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All the ideas for 'Conditionals', 'Russell's Mathematical Logic' and 'Scientific Essentialism'

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48 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Ontology should give insight into or an explanation of the world revealed by science [Ellis]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Humean conceptions of reality drive the adoption of extensional logic [Ellis]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
8. Modes of Existence / B. Properties / 1. Nature of Properties
The extension of a property is a contingent fact, so cannot be the essence of the property [Ellis]
8. Modes of Existence / B. Properties / 5. Natural Properties
There is no property of 'fragility', as things are each fragile in a distinctive way [Ellis]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Typical 'categorical' properties are spatio-temporal, such as shape [Ellis]
The property of 'being an electron' is not of anything, and only electrons could have it [Ellis]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
'Being a methane molecule' is not a property - it is just a predicate [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Causal powers must necessarily act the way they do [Ellis]
Causal powers are often directional (e.g. centripetal, centrifugal, circulatory) [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Basic powers may not be explained by structure, if at the bottom level there is no structure [Ellis]
Maybe dispositions can be explained by intrinsic properties or structures [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
The most fundamental properties of nature (mass, charge, spin ...) all seem to be dispositions [Ellis]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
A causal power is a disposition to produce forces [Ellis]
Powers are dispositions of the essences of kinds that involve them in causation [Ellis]
8. Modes of Existence / D. Universals / 1. Universals
There are 'substantive' (objects of some kind), 'dynamic' (events of some kind) and 'property' universals [Ellis]
Universals are all types of natural kind [Ellis]
9. Objects / D. Essence of Objects / 3. Individual Essences
Scientific essentialism doesn't really need Kripkean individual essences [Ellis]
9. Objects / D. Essence of Objects / 15. Against Essentialism
The old idea that identity depends on essence and behaviour is rejected by the empiricists [Ellis]
10. Modality / A. Necessity / 3. Types of Necessity
Necessities are distinguished by their grounds, not their different modalities [Ellis]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
There are many different conditional mental states, and different conditional speech acts [Edgington]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
Individual essences necessitate that individual; natural kind essences necessitate kind membership [Ellis]
14. Science / C. Induction / 3. Limits of Induction
If events are unconnected, then induction cannot be solved [Ellis]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
Good explanations unify [Ellis]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Explanations of particular events are not essentialist, as they don't reveal essential structures [Ellis]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
To give essentialist explanations there have to be natural kinds [Ellis]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
The point of models in theories is not to idealise, but to focus on what is essential [Ellis]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
There might be uninstantiated natural kinds, such as transuranic elements which have never occurred [Ellis]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Natural kinds are distinguished by resting on essences [Ellis]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
If there are borderline cases between natural kinds, that makes them superficial [Ellis]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Laws don't exist in the world; they are true of the world [Ellis]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
A proton must have its causal role, because without it it wouldn't be a proton [Ellis]
What is most distinctive of scientific essentialism is regarding processes as natural kinds [Ellis]
Scientific essentialism is more concerned with explanation than with identity (Locke, not Kripke) [Ellis]
The ontological fundamentals are dispositions, and also categorical (spatio-temporal and structural) properties [Ellis]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
A primary aim of science is to show the limits of the possible [Ellis]