Combining Texts

All the ideas for 'On the Natural Faculties', 'Knowledge and the Philosophy of Number' and 'Can Mechanisms Replace Laws of Nature?'

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20 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
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 must produce macro-level regularities, but that needs micro-level regularities [Leuridan]
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]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
We just use the word 'faculty' when we don't know the psychological cause [Galen]
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 / 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]