Combining Philosophers

All the ideas for Hermarchus, Georg Kreisel and Dag Prawitz

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9 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13831 Logic is based on transitions between sentences [Prawitz]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13827 Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13825 Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13823 In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13826 Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
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
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]