Combining Philosophers

All the ideas for Herodotus, Mark Colyvan and George Molnar

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60 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Substantive metaphysics says what a property is, not what a predicate means [Molnar]
2. Reason / D. Definition / 4. Real Definition
A real definition gives all the properties that constitute an identity [Molnar]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Rejecting double negation elimination undermines reductio proofs [Colyvan]
Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinal numbers represent order relations [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Intuitionists only accept a few safe infinities [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Most mathematical proofs are using set theory, but without saying so [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
Ontological dependence rests on essential connection, not necessary connection [Molnar]
7. Existence / E. Categories / 3. Proposed Categories
The three categories in ontology are objects, properties and relations [Molnar]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
Reflexive relations are syntactically polyadic but ontologically monadic [Molnar]
8. Modes of Existence / B. Properties / 1. Nature of Properties
If atomism is true, then all properties derive from ultimate properties [Molnar]
8. Modes of Existence / B. Properties / 5. Natural Properties
'Being physical' is a second-order property [Molnar]
8. Modes of Existence / B. Properties / 6. Categorical Properties
'Categorical properties' are those which are not powers [Molnar]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
Are tropes transferable? If they are, that is a version of Platonism [Molnar]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
A power's type-identity is given by its definitive manifestation [Molnar]
Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
The physical world has a feature very like mental intentionality [Molnar]
Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar]
The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar]
Some powers are ungrounded, and others rest on them, and are derivative [Molnar]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions can be causes, so they must be part of the actual world [Molnar]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
Platonic explanations of universals actually diminish our understanding [Molnar]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
For nominalists, predicate extensions are inexplicable facts [Molnar]
Nominalists only accept first-order logic [Molnar]
9. Objects / C. Structure of Objects / 1. Structure of an Object
Structural properties are derivate properties [Molnar]
There are no 'structural properties', as properties with parts [Molnar]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
The essence of a thing need not include everything that is necessarily true of it [Molnar]
10. Modality / B. Possibility / 1. Possibility
What is the truthmaker for a non-existent possible? [Molnar]
14. Science / C. Induction / 6. Bayes's Theorem
Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Mathematics can reveal structural similarities in diverse systems [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
Mathematics can show why some surprising events have to occur [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
Reductio proofs do not seem to be very explanatory [Colyvan]
If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
The two ways proposed to distinguish mind are intentionality or consciousness [Molnar]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
Physical powers like solubility and charge also have directedness [Molnar]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Rule occasionalism says God's actions follow laws, not miracles [Molnar]
26. Natural Theory / C. Causation / 2. Types of cause
Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar]
26. Natural Theory / C. Causation / 4. Naturalised causation
We should analyse causation in terms of powers, not vice versa [Molnar]
26. Natural Theory / C. Causation / 7. Eliminating causation
We should analyse causation in terms of powers [Molnar]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Causal dependence explains counterfactual dependence, not vice versa [Molnar]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Science works when we assume natural kinds have essences - because it is true [Molnar]
Location in space and time are non-power properties [Molnar, by Mumford]
One essential property of a muon doesn't entail the others [Molnar]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
It is contingent which kinds and powers exist in the world [Molnar]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
The laws of nature depend on the powers, not the other way round [Molnar]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
Energy fields are discontinuous at the very small [Molnar]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]