Combining Texts

All the ideas for 'fragments/reports', 'The Meaning of 'Meaning'' and 'Higher-Order Logic'

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23 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 / D. Essence of Objects / 15. Against Essentialism
18890 Putnam smuggles essentialism about liquids into his proof that water must be H2O [Salmon,N on Putnam]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
7705 The Twin Earth theory suggests that intentionality is independent of qualia [Jacquette on Putnam]
18. Thought / C. Content / 5. Twin Earth
4099 If Twins talking about 'water' and 'XYZ' have different thoughts but identical heads, then thoughts aren't in the head [Putnam, by Crane]
12026 We say ice and steam are different forms of water, but not that they are different forms of H2O [Forbes,G on Putnam]
3208 Does 'water' mean a particular substance that was 'dubbed'? [Putnam, by Rey]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
3893 Often reference determines sense, and not (as Frege thought) vice versa [Putnam, by Scruton]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
11191 The hidden structure of a natural kind determines membership in all possible worlds [Putnam]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
11192 If causes are the essence of diseases, then disease is an example of a relational essence [Putnam, by Williams,NE]
11190 Archimedes meant by 'gold' the hidden structure or essence of the stuff [Putnam]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]