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All the ideas for 'Possibility', 'Gorgias' and 'A Structural Account of Mathematics'

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73 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Is a gifted philosopher unmanly if he avoids the strife of the communal world? [Plato]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien]
2. Reason / C. Styles of Reason / 2. Elenchus
In "Gorgias" Socrates is confident that his 'elenchus' will decide moral truth [Vlastos on Plato]
We should test one another, by asking and answering questions [Plato]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Realists about sets say there exists a null set in the real world, with no members [Chihara]
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
A pack of wolves doesn't cease when one member dies [Chihara]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
We only grasp a name if we know whether to apply it when the bearer changes [Jubien]
The baptiser picks the bearer of a name, but social use decides the category [Jubien]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Examples show that ordinary proper names are not rigid designators [Jubien]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
To exist necessarily is to have an essence whose own essence must be instantiated [Jubien]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
If objects are just conventional, there is no ontological distinction between stuff and things [Jubien]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
7. Existence / E. Categories / 1. Categories
The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Any entity has the unique property of being that specific entity [Jubien]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
It is incoherent to think that a given entity depends on its kind for its existence [Jubien]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien]
Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien]
If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
We should not regard essentialism as just nontrivial de re necessity [Jubien]
9. Objects / E. Objects over Time / 9. Ship of Theseus
Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien]
Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien]
10. Modality / A. Necessity / 6. Logical Necessity
Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Modality concerns relations among platonic properties [Jubien]
To analyse modality, we must give accounts of objects, properties and relations [Jubien]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien]
Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / a. Direct reference
First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
19. Language / F. Communication / 1. Rhetoric
Rhetoric can produce conviction, but not educate people about right and wrong [Plato]
Rhetoric is irrational about its means and its ends [Plato]
20. Action / B. Preliminaries of Action / 1. Intention to Act / b. Types of intention
All activity aims at the good [Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
Moral rules are made by the weak members of humanity [Plato]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
A good person is bound to act well, and this brings happiness [Plato]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Is it natural to simply indulge our selfish desires? [Plato]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
In slaking our thirst the goodness of the action and the pleasure are clearly separate [Plato]
Good should be the aim of pleasant activity, not the other way round [Plato]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Good and bad people seem to experience equal amounts of pleasure and pain [Plato]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato]
In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [Plato]
23. Ethics / A. Egoism / 2. Hedonism
Is the happiest state one of sensual, self-indulgent freedom? [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Should we avoid evil because it will bring us bad consequences? [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
I would rather be a victim of crime than a criminal [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
Self-indulgent desire makes friendship impossible, because it makes a person incapable of co-operation [Plato]
If absence of desire is happiness, then nothing is happier than a stone or a corpse [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
A criminal is worse off if he avoids punishment [Plato]
Do most people praise self-discipline and justice because they are too timid to gain their own pleasure? [Plato]
23. Ethics / C. Virtue Theory / 4. External Goods / b. Health
The popular view is that health is first, good looks second, and honest wealth third [Plato]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
As with other things, a good state is organised and orderly [Plato]
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
A good citizen won't be passive, but will redirect the needs of the state [Plato]
25. Social Practice / B. Equalities / 1. Grounds of equality
Do most people like equality because they are second-rate? [Plato]
25. Social Practice / B. Equalities / 4. Economic equality
Does nature imply that it is right for better people to have greater benefits? [Plato]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]