Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'On the Ultimate Origination of Things' and 'Model Theory'

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16 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom involves the desire to achieve perfection [Leibniz]
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
A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
Model theory studies formal or natural language-interpretation using set-theory [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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette]
There must be a straining towards existence in the essence of all possible things [Leibniz]
Because something does exist, there must be a drive in possible things towards existence [Leibniz]
10. Modality / A. Necessity / 7. Natural Necessity
The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The principle of determination in things obtains the greatest effect with the least effort [Leibniz]