Combining Texts

All the ideas for 'Fragments and accounts of Gorgias', 'The Second Coming' and 'Higher-Order Logic'

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20 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23531 Philosophers should interpret the world, by expressing its possibilities [Berardi]
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
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
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]
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]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
23538 Nothingness only exists in consciousness [Berardi]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
16. Persons / F. Free Will / 5. Against Free Will
23532 The delusion of free will brings a sense of guilt [Berardi]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23537 American white men trusted the philosophy of winning, and then discovered losing [Berardi]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
23536 Community is now a nostalgic memory, which no longer exists [Berardi]
24. Political Theory / D. Ideologies / 9. Communism
23534 Communism failed to unite western workers with the oppressed of the south [Berardi]
24. Political Theory / D. Ideologies / 11. Capitalism
23533 The economy has replaced medieval theocracy at the centre of our society [Berardi]
24. Political Theory / D. Ideologies / 14. Nationalism
23535 Western workers turn to nationalism, to avert the effects of globalisation [Berardi]