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All the ideas for 'Goodbye Descartes', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'fragments/reports'

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26 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 / D. Definition / 2. Aims of Definition
13886 Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
9845 We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 11. Ostensive Definition
10019 Only what is logically complex can be defined; what is simple must be pointed to [Frege]
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]
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 / 3. Nature of Numbers / b. Types of number
9886 Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
9889 Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10020 Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
10553 A number is a class of classes of the same cardinality [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9887 Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
8751 Only applicability raises arithmetic from a game to a science [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9891 The first demand of logic is of a sharp boundary [Frege]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
8088 People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9890 The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
11846 If we abstract the difference between two houses, they don't become the same house [Frege]
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 / 2. Abstract Propositions / a. Propositions as sense
8076 The distinction between sentences and abstract propositions is crucial in logic [Devlin]