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All the ideas for 'Sets and Numbers', 'Topics' and 'The View from Nowhere'

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66 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 / 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]
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Begin examination with basics, and subdivide till you can go no further [Aristotle]
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 / C. Styles of Reason / 1. Dialectic
Dialectic starts from generally accepted opinions [Aristotle]
2. Reason / D. Definition / 1. Definitions
There can't be one definition of two things, or two definitions of the same thing [Aristotle]
Definitions are easily destroyed, since they can contain very many assertions [Aristotle]
2. Reason / D. Definition / 5. Genus and Differentia
We describe the essence of a particular thing by means of its differentiae [Aristotle]
The differentia indicate the qualities, but not the essence [Aristotle]
In definitions the first term to be assigned ought to be the genus [Aristotle]
The genera and the differentiae are part of the essence [Aristotle]
Differentia are generic, and belong with genus [Aristotle]
'Genus' is part of the essence shared among several things [Aristotle]
2. Reason / D. Definition / 6. Definition by Essence
The definition is peculiar to one thing, not common to many [Aristotle]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
The master science is physical objects divided into sets [Maddy]
5. Theory of Logic / L. Paradox / 2. Aporiai
Puzzles arise when reasoning seems equal on both sides [Aristotle]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Unit is the starting point of number [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Sets exist where their elements are, but numbers are more like universals [Maddy]
Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
7. Existence / E. Categories / 3. Proposed Categories
There are ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity [Aristotle]
8. Modes of Existence / B. Properties / 1. Nature of Properties
An individual property has to exist (in past, present or future) [Aristotle]
8. Modes of Existence / B. Properties / 3. Types of Properties
An 'accident' is something which may possibly either belong or not belong to a thing [Aristotle]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Genus gives the essence better than the differentiae do [Aristotle]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle]
9. Objects / D. Essence of Objects / 3. Individual Essences
Everything that is has one single essence [Aristotle]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
An 'idion' belongs uniquely to a thing, but is not part of its essence [Aristotle]
9. Objects / E. Objects over Time / 11. End of an Object
Destruction is dissolution of essence [Aristotle]
9. Objects / E. Objects over Time / 12. Origin as Essential
If two things are the same, they must have the same source and origin [Aristotle]
9. Objects / F. Identity among Objects / 9. Sameness
'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle]
Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle]
Numerical sameness and generic sameness are not the same [Aristotle]
10. Modality / A. Necessity / 6. Logical Necessity
Reasoning is when some results follow necessarily from certain claims [Aristotle]
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 / 1. Induction
Induction is the progress from particulars to universals [Aristotle]
14. Science / C. Induction / 3. Limits of Induction
We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle]
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 / C. Virtue Theory / 3. Virtues / a. Virtues
Friendship is preferable to money, since its excess is preferable [Aristotle]
Justice and self-control are better than courage, because they are always useful [Aristotle]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
We value friendship just for its own sake [Aristotle]
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]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
Man is intrinsically a civilized animal [Aristotle]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
All water is the same, because of a certain similarity [Aristotle]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
'Being' and 'oneness' are predicated of everything which exists [Aristotle]