Combining Philosophers

All the ideas for Pittacus, E Sosa / M Tooley and Richard G. Heck

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18 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
Is counting basically mindless, and independent of the cardinality involved? [Heck]
Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
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
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
Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Equinumerosity is not the same concept as one-one correspondence [Heck]
We can understand cardinality without the idea of one-one correspondence [Heck]
10. Modality / A. Necessity / 8. Transcendental Necessity
Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]
15. Nature of Minds / C. Capacities of Minds / 9. Perceiving Causation
Either causal relations are given in experience, or they are unobserved and theoretical [Sosa/Tooley]
26. Natural Theory / C. Causation / 1. Causation
The problem is to explain how causal laws and relations connect, and how they link to the world [Sosa/Tooley]
26. Natural Theory / C. Causation / 4. Naturalised causation
Causation isn't energy transfer, because an electron is caused by previous temporal parts [Sosa/Tooley]
If direction of causation is just direction of energy transfer, that seems to involve causation [Sosa/Tooley]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Are causes sufficient for the event, or necessary, or both? [Sosa/Tooley]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
The dominant view is that causal laws are prior; a minority say causes can be explained singly [Sosa/Tooley]