Combining Philosophers

All the ideas for Carl Ginet, George Cantor and J Ladyman / D Ross

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111 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
There is no test for metaphysics, except devising alternative theories [Ladyman/Ross]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics builds consilience networks across science [Ladyman/Ross]
Progress in metaphysics must be tied to progress in science [Ladyman/Ross]
Metaphysics must involve at least two scientific hypotheses, one fundamental, and add to explanation [Ladyman/Ross]
Some science is so general that it is metaphysical [Ladyman/Ross]
Cutting-edge physics has little to offer metaphysics [Ladyman/Ross]
The aim of metaphysics is to unite the special sciences with physics [Ladyman/Ross]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Modern metaphysics pursues aesthetic criteria like story-writing, and abandons scientific truth [Ladyman/Ross]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Why think that conceptual analysis reveals reality, rather than just how people think? [Ladyman/Ross]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
A metaphysics based on quantum gravity could result in almost anything [Ladyman/Ross]
The supremacy of science rests on its iterated error filters [Ladyman/Ross]
We should abandon intuitions, especially that the world is made of little things, and made of something [Ladyman/Ross]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine]
A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter]
The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / b. Combinatorial sets
Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Maybe mathematical logic rests on information-processing [Ladyman/Ross]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
There are infinite sets that are not enumerable [Cantor, by Smith,P]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Cantor took the ordinal numbers to be primary [Cantor, by Tait]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait]
Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett]
Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine]
Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine]
Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine]
It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman]
Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner]
The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro]
Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD]
Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten]
Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS]
Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy]
Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Pure mathematics is pure set theory [Cantor]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Cantor says that maths originates only by abstraction from objects [Cantor, by Frege]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Only admit into ontology what is explanatory and predictive [Ladyman/Ross]
To be is to be a real pattern [Ladyman/Ross]
7. Existence / B. Change in Existence / 2. Processes
Any process can be described as transfer of measurable information [Ladyman/Ross]
7. Existence / C. Structure of Existence / 6. Fundamentals / a. Fundamental reality
We say there is no fundamental level to ontology, and reality is just patterns [Ladyman/Ross]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics [Ladyman/Ross]
Concrete and abstract are too crude for modern physics [Ladyman/Ross]
7. Existence / D. Theories of Reality / 6. Physicalism
Physicalism is 'part-whole' (all parts are physical), or 'supervenience/levels' (dependence on physical) [Ladyman/Ross]
8. Modes of Existence / A. Relations / 1. Nature of Relations
Relations without relata must be treated as universals, with their own formal properties [Ladyman/Ross]
A belief in relations must be a belief in things that are related [Ladyman/Ross]
8. Modes of Existence / A. Relations / 2. Internal Relations
The normal assumption is that relations depend on properties of the relata [Ladyman/Ross]
8. Modes of Existence / A. Relations / 3. Structural Relations
That there are existent structures not made of entities is no stranger than the theory of universals [Ladyman/Ross]
8. Modes of Existence / B. Properties / 5. Natural Properties
Causal essentialism says properties are nothing but causal relations [Ladyman/Ross]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
If science captures the modal structure of things, that explains why its predictions work [Ladyman/Ross]
9. Objects / A. Existence of Objects / 1. Physical Objects
Things are constructs for tracking patterns (and not linguistic, because animals do it) [Ladyman/Ross]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Maybe individuation can be explained by thermodynamic depth [Ladyman/Ross]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
Physics seems to imply that we must give up self-subsistent individuals [Ladyman/Ross]
There is no single view of individuals, because different sciences operate on different scales [Ladyman/Ross]
There are no cats in quantum theory, and no mountains in astrophysics [Ladyman/Ross]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
Things are abstractions from structures [Ladyman/Ross]
9. Objects / C. Structure of Objects / 5. Composition of an Object
The idea of composition, that parts of the world are 'made of' something, is no longer helpful [Ladyman/Ross]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A sum of things is not a whole if the whole does not support some new generalisation [Ladyman/Ross]
9. Objects / D. Essence of Objects / 13. Nominal Essence
We treat the core of a pattern as an essence, in order to keep track of it [Ladyman/Ross]
9. Objects / E. Objects over Time / 1. Objects over Time
A continuous object might be a type, with instances at each time [Ladyman/Ross]
10. Modality / B. Possibility / 6. Probability
Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross]
In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Rats find some obvious associations easier to learn than less obvious ones [Ladyman/Ross]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The doctrine of empiricism does not itself seem to be empirically justified [Ladyman/Ross]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
There is no reason to think our intuitions are good for science or metaphysics [Ladyman/Ross]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Must all justification be inferential? [Ginet]
Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet]
14. Science / A. Basis of Science / 4. Prediction
What matters is whether a theory can predict - not whether it actually does so [Ladyman/Ross]
The theory of evolution was accepted because it explained, not because of its predictions [Ladyman/Ross]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
The Ramsey-sentence approach preserves observations, but eliminates unobservables [Ladyman/Ross]
The Ramsey sentence describes theoretical entities; it skips reference, but doesn't eliminate it [Ladyman/Ross]
14. Science / C. Induction / 1. Induction
Induction is reasoning from the observed to the unobserved [Ladyman/Ross]
14. Science / C. Induction / 4. Reason in Induction
Inductive defences of induction may be rule-circular, but not viciously premise-circular [Ladyman/Ross]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
We explain by deriving the properties of a phenomenon by embedding it in a large abstract theory [Ladyman/Ross]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
Maybe the only way we can think about a domain is by dividing it up into objects [Ladyman/Ross]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Two versions of quantum theory say that the world is deterministic [Ladyman/Ross]
17. Mind and Body / D. Property Dualism / 4. Emergentism
Science is opposed to downward causation [Ladyman/Ross]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor]
We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
Explanation by kinds and by clusters of properties just express the stability of reality [Ladyman/Ross]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
There is nothing more to a natural kind than a real pattern in nature [Ladyman/Ross]
26. Natural Theory / C. Causation / 7. Eliminating causation
Causation is found in the special sciences, but may have no role in fundamental physics [Ladyman/Ross]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Science may have uninstantiated laws, inferred from approaching some unrealised limit [Ladyman/Ross]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
That the universe must be 'made of' something is just obsolete physics [Ladyman/Ross]
In physics, matter is an emergent phenomenon, not part of fundamental ontology [Ladyman/Ross]
27. Natural Reality / C. Space / 3. Points in Space
Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg]
27. Natural Reality / C. Space / 6. Space-Time
If spacetime is substantial, what is the substance? [Ladyman/Ross]
Spacetime may well be emergent, rather than basic [Ladyman/Ross]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
A fixed foliation theory of quantum gravity could make presentism possible [Ladyman/Ross]
28. God / A. Divine Nature / 2. Divine Nature
Only God is absolutely infinite [Cantor, by Hart,WD]