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All the ideas for 'fragments/reports', 'Four Dimensionalism' and 'Frege's Concept of Numbers as Objects'

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67 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 / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysical enquiry can survive if its conclusions are tentative [Sider]
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 / 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 / B. Change in Existence / 2. Processes
Four-dimensionalism sees things and processes as belonging in the same category [Sider]
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 / 6. Categorical Properties
Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider]
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]
If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The stage view of objects is best for dealing with coincident entities [Sider]
9. Objects / C. Structure of Objects / 5. Composition of an Object
'Composition as identity' says that an object just is the objects which compose it [Sider]
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says an object's parts are necessary for its existence [Sider]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider]
Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider]
4D says intrinsic change is difference between successive parts [Sider]
4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider]
9. Objects / E. Objects over Time / 5. Temporal Parts
Temporal parts exist, but are not prior building blocks for objects [Sider]
Temporal parts are instantaneous [Sider]
How can an instantaneous stage believe anything, if beliefs take time? [Sider]
Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
9. Objects / E. Objects over Time / 9. Ship of Theseus
The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterparts rest on similarity, so there are many such relations in different contexts [Sider]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
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]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider]
27. Natural Reality / C. Space / 6. Space-Time
Space is 3D and lacks a direction; time seems connected to causation [Sider]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
For Presentists there must always be a temporal vantage point for any description [Sider]
Presentists must deny truths about multiple times [Sider]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
The B-theory is adequate, except that it omits to say which time is present [Sider]
The B-series involves eternalism, and the reduction of tense [Sider]