Combining Texts

All the ideas for 'In Defense of Essentialism', 'On the Introduction of Transfinite Numbers' and 'Epistemology: contemporary introduction'

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40 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA]
If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA]
Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA]
9. Objects / D. Essence of Objects / 2. Types of Essence
Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA]
An object's modal properties don't determine its possibilities [Paul,LA]
10. Modality / A. Necessity / 7. Natural Necessity
Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Beliefs are based on perception, memory, introspection or reason [Audi,R]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
Could you have a single belief on its own? [Audi,R]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
We can make certain of what we know, so knowing does not entail certainty [Audi,R]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R]
If you gradually remove a book's sensory properties, what is left at the end? [Audi,R]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R]
The concepts needed for a priori thought may come from experience [Audi,R]
12. Knowledge Sources / B. Perception / 3. Representation
To see something as a field, I obviously need the concept of a field [Audi,R]
How could I see a field and believe nothing regarding it? [Audi,R]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R]
Sense data imply representative realism, possibly only representing primary qualities [Audi,R]
12. Knowledge Sources / B. Perception / 5. Interpretation
Perception is first simple, then objectual (with concepts) and then propositional [Audi,R]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R]
The principles of justification have to be a priori [Audi,R]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
To remember something is to know it [Audi,R]
I might remember someone I can't recall or image, by recognising them on meeting [Audi,R]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Internalism about justification implies that there is a right to believe something [Audi,R]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Maths may be consistent with observations, but not coherent [Audi,R]
It is very hard to show how much coherence is needed for justification [Audi,R]
A consistent madman could have a very coherent belief system [Audi,R]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Consistent accurate prediction looks like knowledge without justified belief [Audi,R]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A reliability theory of knowledge seems to involve truth as correspondence [Audi,R]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R]
16. Persons / C. Self-Awareness / 4. Errors in Introspection
We can be ignorant about ourselves, for example, our desires and motives [Audi,R]