Combining Texts

All the ideas for 'Realistic Rationalism', 'Regressive Method for Premises in Mathematics' and 'Quaestiones de Potentia Dei'

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22 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
2510 Traditionally philosophy is an a priori enquiry into general truths about reality [Katz]
2516 Most of philosophy begins where science leaves off [Katz]
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]
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 / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
2521 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]
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 / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
17555 'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
17637 The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
2513 We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
2522 Experience cannot teach us why maths and logic are necessary [Katz]
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 / A. Nature of Meaning / 1. Meaning
2517 Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
2519 It is generally accepted that sense is defined as the determiner of reference [Katz]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
2520 Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
2518 Sentences are abstract types (like musical scores), not individual tokens [Katz]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations [Russell]