Combining Texts

All the ideas for 'fragments/reports', 'Existentialism: an introduction' and 'Higher-Order Logic'

expand these ideas     |    start again     |     specify just one area for these texts

21 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
20744 Phenomenologists say all experience is about something and is directed [Aho]
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]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
604 Knowledge is mind and knowing 'cohabiting' [Lycophron, by Aristotle]
14. Science / B. Scientific Theories / 2. Aim of Science
20736 Science has to abstract out the subjective attributes of things, focusing on what is objective [Aho]
23. Ethics / F. Existentialism / 3. Angst
20734 Anxiety, nausea, guilt and absurdity shake us up, revealing our freedom and limits [Aho]
23. Ethics / F. Existentialism / 5. Existence-Essence
20733 Our 'existence' is how we create ourselves, unconstrained by any prior 'essence' [Aho]
23. Ethics / F. Existentialism / 6. Authentic Self
20753 The self is constituted by its choices made within a social context [Aho]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
20738 Social contracts and markets have made society seem disconnected and artificial [Aho]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
20737 Protestantism brought the modern emphasis on inner states of the soul [Aho]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
20766 Four Noble Truths: life is suffering, caused by attachment, it is avoidable, there is a path [Aho]