Combining Texts

All the ideas for 'Particulars in Particular Clothing', 'Higher-Order Logic' and 'The Communist Manifesto'

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

21 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
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
18431 Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
5303 For the proletariate, law, morality and religion are just expressions of bourgeois interests [Marx/Engels]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
21998 Bourgeois interests create our morality, law and religion [Marx/Engels]
24. Political Theory / D. Ideologies / 9. Communism
5302 Modern governments are just bourgeois management committees [Marx/Engels]
5304 Communism aims to abolish not all property, but bourgeois property [Marx/Engels]
5307 Many of the bourgeois rights grievances are a form of self-defence [Marx/Engels]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
5306 The free development of each should be the condition for the free development of all [Marx/Engels]
25. Social Practice / E. Policies / 5. Education / b. Education principles
5305 Communists want to rescue education from the ruling class [Marx/Engels]
25. Social Practice / E. Policies / 5. Education / d. Study of history
5301 The history of all existing society is the history of class struggles [Marx/Engels]