Combining Texts

All the ideas for 'Investigations in the Foundations of Set Theory I', 'The View from Nowhere' and 'On Cruelty'

expand these ideas     |    start again     |     specify just one area for these texts


39 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
There is more insight in fundamental perplexity about problems than in their supposed solutions [Nagel]
1. Philosophy / B. History of Ideas / 4. Early European Thought
Montaigne was the founding father of liberalism [Montaigne, by Gopnik]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy is the childhood of the intellect, and a culture can't skip it [Nagel]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
It seems mad, but the aim of philosophy is to climb outside of our own minds [Nagel]
2. Reason / A. Nature of Reason / 5. Objectivity
Realism invites scepticism because it claims to be objective [Nagel]
Views are objective if they don't rely on a person's character, social position or species [Nagel]
Things cause perceptions, properties have other effects, hence we reach a 'view from nowhere' [Nagel, by Reiss/Sprenger]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
Modern science depends on the distinction between primary and secondary qualities [Nagel]
We achieve objectivity by dropping secondary qualities, to focus on structural primary qualities [Nagel]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
Epistemology is centrally about what we should believe, not the definition of knowledge [Nagel]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Scepticism is based on ideas which scepticism makes impossible [Nagel]
14. Science / C. Induction / 4. Reason in Induction
Observed regularities are only predictable if we assume hidden necessity [Nagel]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
Personal identity cannot be fully known a priori [Nagel]
The question of whether a future experience will be mine presupposes personal identity [Nagel]
16. Persons / D. Continuity of the Self / 4. Split Consciousness
I can't even conceive of my brain being split in two [Nagel]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
Total objectivity can't see value, but it sees many people with values [Nagel]
22. Metaethics / B. Value / 2. Values / e. Death
We don't worry about the time before we were born the way we worry about death [Nagel]
22. Metaethics / B. Value / 2. Values / f. Altruism
If our own life lacks meaning, devotion to others won't give it meaning [Nagel]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Pain doesn't have a further property of badness; it gives a reason for its avoidance [Nagel]
23. Ethics / D. Deontological Ethics / 1. Deontology
Something may be 'rational' either because it is required or because it is acceptable [Nagel]
23. Ethics / D. Deontological Ethics / 2. Duty
If cockroaches can't think about their actions, they have no duties [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
If we can decide how to live after stepping outside of ourselves, we have the basis of a moral theory [Nagel]
We should see others' viewpoints, but not lose touch with our own values [Nagel]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
We find new motives by discovering reasons for action different from our preexisting motives [Nagel]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
Utilitarianism is too demanding [Nagel]