Combining Philosophers

All the ideas for Anaxarchus, Keith Devlin and Bernard Bolzano

expand these ideas     |    start again     |     specify just one area for these philosophers

25 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
8092 Logic was merely a branch of rhetoric until the scientific 17th century [Devlin]
2. Reason / B. Laws of Thought / 1. Laws of Thought
7807 The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
8081 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
8085 Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
8086 Predicate logic retains the axioms of propositional logic [Devlin]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
8091 Situation theory is logic that takes account of context [Devlin]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
8087 Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin]
8089 Montague's intensional logic incorporated the notion of meaning [Devlin]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
8082 Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
8072 Sentences of apparent identical form can have different contextual meanings [Devlin]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
8075 Space and time are atomic in the arrow, and divisible in the tortoise [Devlin]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618 Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830 Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17265 Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9185 Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
8088 People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin]
19. Language / C. Assigning Meanings / 1. Syntax
8073 How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin]
19. Language / D. Propositions / 1. Propositions
22276 Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
17264 Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
12232 A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
8076 The distinction between sentences and abstract propositions is crucial in logic [Devlin]
19. Language / E. Analyticity / 2. Analytic Truths
12233 The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]