Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Model Theory' and 'Identity'

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18 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 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
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
16014 It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
16024 I could have died at five, but the summation of my adult stages could not [Noonan]
9. Objects / E. Objects over Time / 5. Temporal Parts
16023 Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan]
9. Objects / F. Identity among Objects / 2. Defining Identity
16016 Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
16017 Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
16015 Problems about identity can't even be formulated without the concept of identity [Noonan]
16020 Identity can only be characterised in a second-order language [Noonan]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
16019 Leibniz's Law must be kept separate from the substitutivity principle [Noonan]
16018 Indiscernibility is basic to our understanding of identity and distinctness [Noonan]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]