Combining Texts

All the ideas for 'reports', 'comedies (frags)' and 'Higher-Order Logic'

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25 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
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]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
7352 Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P]
22. Metaethics / B. Value / 2. Values / g. Love
6289 Love your enemies [Jesus]
6292 Love thy neighbour as thyself [Jesus]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
3032 I can form no notion of what the good is [Amphis]
23. Ethics / B. Contract Ethics / 2. Golden Rule
5356 Treat others as you would have them treat you [Jesus]
23. Ethics / B. Contract Ethics / 4. Value of Authority
6286 Blessed are the merciful: for they shall obtain mercy [Jesus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
6290 Except ye become as little children, ye shall not enter heaven [Jesus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
6287 If you lust after a woman, you have committed adultery [Jesus]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
6285 Blessed are the meek; for they shall inherit the earth [Jesus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
6288 Don't resist evil, but turn the other cheek [Jesus]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
6293 It is almost impossible for the rich to go to heaven [Jesus]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
6291 No one is good except God [Jesus]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
7351 Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P]