Combining Philosophers

All the ideas for Verity Harte, John von Neumann and Sebastian Gardner

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27 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
21463 Hamann, Herder and Jacobi were key opponents of the Enlightenment [Gardner]
21459 Kant halted rationalism, and forced empiricists to worry about foundations [Gardner]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
21460 Only Kant and Hegel have united nature, morals, politics, aesthetics and religion [Gardner]
2. Reason / E. Argument / 2. Transcendental Argument
21443 Transcendental proofs derive necessities from possibilities (e.g. possibility of experiencing objects) [Gardner]
2. Reason / F. Fallacies / 7. Ad Hominem
15842 An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
4. Formal Logic / G. Formal Mereology / 1. Mereology
15841 Mereology began as a nominalist revolt against the commitments of set theory [Harte,V]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
21444 Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori) [Gardner]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
7. Existence / B. Change in Existence / 1. Nature of Change
15858 Traditionally, the four elements are just what persists through change [Harte,V]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21453 Leibnizian monads qualify as Kantian noumena [Gardner]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
15848 Mereology treats constitution as a criterion of identity, as shown in the axiom of extensionality [Harte,V]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
15837 What exactly is a 'sum', and what exactly is 'composition'? [Harte,V]
15839 If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V]
15838 The problem with the term 'sum' is that it is singular [Harte,V]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
8108 Aesthetics presupposes a distinctive sort of experience, and a unified essence for art [Gardner]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
8112 Art works originate in the artist's mind, and appreciation is re-creating this mental object [Gardner]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
8111 Aesthetic objectivists must explain pleasure being essential, but not in the object [Gardner]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
8109 Aesthetic judgements necessarily require first-hand experience, unlike moral judgements [Gardner]