Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Model Theory' and 'The Foundations of Mathematics'

expand these ideas     |    start again     |     specify just one area for these texts

17 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13430 Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
13428 Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
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 / D. Assumptions for Logic / 4. Identity in Logic
13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
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
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
5. Theory of Logic / L. Paradox / 1. Paradox
13334 Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13426 Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
13425 Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
22328 I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
22325 A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]