Combining Texts

All the ideas for 'Against Structural Universals', 'works' and 'First-Order Logic'

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26 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
15435 If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
15451 I assume there could be natural properties that are not instantiated in our world [Lewis]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
15433 Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis]
8. Modes of Existence / D. Universals / 2. Need for Universals
15436 Universals are meant to give an account of resemblance [Lewis]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
15438 We can add a primitive natural/unnatural distinction to class nominalism [Lewis]
9. Objects / C. Structure of Objects / 1. Structure of an Object
15448 The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis]
15449 If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis]
15439 The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis]
15441 The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis]
15445 Butane and Isobutane have the same atoms, but different structures [Lewis]
15434 Structural universals have a necessary connection to the universals forming its parts [Lewis]
15437 We can't get rid of structural universals if there are no simple universals [Lewis]
9. Objects / C. Structure of Objects / 5. Composition of an Object
15446 Composition is not just making new things from old; there are too many counterexamples [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
15440 A whole is distinct from its parts, but is not a further addition in ontology [Lewis]
15444 Different things (a toy house and toy car) can be made of the same parts at different times [Lewis]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
15450 Maybe abstraction is just mereological subtraction [Lewis]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
15443 Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16714 The state should kill blasphemous heretics [Erasmus]