Combining Philosophers

All the ideas for Thales, Wilfrid Hodges and Edward N. Zalta

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

25 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
1597 Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales]
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 / 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]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10414 Abstract objects are constituted by encoded collections of properties [Zalta, by Swoyer]
10558 Abstract objects are actually constituted by the properties by which we conceive them [Zalta]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10415 Properties make round squares and round triangles distinct, unlike exemplification [Zalta, by Swoyer]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
3013 Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10557 Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
1494 Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
1713 Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
1742 Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius]