Combining Philosophers

All the ideas for Bert Leuridan, Richard G. Heck and William Crathorn

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23 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
17453 The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17459 Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17454 Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
12790 Generalisations must be invariant to explain anything [Leuridan]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
12789 Biological functions are explained by disposition, or by causal role [Leuridan]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
14386 Mechanisms are ontologically dependent on regularities [Leuridan]
12787 Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan]
14384 We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan]
14388 Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
14389 There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
14387 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
14382 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
14385 Strict regularities are rarely discovered in life sciences [Leuridan]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
14383 A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan]
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
16697 Time is independent of motion, because God could stop everything for a short or long time [Crathorn, by Pasnau]