Combining Philosophers

All the ideas for Hermarchus, Carrie Jenkins and Leslie H. Tharp

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34 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Examining concepts can recover information obtained through the senses [Jenkins]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins]
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
The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
Skolem mistakenly inferred that Cantor's conceptions were illusory [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]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
We can learn about the world by studying the grounding of our concepts [Jenkins]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG]
7. Existence / E. Categories / 4. Category Realism
The concepts we have to use for categorising are ones which map the real world well [Jenkins]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
Grounded concepts are trustworthy maps of the world [Jenkins]
The physical effect of world on brain explains the concepts we possess [Jenkins]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins]
19. Language / C. Assigning Meanings / 2. Semantics
Success semantics explains representation in terms of success in action [Jenkins]
19. Language / E. Analyticity / 1. Analytic Propositions
'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]