Combining Texts

All the ideas for 'reports', 'Infinitism solution to regress problem' and 'Cardinality, Counting and Equinumerosity'

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16 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Why should we prefer coherent beliefs? [Klein,P]
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]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Infinitism avoids a regress, circularity or arbitrariness, by saying warrant just increases [Klein,P]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
If justification is endless, no link in the chain is ultimately justified [Ginet on Klein,P]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Reasons acquire warrant through being part of a lengthening series [Klein,P]
25. Social Practice / D. Justice / 3. Punishment / c. Deterrence of crime
The greatest deterrence for injustice is if uninjured parties feel as much indignation as those who are injured [Solon, by Diog. Laertius]