Combining Texts

All the ideas for 'fragments/reports', 'The Limits of Contingency' and 'Regressive Method for Premises in Mathematics'

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24 ideas

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 [Russell]
2. Reason / A. Nature of Reason / 6. Coherence
17638 If one proposition is deduced from another, they are more certain together than alone [Russell]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
17632 Non-contradiction was learned from instances, and then found to be indubitable [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
18851 Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17640 Finding the axioms may be the only route to some new results [Russell]
17629 Which premises are ultimate varies with context [Russell]
17630 The sources of a proof are the reasons why we believe its conclusion [Russell]
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 [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17628 Arithmetic was probably inferred from relationships between physical objects [Russell]
9. Objects / A. Existence of Objects / 4. Impossible objects
18852 A Meinongian principle might say that there is an object for any modest class of properties [Rosen]
10. Modality / A. Necessity / 5. Metaphysical Necessity
18850 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen]
18849 Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen]
18857 Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen]
18858 Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen]
18856 Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen]
10. Modality / A. Necessity / 6. Logical Necessity
18848 Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
10. Modality / B. Possibility / 3. Combinatorial possibility
18855 Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
18853 A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
17637 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
17639 Believing a whole science is more than believing each of its propositions [Russell]
14. Science / C. Induction / 2. Aims of Induction
17631 Induction is inferring premises from consequences [Russell]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations [Russell]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
18854 The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen]