Combining Texts

All the ideas for 'Super Epistolam Pauli Apostoli', 'Higher-Order Logic' and 'Guidebook to Wittgenstein's Tractatus'

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20 ideas

1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
23449 Interpreting a text is representing it as making sense [Morris,M]
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 / D. Assumptions for Logic / 1. Bivalence
23484 Bipolarity adds to Bivalence the capacity for both truth values [Morris,M]
5. Theory of Logic / G. Quantification / 1. Quantification
23494 Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M]
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 / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
23451 Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M]
23460 To count, we must distinguish things, and have a series with successors in it [Morris,M]
23452 Discriminating things for counting implies concepts of identity and distinctness [Morris,M]
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]
19. Language / D. Propositions / 1. Propositions
23491 There must exist a general form of propositions, which are predictabe. It is: such and such is the case [Morris,M]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1863 If the soul achieves well-being in another life, it doesn't follow that I do [Aquinas]