Combining Philosophers

All the ideas for Hermarchus, Wilfrid Hodges and Edwin D. Mares

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44 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
17713 After 1903, Husserl avoids metaphysical commitments [Mares]
2. Reason / A. Nature of Reason / 9. Limits of Reason
18781 Inconsistency doesn't prevent us reasoning about some system [Mares]
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 / E. Nonclassical Logics / 2. Intuitionist Logic
18789 Intuitionist logic looks best as natural deduction [Mares]
18790 Intuitionism as natural deduction has no rule for negation [Mares]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
18787 Three-valued logic is useful for a theory of presupposition [Mares]
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 / A. Overview of Logic / 6. Classical Logic
18793 Material implication (and classical logic) considers nothing but truth values for implications [Mares]
18784 In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares]
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 / 1. Bivalence
18780 Standard disjunction and negation force us to accept the principle of bivalence [Mares]
18786 Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18782 The connectives are studied either through model theory or through proof theory [Mares]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18783 Many-valued logics lack a natural deduction system [Mares]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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]
18792 Situation semantics for logics: not possible worlds, but information in situations [Mares]
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [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
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10473 Model theory studies formal or natural language-interpretation using set-theory [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
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
5. Theory of Logic / K. Features of Logics / 2. Consistency
18785 Consistency is semantic, but non-contradiction is syntactic [Mares]
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 / 4. Axioms for Number / a. Axioms for numbers
17715 The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
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]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17716 Mathematics is relations between properties we abstract from experience [Mares]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
18788 For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
17703 Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
17714 Aristotelians dislike the idea of a priori judgements from pure reason [Mares]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
17705 Empiricists say rationalists mistake imaginative powers for modal insights [Mares]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
17700 The most popular view is that coherent beliefs explain one another [Mares]
14. Science / B. Scientific Theories / 3. Instrumentalism
17704 Operationalism defines concepts by our ways of measuring them [Mares]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
17710 Aristotelian justification uses concepts abstracted from experience [Mares]
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
17706 The essence of a concept is either its definition or its conceptual relations? [Mares]
19. Language / C. Assigning Meanings / 2. Semantics
18791 In 'situation semantics' our main concepts are abstracted from situations [Mares]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
17701 Possible worlds semantics has a nice compositional account of modal statements [Mares]
19. Language / D. Propositions / 3. Concrete Propositions
17702 Unstructured propositions are sets of possible worlds; structured ones have components [Mares]
25. Social Practice / F. Life Issues / 6. Animal Rights
6005 Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]
27. Natural Reality / C. Space / 3. Points in Space
17708 Maybe space has points, but processes always need regions with a size [Mares]