Combining Texts

All the ideas for 'Paradoxes: Form and Predication', 'Model Theory' and 'Necessity and Non-Existence'

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25 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
15063 Some sentences depend for their truth on worldly circumstances, and others do not [Fine,K]
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 / G. Quantification / 6. Plural Quantification
14235 Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
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]
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]
7. Existence / A. Nature of Existence / 2. Types of Existence
15078 There are levels of existence, as well as reality; objects exist at the lowest level in which they can function [Fine,K]
7. Existence / D. Theories of Reality / 3. Reality
15072 Bottom level facts are subject to time and world, middle to world but not time, and top to neither [Fine,K]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
15071 Tensed and tenseless sentences state two sorts of fact, which belong to two different 'realms' of reality [Fine,K]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
15075 Modal features are not part of entities, because they are accounted for by the entity [Fine,K]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
15065 What it is is fixed prior to existence or the object's worldly features [Fine,K]
9. Objects / D. Essence of Objects / 9. Essence and Properties
15076 Essential features of an object have no relation to how things actually are [Fine,K]
9. Objects / F. Identity among Objects / 5. Self-Identity
15073 Self-identity should have two components, its existence, and its neutral identity with itself [Fine,K]
9. Objects / F. Identity among Objects / 6. Identity between Objects
15074 We would understand identity between objects, even if their existence was impossible [Fine,K]
10. Modality / A. Necessity / 8. Transcendental Necessity
15064 Proper necessary truths hold whatever the circumstances; transcendent truths regardless of circumstances [Fine,K]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
15070 It is the nature of Socrates to be a man, so necessarily he is a man [Fine,K]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
15069 Possible worlds may be more limited, to how things might actually turn out [Fine,K]
15068 The actual world is a totality of facts, so we also think of possible worlds as totalities [Fine,K]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
15067 A-theorists tend to reject the tensed/tenseless distinction [Fine,K]
15077 It is said that in the A-theory, all existents and objects must be tensed, as well as the sentences [Fine,K]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
15066 B-theorists say tensed sentences have an unfilled argument-place for a time [Fine,K]