Ideas from 'Regressive Method for Premises in Mathematics' by Bertrand Russell [1907], by Theme Structure

[found in 'Essays in Analysis' by Russell,Bertrand (ed/tr Lackey,Douglas) [George Braziller 1973,0-8076-0699-5]].

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1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason

17641

Discoveries in mathematics can challenge philosophy, and offer it a new foundation

2. Reason / A. Nature of Reason / 6. Coherence

17638

If one proposition is deduced from another, they are more certain together than alone

2. Reason / B. Laws of Thought / 3. Non-Contradiction

17632

Non-contradiction was learned from instances, and then found to be indubitable

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17640

Finding the axioms may be the only route to some new results

17629

Which premises are ultimate varies with context

17630

The sources of a proof are the reasons why we believe its conclusion

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

17627

It seems absurd to prove 2+2=4, where the conclusion is more certain than premises

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

17628

Arithmetic was probably inferred from relationships between physical objects

11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism

17637

The most obvious beliefs are not infallible, as other obvious beliefs may conflict

13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification

17639

Believing a whole science is more than believing each of its propositions

14. Science / C. Induction / 2. Aims of Induction

17631

Induction is inferring premises from consequences

26. Natural Theory / D. Laws of Nature / 1. Laws of Nature

17633

The law of gravity has many consequences beyond its grounding observations