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All the ideas for 'Frege's Concept of Numbers as Objects', 'New work for a theory of universals' and 'Of liberty, Fate and God's grace'

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70 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 / F. Analytic Philosophy / 4. Conceptual Analysis
In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis]
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 / C. Structure of Existence / 2. Reduction
Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
A supervenience thesis is a denial of independent variation [Lewis]
7. Existence / D. Theories of Reality / 6. Physicalism
Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis]
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
Universals are wholly present in their instances, whereas properties are spread around [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver]
Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley]
Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis]
Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis]
Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis]
For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis]
All perfectly natural properties are intrinsic [Lewis, by Lewis]
Natural properties fix resemblance and powers, and are picked out by universals [Lewis]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Lewis says properties are sets of actual and possible objects [Lewis, by Heil]
Any class of things is a property, no matter how whimsical or irrelevant [Lewis]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
There are far more properties than any brain could ever encodify [Lewis]
We need properties as semantic values for linguistic expressions [Lewis]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis]
8. Modes of Existence / D. Universals / 1. Universals
I suspend judgements about universals, but their work must be done [Lewis]
8. Modes of Existence / D. Universals / 2. Need for Universals
Physics aims to discover which universals actually exist [Lewis, by Moore,AW]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
To have a property is to be a member of a class, usually a class of things [Lewis]
Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis]
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 / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
The complete concept of an individual includes contingent properties, as well as necessary ones [Leibniz]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Psychophysical identity implies the possibility of idealism or panpsychism [Lewis]
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]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
A sophisticated principle of charity sometimes imputes error as well as truth [Lewis]
We need natural properties in order to motivate the principle of charity [Lewis]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Counterfactuals 'backtrack' if a different present implies a different past [Lewis]
Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Physics discovers laws and causal explanations, and also the natural properties required [Lewis]
Physics aims for a list of natural properties [Lewis]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
A law of nature is any regularity that earns inclusion in the ideal system [Lewis]