Combining Philosophers

All the ideas for Thales, Joseph Almog and Wilfrid Hodges

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33 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]
17867 If a concept is not compact, it will not be presentable to finite minds [Almog]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17877 The number series is primitive, not the result of some set theoretic axioms [Almog]
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 / D. Essence of Objects / 4. Essence as Definition
17872 Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog]
17871 Fregean meanings are analogous to conceptual essence, defining a kind [Almog]
17866 Essential definition aims at existence conditions and structural truths [Almog]
17868 Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog]
9. Objects / D. Essence of Objects / 10. Essence as Species
17870 Alien 'tigers' can't be tigers if they are not related to our tigers [Almog]
9. Objects / D. Essence of Objects / 13. Nominal Essence
17869 Kripke and Putnam offer an intermediary between real and nominal essences [Almog]
9. Objects / D. Essence of Objects / 15. Against Essentialism
17876 Individual essences are just cobbled together classificatory predicates [Almog]
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 / C. Content / 5. Twin Earth
17873 Water must be related to water, just as tigers must be related to tigers [Almog]
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]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
17864 Defining an essence comes no where near giving a thing's nature [Almog]
17863 Essences promise to reveal reality, but actually drive us away from it [Almog]
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]