Combining Philosophers

All the ideas for Hermarchus, Gregory L. Murphy and Leslie H. Tharp

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41 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is either for demonstration, or for characterizing structures [Tharp]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Elementary logic is complete, but cannot capture mathematics [Tharp]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
There are at least five unorthodox quantifiers that could be used [Tharp]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness would seem to be an essential requirement of a proof procedure [Tharp]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness and compactness together give axiomatizability [Tharp]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
If completeness fails there is no algorithm to list the valid formulas [Tharp]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness is important for major theories which have infinitely many axioms [Tharp]
Compactness blocks infinite expansion, and admits non-standard models [Tharp]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A complete logic has an effective enumeration of the valid formulas [Tharp]
Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
12. Knowledge Sources / B. Perception / 5. Interpretation
Research shows perceptual discrimination is sharper at category boundaries [Murphy]
14. Science / C. Induction / 1. Induction
Induction is said to just compare properties of categories, but the type of property also matters [Murphy]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
The main theories of concepts are exemplar, prototype and knowledge [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
The theoretical and practical definitions for the classical view are very hard to find [Murphy]
The classical definitional approach cannot distinguish typical and atypical category members [Murphy]
Classical concepts follow classical logic, but concepts in real life don't work that way [Murphy]
Classical concepts are transitive hierarchies, but actual categories may be intransitive [Murphy]
The classical core is meant to be the real concept, but actually seems unimportant [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
There is no 'ideal' bird or dog, and prototypes give no information about variability [Murphy]
Prototypes are unified representations of the entire category (rather than of members) [Murphy]
The prototype theory uses observed features, but can't include their construction [Murphy]
The prototype theory handles hierarchical categories and combinations of concepts well [Murphy]
Prototypes theory of concepts is best, as a full description with weighted typical features [Murphy]
Learning concepts is forming prototypes with a knowledge structure [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / e. Concepts from exemplars
The most popular theories of concepts are based on prototypes or exemplars [Murphy]
The exemplar view of concepts says 'dogs' is the set of dogs I remember [Murphy]
Exemplar theory struggles with hierarchical classification and with induction [Murphy]
Children using knowing and essentialist categories doesn't fit the exemplar view [Murphy]
Conceptual combination must be compositional, and can't be built up from exemplars [Murphy]
The concept of birds from exemplars must also be used in inductions about birds [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
We do not learn concepts in isolation, but as an integrated part of broader knowledge [Murphy]
Concepts with familiar contents are easier to learn [Murphy]
Some knowledge is involved in instant use of categories, other knowledge in explanations [Murphy]
People categorise things consistent with their knowledge, even rejecting some good evidence [Murphy]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]