Combining Texts

All the ideas for 'Logical Investigations', 'Letters to Oldenburg' and 'Higher-Order Logic'

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19 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
15570 Phenomenology is the science of essences - necessary universal structures for art, representation etc. [Husserl, by Polt]
7614 Bracketing subtracts entailments about external reality from beliefs [Husserl, by Putnam]
6893 Phenomenology aims to describe experience directly, rather than by its origins or causes [Husserl, by Mautner]
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]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
21216 Husserl says we have intellectual intuitions (of categories), as well as of the senses [Husserl, by Velarde-Mayol]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
4867 Whether nature is beautiful or orderly is entirely in relation to human imagination [Spinoza]
28. God / A. Divine Nature / 3. Divine Perfections
4866 God is a being with infinite attributes, each of them infinite or perfect [Spinoza]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
4868 Trying to prove God's existence through miracles is proving the obscure by the more obscure [Spinoza]