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All the ideas for 'Frege's Concept of Numbers as Objects', '06: Book of Joshua' and 'The Universe as We Find It'

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80 ideas

1. Philosophy / A. Wisdom / 2. Wise People
The best philosophers I know are the best people I know [Heil]
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
Using a technical vocabulary actually prevents discussion of the presuppositions [Heil]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Questions of explanation should not be confused with metaphyics [Heil]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Without abstraction we couldn't think systematically [Heil]
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]
3. Truth / A. Truth Problems / 4. Uses of Truth
Truth relates truthbearers to truthmakers [Heil]
3. Truth / B. Truthmakers / 1. For Truthmakers
Philosophers of the past took the truthmaking idea for granted [Heil]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Not all truths need truthmakers - mathematics and logic seem to be just true [Heil]
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 / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Infinite numbers are qualitatively different - they are not just very large numbers [Heil]
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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
How could structures be mathematical truthmakers? Maths is just true, without truthmakers [Heil]
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
Our categories lack the neat arrangement needed for reduction [Heil]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
Fundamental ontology aims at the preconditions for any true theory [Heil]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Our quantifications only reveal the truths we accept; the ontology and truthmakers are another matter [Heil]
7. Existence / E. Categories / 4. Category Realism
Ontology aims to give the fundamental categories of being [Heil]
8. Modes of Existence / A. Relations / 1. Nature of Relations
Most philosophers now (absurdly) believe that relations fully exist [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
If causal relations are power manifestations, that makes them internal relations [Heil]
8. Modes of Existence / B. Properties / 2. Need for Properties
We need properties to explain how the world works [Heil]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Categorical properties were introduced by philosophers as actual properties, not if-then properties [Heil]
8. Modes of Existence / B. Properties / 7. Emergent Properties
Emergent properties will need emergent substances to bear them [Heil]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Predicates only match properties at the level of fundamentals [Heil]
In Fa, F may not be a property of a, but a determinable, satisfied by some determinate [Heil]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Properties have causal roles which sets can't possibly have [Heil]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
Are all properties powers, or are there also qualities, or do qualities have the powers? [Heil]
Properties are both qualitative and dispositional - they are powerful qualities [Heil]
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 / 2. Abstract Objects / d. Problems with abstracta
Abstract objects wouldn't be very popular without the implicit idea of truthmakers [Heil]
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 / a. Substance
Substances bear properties, so must be simple, and not consist of further substances [Heil]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Spatial parts are just regions, but objects depend on and are made up of substantial parts [Heil]
A 'gunky' universe would literally have no parts at all [Heil]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Many wholes can survive replacement of their parts [Heil]
Dunes depend on sand grains, but line segments depend on the whole line [Heil]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
If basic physics has natures, then why not reality itself? That would then found the deepest necessities [Heil]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
If possible worlds are just fictions, they can't be truthmakers for modal judgements [Heil]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Mental abstraction does not make what is abstracted mind-dependent [Heil]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Only particulars exist, and generality is our mode of presentation [Heil]
18. Thought / A. Modes of Thought / 1. Thought
You can think of tomatoes without grasping what they are [Heil]
18. Thought / A. Modes of Thought / 8. Human Thought
Linguistic thought is just as imagistic as non-linguistic thought [Heil]
Non-conscious thought may be unlike conscious thought [Heil]
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]
The subject-predicate form reflects reality [Heil]
22. Metaethics / B. Value / 2. Values / a. Normativity
Many reject 'moral realism' because they can't see any truthmakers for normative judgements [Heil]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
If there were infinite electrons, they could vanish without affecting total mass-energy [Heil]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
We should focus on actual causings, rather than on laws and causal sequences [Heil]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
Probabilistic causation is not a weak type of cause; it is just a probability of there being a cause [Heil]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
Electrons are treated as particles, but they lose their individuality in relations [Heil]
27. Natural Reality / E. Cosmology / 1. Cosmology
Joshua said, Sun, stand thou still [Anon (Josh)]
27. Natural Reality / E. Cosmology / 9. Fine-Tuned Universe
Maybe the universe is fine-tuned because it had to be, despite plans by God or Nature? [Heil]