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All the ideas for 'Frege's Concept of Numbers as Objects', 'works' and 'How Things Persist'

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76 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophers are good at denying the obvious [Hawley]
2. Reason / C. Styles of Reason / 1. Dialectic
The best way to understand a philosophical idea is to defend it [Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Part of the sense of a proper name is a criterion of the thing's identity [Hawley]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
There are five Peano axioms, which can be expressed informally [Wright,C]
Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C]
What facts underpin the truths of the Peano axioms? [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Number platonism says that natural number is a sortal concept [Wright,C]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Treating numbers adjectivally is treating them as quantifiers [Wright,C]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C]
The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]
7. Existence / A. Nature of Existence / 2. Types of Existence
The idea that 'exist' has multiple senses is not coherent [Wright,C]
7. Existence / C. Structure of Existence / 5. Supervenience / d. Humean supervenience
A homogeneous rotating disc should be undetectable according to Humean supervenience [Hawley]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
Non-linguistic things cannot be indeterminate, because they don't have truth-values at all [Hawley]
Maybe for the world to be vague, it must be vague in its foundations? [Hawley]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Epistemic vagueness seems right in the case of persons [Hawley]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
Supervaluation refers to one vaguely specified thing, through satisfaction by everything in some range [Hawley]
Supervaluationism takes what the truth-value would have been if indecision was resolved [Hawley]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Maybe the only properties are basic ones like charge, mass and spin [Hawley]
9. Objects / A. Existence of Objects / 1. Physical Objects
An object is 'natural' if its stages are linked by certain non-supervenient relations [Hawley]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
We accept substance, to avoid infinite backwards chains of meaning [Wittgenstein, by Potter]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Are sortals spatially maximal - so no cat part is allowed to be a cat? [Hawley]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
The modal features of statue and lump are disputed; when does it stop being that statue? [Hawley]
Perdurantists can adopt counterpart theory, to explain modal differences of identical part-sums [Hawley]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vagueness is either in our knowledge, in our talk, or in reality [Hawley]
Indeterminacy in objects and in properties are not distinct cases [Hawley]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
The constitution theory is endurantism plus more than one object in a place [Hawley]
Constitution theory needs sortal properties like 'being a sweater' to distinguish it from its thread [Hawley]
If the constitution view says thread and sweater are two things, why do we talk of one thing? [Hawley]
9. Objects / E. Objects over Time / 2. Objects that Change
'Adverbialism' explains change by saying an object has-at-some-time a given property [Hawley]
Presentism solves the change problem: the green banana ceases, so can't 'relate' to the yellow one [Hawley]
The problem of change arises if there must be 'identity' of a thing over time [Hawley]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
Endurance theory can relate properties to times, or timed instantiations to properties [Hawley]
Endurance is a sophisticated theory, covering properties, instantiation and time [Hawley]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
How does perdurance theory explain our concern for our own future selves? [Hawley]
Perdurance needs an atemporal perspective, to say that the object 'has' different temporal parts [Hawley]
If an object is the sum of all of its temporal parts, its mass is staggeringly large! [Hawley]
Perdurance says things are sums of stages; Stage Theory says each stage is the thing [Hawley]
If a life is essentially the sum of its temporal parts, it couldn't be shorter or longer than it was? [Hawley]
9. Objects / E. Objects over Time / 5. Temporal Parts
Stage Theory seems to miss out the link between stages of the same object [Hawley]
Stage Theory says every stage is a distinct object, which gives too many objects [Hawley]
An isolated stage can't be a banana (which involves suitable relations to other stages) [Hawley]
Stages of one thing are related by extrinsic counterfactual and causal relations [Hawley]
The stages of Stage Theory seem too thin to populate the world, or to be referred to [Hawley]
Stages must be as fine-grained in length as change itself, so any change is a new stage [Hawley]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
If two things might be identical, there can't be something true of one and false of the other [Hawley]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
To decide whether something is a counterpart, we need to specify a relevant sortal concept [Hawley]
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
On any theory of self, it is hard to explain why we should care about our future selves [Hawley]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
A concept is only a sortal if it gives genuine identity [Wright,C]
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A milder claim is that understanding requires some evidence of that understanding [Wright,C]
19. Language / B. Reference / 1. Reference theories
If apparent reference can mislead, then so can apparent lack of reference [Wright,C]
19. Language / C. Assigning Meanings / 3. Predicates
We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Causation is nothing more than the counterfactuals it grounds? [Hawley]
27. Natural Reality / D. Time / 3. Parts of Time / b. Instants
Time could be discrete (like integers) or dense (rationals) or continuous (reals) [Hawley]