Combining Texts

All the ideas for 'fragments/reports', 'Foundations of Geometry' and 'Can Mechanisms Replace Laws of Nature?'

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17 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Generalisations must be invariant to explain anything [Leuridan]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
Biological functions are explained by disposition, or by causal role [Leuridan]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Mechanisms are ontologically dependent on regularities [Leuridan]
Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan]
We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan]
Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Strict regularities are rarely discovered in life sciences [Leuridan]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]