Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Regressive Method for Premises in Mathematics' and 'Laudatio: Prof Ruth Barcan Marcus'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
2. Reason / A. Nature of Reason / 6. Coherence
If one proposition is deduced from another, they are more certain together than alone [Russell]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Non-contradiction was learned from instances, and then found to be indubitable [Russell]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
If a property is possible, there is something which can have it [Williamson]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Finding the axioms may be the only route to some new results [Russell]
Which premises are ultimate varies with context [Russell]
The sources of a proof are the reasons why we believe its conclusion [Russell]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic was probably inferred from relationships between physical objects [Russell]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Believing a whole science is more than believing each of its propositions [Russell]
14. Science / C. Induction / 2. Aims of Induction
Induction is inferring premises from consequences [Russell]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The law of gravity has many consequences beyond its grounding observations [Russell]