Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Symposium' and 'Higher-Order Logic'

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32 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
14179 The finest branch of wisdom is justice and moderation in ordering states and families [Plato]
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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
1607 Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
174 True opinion without reason is midway between wisdom and ignorance [Plato]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
180 We call a person the same throughout life, but all their attributes change [Plato]
181 Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
173 Beauty and goodness are the same [Plato]
4026 Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato]
172 Love of ugliness is impossible [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
183 Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato]
184 Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
171 Music is a knowledge of love in the realm of harmony and rhythm [Plato]
22. Metaethics / B. Value / 2. Values / g. Love
176 Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato]
14177 Love assists men in achieving merit and happiness [Plato]
179 Love is desire for perpetual possession of the good [Plato]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
177 If a person is good they will automatically become happy [Plato]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
14178 Happiness is secure enjoyment of what is good and beautiful [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
170 The only slavery which is not dishonourable is slavery to excellence [Plato]
182 The first step on the right path is the contemplation of physical beauty when young [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
28. God / A. Divine Nature / 3. Divine Perfections
175 Gods are not lovers of wisdom, because they are already wise [Plato]