Combining Texts

All the ideas for 'fragments/reports', 'Plural Quantification' and 'Regressive Method for Premises in Mathematics'

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23 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]
2. Reason / D. Definition / 12. Paraphrase
10633 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10638 A pure logic is wholly general, purely formal, and directly known [Linnebo]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10635 Second-order quantification and plural quantification are different [Linnebo]
10641 Traditionally we eliminate plurals by quantifying over sets [Linnebo]
10640 Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
10636 Plural plurals are unnatural and need a first-level ontology [Linnebo]
10639 Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17629 Which premises are ultimate varies with context [Russell]
17630 The sources of a proof are the reasons why we believe its conclusion [Russell]
17640 Finding the axioms may be the only route to some new results [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 / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17628 Arithmetic was probably inferred from relationships between physical objects [Russell]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
10643 We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
10637 Ordinary speakers posit objects without concern for ontology [Linnebo]
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]
19. Language / C. Assigning Meanings / 3. Predicates
10634 Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations [Russell]