Combining Texts

All the ideas for 'Hippias Major', 'Higher-Order Logic' and 'The Meditations (To Himself)'

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21 ideas

1. Philosophy / A. Wisdom / 2. Wise People
3067 A philosopher should have principles ready for understanding, like a surgeon with instruments [Aurelius]
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]
7. Existence / B. Change in Existence / 1. Nature of Change
3072 Everything is changing, including yourself and the whole universe [Aurelius]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
299 What is fine is always difficult [Plato]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
297 What is fine is the parent of goodness [Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
3066 Nothing is evil which is according to nature [Aurelius]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
3071 Justice has no virtue opposed to it, but pleasure has temperance opposed to it [Aurelius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / b. Living naturally
3069 The art of life is more like the wrestler's than the dancer's [Aurelius]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
3065 Humans are naturally made for co-operation [Aurelius]
25. Social Practice / F. Life Issues / 5. Sexual Morality
298 While sex is very pleasant, it should be in secret, as it looks contemptible [Plato]