Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Model Theory' and 'Analogy of Religion'

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14 ideas

2. Reason / D. Definition / 7. Contextual Definition
The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
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]
9. Objects / F. Identity among Objects / 9. Sameness
A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
Despite consciousness fluctuating, we are aware that it belongs to one person [Butler]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
Consciousness presupposes personal identity, so it cannot constitute it [Butler]
16. Persons / D. Continuity of the Self / 5. Concerns of the Self
If the self changes, we have no responsibilities, and no interest in past or future [Butler]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]