Combining Texts

All the ideas for 'Laches', 'fragments/reports' and 'Model Theory'

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15 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Contradiction is impossible [Antisthenes (I), by Aristotle]
2. Reason / D. Definition / 7. Contextual Definition
The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
2. Reason / D. Definition / 13. Against Definition
Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
I would rather go mad than experience pleasure [Antisthenes (I)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]
28. God / C. Attitudes to God / 2. Pantheism
Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero]