Combining Texts

All the ideas for 'Quodlibeta', 'Scientific Attitude and Fallibilism' 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]
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 / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
14775 Numbers are just names devised for counting [Peirce]
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]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
14776 That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce]
7. Existence / E. Categories / 3. Proposed Categories
16657 Substance, Quantity and Quality are real; other categories depend on those three [Henry of Ghent]
8. Modes of Existence / A. Relations / 1. Nature of Relations
16658 The only reality in the category of Relation is things from another category [Henry of Ghent]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16645 Accidents are diminished beings, because they are dispositions of substance (unqualified being) [Henry of Ghent]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14770 Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce]
17637 The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
22012 Kant says things-in-themselves cause sensations, but then makes causation transcendental! [Henry of Ghent, by Pinkard]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
14774 Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce]
12. Knowledge Sources / E. Direct Knowledge / 3. Inspiration
14773 A truth is hard for us to understand if it rests on nothing but inspiration [Peirce]
14772 If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce]
14771 Only reason can establish whether some deliverance of revelation really is inspired [Peirce]
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]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
14769 Only imagination can connect phenomena together in a rational way [Peirce]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations [Russell]