Combining Philosophers

All the ideas for Xenophon, Bernard Bolzano and Lawrence M. Krauss

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22 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
7807 The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618 Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830 Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17265 Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
7. Existence / C. Structure of Existence / 2. Reduction
21110 An understanding of the most basic physics should explain all of the subject's mysteries [Krauss]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21105 In 1676 it was discovered that water is teeming with life [Krauss]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9185 Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
19. Language / D. Propositions / 1. Propositions
22276 Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
17264 Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
12232 A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
19. Language / E. Analyticity / 2. Analytic Truths
12233 The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
5845 Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
25. Social Practice / E. Policies / 5. Education / b. Education principles
5833 Education is the greatest of human goods [Xenophon]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
21109 Space itself can expand (and separate its contents) at faster than light speeds [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
21104 General Relativity: the density of energy and matter determines curvature and gravity [Krauss]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21107 Uncertainty says that energy can be very high over very short time periods [Krauss]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
21106 Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss]
27. Natural Reality / C. Space / 2. Space
21112 Empty space contains a continual flux of brief virtual particles [Krauss]
27. Natural Reality / E. Cosmology / 3. The Beginning
21108 The universe is precisely 13.72 billion years old [Krauss]
27. Natural Reality / E. Cosmology / 10. Multiverse
21111 It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss]