Combining Texts

All the ideas for 'Two Problems of Epistemology', 'Pref to new 'Materialist Theory'' and 'Cardinality, Counting and Equinumerosity'

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20 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
We can understand cardinality without the idea of one-one correspondence [Heck]
Equinumerosity is not the same concept as one-one correspondence [Heck]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Secondary qualities are microscopic primary qualities of physical things [Armstrong]
14. Science / A. Basis of Science / 6. Falsification
Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Consciousness and experience of qualities are not the same [Armstrong]
17. Mind and Body / B. Behaviourism / 1. Behaviourism
Behaviourism is false, but mind is definable as the cause of behaviour [Armstrong]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
The manifestations of a disposition need never actually exist [Armstrong]
17. Mind and Body / C. Functionalism / 4. Causal Functionalism
Causal Functionalism says mental states are apt for producing behaviour [Armstrong]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
A causal theory of mentality would be improved by a teleological element [Armstrong]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The identity of mental states with physical properties is contingent, because the laws of nature are contingent [Armstrong]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
One mental role might be filled by a variety of physical types [Armstrong]