Combining Texts

All the ideas for 'fragments/reports', 'Change in View: Principles of Reasoning' and 'On the Introduction of Transfinite Numbers'

expand these ideas     |    start again     |     specify just one area for these texts


16 ideas

2. Reason / A. Nature of Reason / 1. On Reason
The rules of reasoning are not the rules of logic [Harman]
It is a principle of reasoning not to clutter your mind with trivialities [Harman]
If there is a great cost to avoiding inconsistency, we learn to reason our way around it [Harman]
Logic has little relevance to reasoning, except when logical conclusions are immediate [Harman]
2. Reason / A. Nature of Reason / 4. Aims of Reason
Implication just accumulates conclusions, but inference may also revise our views [Harman]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
10. Modality / B. Possibility / 6. Probability
The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman]
High probability premises need not imply high probability conclusions [Harman]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
We strongly desire to believe what is true, even though logic does not require it [Harman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
In revision of belief, we need to keep track of justifications for foundations, but not for coherence [Harman]
Coherence is intelligible connections, especially one element explaining another [Harman]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]