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All the ideas for 'Frege's Concept of Numbers as Objects', 'From an Ontological Point of View' and 'Mere Possibilities'

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117 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 / 1. Nature of Metaphysics
I don't think Lewis's cost-benefit reflective equilibrium approach offers enough guidance [Stalnaker]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
If you begin philosophy with language, you find yourself trapped in it [Heil]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
A theory with few fundamental principles might still posit a lot of entities [Heil]
Parsimony does not imply the world is simple, but that our theories should try to be [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 / B. Truthmakers / 4. Truthmaker Necessitarianism
The view that truth making is entailment is misguided and misleading [Heil]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Non-S5 can talk of contingent or necessary necessities [Stalnaker]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
God does not create the world, and then add the classes [Heil]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker]
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 / 1. Nature of Existence
Some say what exists must do so, and nothing else could possible exist [Stalnaker]
A nominalist view says existence is having spatio-temporal location [Stalnaker]
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
The reductionist programme dispenses with levels of reality [Heil]
7. Existence / C. Structure of Existence / 3. Levels of Reality
There are levels of organisation, complexity, description and explanation, but not of reality [Heil]
7. Existence / D. Theories of Reality / 2. Realism
Realism says some of our concepts 'cut nature at the joints' [Heil]
7. Existence / D. Theories of Reality / 4. Anti-realism
Anti-realists who reduce reality to language must explain the existence of language [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 / E. Categories / 5. Category Anti-Realism
Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Properties are modal, involving possible situations where they are exemplified [Stalnaker]
8. Modes of Existence / B. Properties / 9. Qualities
I think of properties as simultaneously dispositional and qualitative [Heil]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
I accept a hierarchy of properties of properties of properties [Stalnaker]
A predicate applies truly if it picks out a real property of objects [Heil]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Powers or dispositions are usually seen as caused by lower-level qualities [Heil]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions have modal properties, of which properties things would have counterfactually [Stalnaker]
Are a property's dispositions built in, or contingently added? [Heil]
8. Modes of Existence / D. Universals / 2. Need for Universals
Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
How could you tell if the universals were missing from a world of instances? [Heil]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Similarity among modes will explain everthing universals were for [Heil]
Similar objects have similar properties; properties are directly similar [Heil]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
Objects join sets because of properties; the property is not bestowed by set membership [Heil]
9. Objects / A. Existence of Objects / 1. Physical Objects
Trope theorists usually see objects as 'bundles' of tropes [Heil]
Objects are substances, which are objects considered as the bearer of properties [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 / 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 / c. Types of substance
Maybe there is only one substance, space-time or a quantum field [Heil]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
Rather than 'substance' I use 'objects', which have properties [Heil]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Statues and bronze lumps have discernible differences, so can't be identical [Heil]
Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
'Socrates is essentially human' seems to say nothing could be Socrates if it was not human [Stalnaker]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties [Stalnaker]
10. Modality / A. Necessity / 3. Types of Necessity
Strong necessity is always true; weak necessity is cannot be false [Stalnaker]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
Necessity and possibility are fundamental, and there can be no reductive analysis of them [Stalnaker]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Modal concepts are central to the actual world, and shouldn't need extravagant metaphysics [Stalnaker]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Given actualism, how can there be possible individuals, other than the actual ones? [Stalnaker]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are properties [Stalnaker]
Possible worlds don't reduce modality, they regiment it to reveal its structure [Stalnaker]
I think of worlds as cells (rather than points) in logical space [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Modal properties depend on the choice of a counterpart, which is unconstrained by metaphysics [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Anti-haecceitism says there is no more to an individual than meeting some qualitative conditions [Stalnaker]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
Properties don't possess ways they are, because that just is the property [Heil]
If properties were qualities without dispositions, they would be undetectable [Heil]
Can we distinguish the way a property is from the property? [Heil]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
Objects only have secondary qualities because they have primary qualities [Heil]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Secondary qualities are just primary qualities considered in the light of their effect on us [Heil]
Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
Treating colour as light radiation has the implausible result that tomatoes are not red [Heil]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
If the world is just texts or social constructs, what are texts and social constructs? [Heil]
14. Science / B. Scientific Theories / 1. Scientific Theory
If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil]
14. Science / B. Scientific Theories / 2. Aim of Science
Science is sometimes said to classify powers, neglecting qualities [Heil]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
One form of explanation is by decomposition [Heil]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Dispositionality provides the grounding for intentionality [Heil]
Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil]
17. Mind and Body / A. Mind-Body Dualism / 7. Zombies
Philosophers' zombies aim to show consciousness is over and above the physical world [Heil]
Zombies are based on the idea that consciousness relates contingently to the physical [Heil]
Functionalists deny zombies, since identity of functional state means identity of mental state [Heil]
17. Mind and Body / C. Functionalism / 1. Functionalism
Functionalists say objects can be the same in disposition but differ in quality [Heil]
17. Mind and Body / C. Functionalism / 8. Functionalism critique
Functionalism cannot explain consciousness just by functional organisation [Heil]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil]
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Multiple realisability is actually one predicate applying to a diverse range of properties [Heil]
18. Thought / C. Content / 6. Broad Content
How can we know what we are thinking, if content depends on something we don't know? [Stalnaker]
Externalism is causal-historical, or social, or biological [Heil]
18. Thought / C. Content / 7. Narrow Content
Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [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 / 2. Meaning as Mental
The Picture Theory claims we can read reality from our ways of speaking about it [Heil]
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 / 2. Semantics
We still lack an agreed semantics for quantifiers in natural language [Stalnaker]
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 / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible world semantics may not reduce modality, but it can explain it [Stalnaker]
19. Language / D. Propositions / 1. Propositions
I take propositions to be truth conditions [Stalnaker]
A theory of propositions at least needs primitive properties of consistency and of truth [Stalnaker]
19. Language / D. Propositions / 2. Abstract Propositions / b. Propositions as possible worlds
If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions presumably don't exist if the things they refer to don't exist [Stalnaker]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
The standard view is that causal sequences are backed by laws, and between particular events [Heil]
27. Natural Reality / F. Chemistry / 2. Modern Elements
The real natural properties are sparse, but there are many complex properties [Heil]