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All the ideas for 'Higher-Order Logic', 'The Principles of Chemistry' and 'Metaphysical Dependence'

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26 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
14092 Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen]
2. Reason / D. Definition / 1. Definitions
14100 Figuring in the definition of a thing doesn't make it a part of that thing [Rosen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 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
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 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
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 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
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
14096 Explanations fail to be monotonic [Rosen]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
14097 Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
14095 Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14093 An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
10. Modality / A. Necessity / 5. Metaphysical Necessity
14094 The excellent notion of metaphysical 'necessity' cannot be defined [Rosen]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14101 Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen]
19. Language / E. Analyticity / 1. Analytic Propositions
14099 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
17402 Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri]
27. Natural Reality / F. Chemistry / 1. Chemistry
14098 An acid is just a proton donor [Rosen]
27. Natural Reality / F. Chemistry / 2. Modern Elements
17399 Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev]
27. Natural Reality / F. Chemistry / 3. Periodic Table
17400 Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri]
17401 Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev]