Combining Texts

All the ideas for 'Laches', 'First-order Logic, 2nd-order, Completeness' and 'The Art of Rhetoric'

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29 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / A. Nature of Reason / 1. On Reason
Desired responsible actions result either from rational or from irrational desire [Aristotle]
2. Reason / C. Styles of Reason / 1. Dialectic
It is the role of dialectic to survey syllogisms [Aristotle]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
A deductive system is only incomplete with respect to a formal semantics [Rossberg]
14. Science / A. Basis of Science / 6. Falsification
A single counterexample is enough to prove that a truth is not necessary [Aristotle]
14. Science / C. Induction / 1. Induction
Nobody fears a disease which nobody has yet caught [Aristotle]
19. Language / F. Communication / 1. Rhetoric
Rhetoric is a political offshoot of dialectic and ethics [Aristotle]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Pentathletes look the most beautiful, because they combine speed and strength [Aristotle]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
We all feel universal right and wrong, independent of any community or contracts [Aristotle]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Happiness is composed of a catalogue of internal and external benefits [Aristotle]
23. Ethics / A. Egoism / 1. Ethical Egoism
Self-interest is a relative good, but nobility an absolute good [Aristotle]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
The best virtues are the most useful to others [Aristotle]
All good things can be misused, except virtue [Aristotle]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
The young feel pity from philanthropy, but the old from self-concern [Aristotle]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
Rich people are mindlessly happy [Aristotle]
24. Political Theory / B. Nature of a State / 3. Constitutions
The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle]
26. Natural Theory / C. Causation / 5. Direction of causation
People assume events cause what follows them [Aristotle]