Combining Texts

All the ideas for 'Explaining the A Priori', 'What is a Law of Nature?' and 'Higher-Order Logic'

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48 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
If you know what it is, investigation is pointless. If you don't, investigation is impossible [Armstrong]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Some say that second-order logic is mathematics, not logic [Shapiro]
If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
Negative facts are supervenient on positive facts, suggesting they are positive facts [Armstrong]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
Nothing is genuinely related to itself [Armstrong]
8. Modes of Existence / B. Properties / 1. Nature of Properties
All instances of some property are strictly identical [Armstrong]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Armstrong holds that all basic properties are categorical [Armstrong, by Ellis]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
Actualism means that ontology cannot contain what is merely physically possible [Armstrong]
Dispositions exist, but their truth-makers are actual or categorical properties [Armstrong]
If everything is powers there is a vicious regress, as powers are defined by more powers [Armstrong]
8. Modes of Existence / D. Universals / 1. Universals
Universals are just the repeatable features of a world [Armstrong]
8. Modes of Existence / D. Universals / 2. Need for Universals
Realist regularity theories of laws need universals, to pick out the same phenomena [Armstrong]
8. Modes of Existence / D. Universals / 3. Instantiated Universals
Past, present and future must be equally real if universals are instantiated [Armstrong]
Universals are abstractions from states of affairs [Armstrong]
Universals are abstractions from their particular instances [Armstrong, by Lewis]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
It is likely that particulars can be individuated by unique conjunctions of properties [Armstrong]
9. Objects / F. Identity among Objects / 5. Self-Identity
The identity of a thing with itself can be ruled out as a pseudo-property [Armstrong]
10. Modality / B. Possibility / 5. Contingency
The necessary/contingent distinction may need to recognise possibilities as real [Armstrong]
14. Science / C. Induction / 3. Limits of Induction
Induction aims at 'all Fs', but abduction aims at hidden or theoretical entities [Armstrong]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Science suggests that the predicate 'grue' is not a genuine single universal [Armstrong]
Unlike 'green', the 'grue' predicate involves a time and a change [Armstrong]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
The raven paradox has three disjuncts, confirmed by confirming any one of them [Armstrong]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
A good reason for something (the smoke) is not an explanation of it (the fire) [Armstrong]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
To explain observations by a regular law is to explain the observations by the observations [Armstrong]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
Best explanations explain the most by means of the least [Armstrong]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
The concept 'red' is tied to what actually individuates red things [Peacocke]
18. Thought / E. Abstraction / 1. Abstract Thought
Each subject has an appropriate level of abstraction [Armstrong]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
We can't deduce the phenomena from the One [Armstrong]
26. Natural Theory / C. Causation / 2. Types of cause
Absences might be effects, but surely not causes? [Armstrong]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Science depends on laws of nature to study unobserved times and spaces [Armstrong]
A universe couldn't consist of mere laws [Armstrong]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
Oaken conditional laws, Iron universal laws, and Steel necessary laws [Armstrong, by PG]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Newton's First Law refers to bodies not acted upon by a force, but there may be no such body [Armstrong]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Regularities are lawful if a second-order universal unites two first-order universals [Armstrong, by Lewis]
A naive regularity view says if it never occurs then it is impossible [Armstrong]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
The laws of nature link properties with properties [Armstrong]
Rather than take necessitation between universals as primitive, just make laws primitive [Maudlin on Armstrong]
Armstrong has an unclear notion of contingent necessitation, which can't necessitate anything [Bird on Armstrong]