Combining Texts

All the ideas for 'Extrinsic Properties', 'Intuitionism and Formalism' and 'Change in View: Principles of Reasoning'

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18 ideas

2. Reason / A. Nature of Reason / 1. On Reason
It is a principle of reasoning not to clutter your mind with trivialities [Harman]
The rules of reasoning are not the rules of logic [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]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Scientific laws largely rest on the results of counting and measuring [Brouwer]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionists only accept denumerable sets [Brouwer]
Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider]
Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
Total intrinsic properties give us what a thing is [Lewis]
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]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]