Combining Philosophers

All the ideas for Nicolas Malebranche, M.R. Ayers and Wilfrid Hodges

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

34 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 / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [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 / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [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
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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17518 Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
17516 If counting needs a sortal, what of things which fall under two sortals? [Ayers]
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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
17520 Events do not have natural boundaries, and we have to set them [Ayers]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16669 Everything that exists is either a being, or some mode of a being [Malebranche]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
17519 To express borderline cases of objects, you need the concept of an 'object' [Ayers]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
17510 Speakers need the very general category of a thing, if they are to think about it [Ayers]
17522 We use sortals to classify physical objects by the nature and origin of their unity [Ayers]
17515 Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers]
17511 Recognising continuity is separate from sortals, and must precede their use [Ayers]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
17517 Could the same matter have more than one form or principle of unity? [Ayers]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17513 If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers]
9. Objects / D. Essence of Objects / 5. Essence as Kind
17523 Sortals basically apply to individuals [Ayers]
9. Objects / E. Objects over Time / 5. Temporal Parts
17521 You can't have the concept of a 'stage' if you lack the concept of an object [Ayers]
17514 Temporal 'parts' cannot be separated or rearranged [Ayers]
9. Objects / F. Identity among Objects / 1. Concept of Identity
17509 Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers]
9. Objects / F. Identity among Objects / 3. Relative Identity
17512 If diachronic identities need covering concepts, why not synchronic identities too? [Ayers]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
12726 In a true cause we see a necessary connection [Malebranche]
2594 A true cause must involve a necessary connection between cause and effect [Malebranche]