Combining Texts

All the ideas for 'Evil and Omnipotence', 'Review of Tait 'Provenance of Pure Reason'' and 'Regressive Method for Premises in Mathematics'

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17 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 / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Which premises are ultimate varies with context [Russell]
The sources of a proof are the reasons why we believe its conclusion [Russell]
Finding the axioms may be the only route to some new results [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]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
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]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The law of gravity has many consequences beyond its grounding observations [Russell]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG]
Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG]