Combining Philosophers

All the ideas for Anaxarchus, Mark Colyvan and G.E. Moore

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45 ideas

1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / b. Modern philosophy beginnings
Moore's 'The Nature of Judgement' (1898) marked the rejection (with Russell) of idealism [Moore,GE, by Grayling]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
The main aim of philosophy is to describe the whole Universe. [Moore,GE]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analysis for Moore and Russell is carving up the world, not investigating language [Moore,GE, by Monk]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Rejecting double negation elimination undermines reductio proofs [Colyvan]
Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinal numbers represent order relations [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Intuitionists only accept a few safe infinities [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Most mathematical proofs are using set theory, but without saying so [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
8. Modes of Existence / A. Relations / 2. Internal Relations
A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Moore's Paradox: you can't assert 'I believe that p but p is false', but can assert 'You believe p but p is false' [Moore,GE, by Lowe]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
Arguments that my finger does not exist are less certain than your seeing my finger [Moore,GE]
I can prove a hand exists, by holding one up, pointing to it, and saying 'here is one hand' [Moore,GE]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
14. Science / C. Induction / 6. Bayes's Theorem
Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Mathematics can reveal structural similarities in diverse systems [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
Mathematics can show why some surprising events have to occur [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
Reductio proofs do not seem to be very explanatory [Colyvan]
If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
19. Language / D. Propositions / 3. Concrete Propositions
Moor bypassed problems of correspondence by saying true propositions ARE facts [Moore,GE, by Potter]
19. Language / D. Propositions / 5. Unity of Propositions
Hegelians say propositions defy analysis, but Moore says they can be broken down [Moore,GE, by Monk]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
The beautiful is whatever it is intrinsically good to admire [Moore,GE]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Moore tries to show that 'good' is indefinable, but doesn't understand what a definition is [MacIntyre on Moore,GE]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
The Open Question argument leads to anti-realism and the fact-value distinction [Boulter on Moore,GE]
The naturalistic fallacy claims that natural qualties can define 'good' [Moore,GE]
Moore cannot show why something being good gives us a reason for action [MacIntyre on Moore,GE]
Can learning to recognise a good friend help us to recognise a good watch? [MacIntyre on Moore,GE]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Moore's combination of antinaturalism with strong supervenience on the natural is incoherent [Hanna on Moore,GE]
Despite Moore's caution, non-naturalists incline towards intuitionism [Moore,GE, by Smith,M]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
We should ask what we would judge to be good if it existed in absolute isolation [Moore,GE]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
It is always an open question whether anything that is natural is good [Moore,GE]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
The three main values are good, right and beauty [Moore,GE, by Ross]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
For Moore, 'right' is what produces good [Moore,GE, by Ross]
'Right' means 'cause of good result' (hence 'useful'), so the end does justify the means [Moore,GE]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Relationships imply duties to people, not merely the obligation to benefit them [Ross on Moore,GE]