Combining Texts

All the ideas for 'Law and Causality', 'Higher-Order Logic' and 'How Things Might Have Been'

expand these ideas     |    start again     |     specify just one area for these texts

35 ideas

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]
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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
11897 A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P]
11898 Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
11883 A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11889 Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P]
9. Objects / D. Essence of Objects / 3. Individual Essences
11877 An individual essence is the properties the object could not exist without [Mackie,P]
11882 No other object can possibly have the same individual essence as some object [Mackie,P]
11886 There are problems both with individual essences and without them [Mackie,P]
9. Objects / D. Essence of Objects / 5. Essence as Kind
11909 Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P]
11899 Why are any sortals essential, and why are only some of them essential? [Mackie,P]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
11906 The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P]
9. Objects / E. Objects over Time / 12. Origin as Essential
11894 Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
10993 Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
14279 Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
11887 Transworld identity without individual essences leads to 'bare identities' [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11890 De re modality without bare identities or individual essence needs counterparts [Mackie,P]
11892 Things may only be counterparts under some particular relation [Mackie,P]
11893 Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
11884 The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
6894 Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
11905 Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P]
26. Natural Theory / B. Natural Kinds / 6. Necessity of Kinds
11907 Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
9418 All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey]
9420 Causal laws result from the simplest axioms of a complete deductive system [Ramsey]