Combining Texts

All the ideas for 'What are Sets and What are they For?', 'Philosophical Analysis' and 'Physics and Philosophy'

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28 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
13750 Analysis aims at the structure of facts, which are needed to give a rationale to analysis [Urmson, by Schaffer,J]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
17536 If it can't be expressed mathematically, it can't occur in nature? [Heisenberg]
7. Existence / D. Theories of Reality / 2. Realism
17545 Quantum theory shows that exact science does not need dogmatic realism [Heisenberg]
7. Existence / D. Theories of Reality / 4. Anti-realism
17538 Quantum theory does not introduce minds into atomic events [Heisenberg]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
17534 A 'probability wave' is a quantitative version of Aristotle's potential, a mid-way type of reality [Heisenberg]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
17553 We can retain the idea of 'substance', as indestructible mass or energy [Heisenberg]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
17544 Basic particles have a mathematical form, which is more important than their substance [Heisenberg]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
17550 We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
17549 Seven theories in science: mechanics, heat, electricity, quantum, particles, relativity, life [Heisenberg, by PG]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
17540 Energy is that which moves, and is the substance from which everything is made [Heisenberg]
17541 Energy is an unchanging substance, having many forms, and causing all change [Heisenberg]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
17548 Maxwell introduced real fields, which transferred forces from point to point [Heisenberg]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
17533 Radiation interference needs waves, but radiation photoelectric effects needs particles [Heisenberg]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
17537 Position is complementary to velocity or momentum, so the whole system is indeterminate [Heisenberg]
17551 It was formerly assumed that electromagnetic waves could not be a reality in themselves [Heisenberg]
17532 An atom's stability after collisions needs explaining (which Newton's mechanics can't do) [Heisenberg]
27. Natural Reality / C. Space / 4. Substantival Space
17543 So-called 'empty' space is the carrier of geometry and kinematics [Heisenberg]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
17552 In relativity the length of the 'present moment' is relative to distance from the observer [Heisenberg]