Combining Texts

All the ideas for 'Theory of Science (4 vols)', 'Mathematical Explanation' and 'The Strangest Man'

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15 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
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
Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
9. Objects / D. Essence of Objects / 3. Individual Essences
Particular essence is often captured by generality [Steiner,M]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
19. Language / D. Propositions / 1. Propositions
Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
19. Language / E. Analyticity / 2. Analytic Truths
The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Instead of gravitational force, we now have a pervasive gravitational field [Farmelo]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
Experiments show that fundamental particles of one type are identical [Farmelo]