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All the ideas for 'Reply to 'Rorarius' 2nd ed', 'Frege's Concept of Numbers as Objects' and 'Laws of Nature'

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64 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]
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]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré]
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]
5. Theory of Logic / G. Quantification / 1. Quantification
Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
Some quantifiers, such as 'any', rule out any notion of order within their range [Harré]
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 / 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 / 4. Intrinsic Properties
Scientific properties are not observed qualities, but the dispositions which create them [Harré]
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]
10. Modality / A. Necessity / 7. Natural Necessity
Laws of nature remain the same through any conditions, if the underlying mechanisms are unchanged [Harré]
14. Science / A. Basis of Science / 1. Observation
In physical sciences particular observations are ordered, but in biology only the classes are ordered [Harré]
14. Science / A. Basis of Science / 3. Experiment
Reports of experiments eliminate the experimenter, and present results as the behaviour of nature [Harré]
14. Science / A. Basis of Science / 5. Anomalies
We can save laws from counter-instances by treating the latter as analytic definitions [Harré]
14. Science / B. Scientific Theories / 1. Scientific Theory
Since there are three different dimensions for generalising laws, no one system of logic can cover them [Harré]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
The grue problem shows that natural kinds are central to science [Harré]
'Grue' introduces a new causal hypothesis - that emeralds can change colour [Harré]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
It is because ravens are birds that their species and their colour might be connected [Harré]
Non-black non-ravens just aren't part of the presuppositions of 'all ravens are black' [Harré]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
The necessity of Newton's First Law derives from the nature of material things, not from a mechanism [Harré]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré]
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 / B. Natural Kinds / 1. Natural Kinds
Science rests on the principle that nature is a hierarchy of natural kinds [Harré]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Classification is just as important as laws in natural science [Harré]
Newton's First Law cannot be demonstrated experimentally, as that needs absence of external forces [Harré]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
Laws can come from data, from theory, from imagination and concepts, or from procedures [Harré]
Are laws of nature about events, or types and universals, or dispositions, or all three? [Harré]
Are laws about what has or might happen, or do they also cover all the possibilities? [Harré]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Maybe laws of nature are just relations between properties? [Harré]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
We take it that only necessary happenings could be laws [Harré]
Must laws of nature be universal, or could they be local? [Harré]
Laws describe abstract idealisations, not the actual mess of nature [Harré]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Laws of nature state necessary connections of things, events and properties, based on models of mechanisms [Harré]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
In counterfactuals we keep substances constant, and imagine new situations for them [Harré]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
Space and time are the order of all possibilities, and don't just relate to what is actual [Leibniz]