Combining Texts

All the ideas for 'Explaining Explanation', 'Higher-Order Logic' and 'works'

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21 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
17082 Paradox: why do you analyse if you know it, and how do you analyse if you don't? [Ruben]
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]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
13536 Skolem did not believe in the existence of uncountable sets [Skolem]
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]
14. Science / A. Basis of Science / 4. Prediction
17087 The 'symmetry thesis' says explanation and prediction only differ pragmatically [Ruben]
14. Science / D. Explanation / 1. Explanation / a. Explanation
17081 Usually explanations just involve giving information, with no reference to the act of explanation [Ruben]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
17092 An explanation needs the world to have an appropriate structure [Ruben]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17090 Most explanations are just sentences, not arguments [Ruben]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
17094 The causal theory of explanation neglects determinations which are not causal [Ruben]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
17088 Reducing one science to another is often said to be the perfect explanation [Ruben]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
17089 Facts explain facts, but only if they are conceptualised or named appropriately [Ruben]