise the infinitely small [Hilbert]
###### 6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
 17967 To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
###### 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]
 17965 The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
###### 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
 17964 Number theory just needs calculation laws and rules for integers [Hilbert]
###### 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
 17697 The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
###### 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
 17698 Logic already contains some arithmetic, so the two must be developed together [Hilbert]
###### 6. Mathematics / C. Sources of Mathematics / 7. Formalism
 10113 The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
 10115 Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
 22293 Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
 12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
###### 6. Mathematics / C. Sources of Mathematics / 8. Finitism
 10116 Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]
 18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
###### 11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
 9636 My theory aims at the certitude of mathematical methods [Hilbert]
###### 11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
 21912 Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
 21911 Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
###### 16. Persons / B. Nature of the Self / 2. Ethical Self
 1457 Morality requires a minimum commitment to the self [Rashdall]
###### 22. Metaethics / A. Value / 1. Nature of Value / e. Means and ends
 6674 All moral judgements ultimately concern the value of ends [Rashdall]
###### 23. Ethics / E. Utilitarianism / 6. Ideal Utilitarianism
 6673 Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall]
###### 26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
 17968 By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]
###### 28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
 1458 Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall]
 1459 Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG]