Combining Philosophers

All the ideas for Hermarchus, John von Neumann and Martin Kusch

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39 ideas

3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence could be with other beliefs, rather than external facts [Kusch]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarskians distinguish truth from falsehood by relations between members of sets [Kusch]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
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
Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
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]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
All the axioms for mathematics presuppose set theory [Neumann]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We can have knowledge without belief, if others credit us with knowledge [Kusch]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
Methodological Solipsism assumes all ideas could be derived from one mind [Kusch]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Foundations seem utterly private, even from oneself at a later time [Kusch]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch]
The coherentist restricts the space of reasons to the realm of beliefs [Kusch]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch]
Individual coherentism cannot generate the necessary normativity [Kusch]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Cultures decide causal routes, and they can be critically assessed [Kusch]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Justification depends on the audience and one's social role [Kusch]
13. Knowledge Criteria / C. External Justification / 7. Testimony
Testimony is an area in which epistemology meets ethics [Kusch]
Powerless people are assumed to be unreliable, even about their own lives [Kusch]
Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch]
Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch]
Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch]
A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch]
Vindicating testimony is an expression of individualism [Kusch]
13. Knowledge Criteria / C. External Justification / 8. Social Justification
Myths about lonely genius are based on epistemological individualism [Kusch]
Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch]
Private justification is justification to imagined other people [Kusch]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
To be considered 'an individual' is performed by a society [Kusch]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Our experience may be conceptual, but surely not the world itself? [Kusch]
19. Language / F. Communication / 1. Rhetoric
Often socialising people is the only way to persuade them [Kusch]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Communitarianism in epistemology sees the community as the primary knower [Kusch]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Natural kinds are social institutions [Kusch]
28. God / A. Divine Nature / 4. Divine Contradictions
Omniscience is incoherent, since knowledge is a social concept [Kusch]