Combining Philosophers

All the ideas for Sebastian Gardner, Jos�� Ortega y Gassett and Paul Benacerraf

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43 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Hamann, Herder and Jacobi were key opponents of the Enlightenment [Gardner]
Kant halted rationalism, and forced empiricists to worry about foundations [Gardner]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Only Kant and Hegel have united nature, morals, politics, aesthetics and religion [Gardner]
2. Reason / E. Argument / 2. Transcendental Argument
Transcendental proofs derive necessities from possibilities (e.g. possibility of experiencing objects) [Gardner]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori) [Gardner]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
There are no such things as numbers [Benacerraf]
Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
Numbers can't be sets if there is no agreement on which sets they are [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C]
A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf]
To explain numbers you must also explain cardinality, the counting of things [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf]
Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The application of a system of numbers is counting and measurement [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
The successor of x is either x and all its members, or just the unit set of x [Benacerraf]
For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend]
No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe]
If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
An adequate account of a number must relate it to its series [Benacerraf]
The job is done by the whole system of numbers, so numbers are not objects [Benacerraf]
If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf]
The number 3 defines the role of being third in a progression [Benacerraf]
Number words no more have referents than do the parts of a ruler [Benacerraf]
Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf]
How can numbers be objects if order is their only property? [Benacerraf, by Putnam]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Number-as-objects works wholesale, but fails utterly object by object [Benacerraf]
Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan]
The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are not predicates, as they function very differently from adjectives [Benacerraf]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
For man, being is not what he is, but what he is going to be [Ortega y Gassett]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Leibnizian monads qualify as Kantian noumena [Gardner]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity statements make sense only if there are possible individuating conditions [Benacerraf]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
Aesthetics presupposes a distinctive sort of experience, and a unified essence for art [Gardner]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
Art works originate in the artist's mind, and appreciation is re-creating this mental object [Gardner]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
Aesthetic objectivists must explain pleasure being essential, but not in the object [Gardner]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Instead of having a nature, man only has a history [Ortega y Gassett]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Aesthetic judgements necessarily require first-hand experience, unlike moral judgements [Gardner]