Combining Texts

All the ideas for 'Commentary on 'De Anima'', 'Inexpressible Properties and Propositions' and 'Higher-Order Logic'

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17 ideas

3. Truth / H. Deflationary Truth / 3. Minimalist Truth
17990 Instances of minimal truth miss out propositions inexpressible in current English [Hofweber]
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 / 4. Substitutional Quantification
17988 Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]
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
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
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]
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 / 1. Nature of Properties
17989 Since properties have properties, there can be a typed or a type-free theory of them [Hofweber]
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 / F. Communication / 6. Interpreting Language / a. Translation
17991 Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber]
22. Metaethics / B. Value / 2. Values / e. Death
16764 The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]