Combining Texts

All the ideas for 'Philosophical Explanations', 'The Foundations of Mathematics' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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19 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13430 Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
13428 Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
13733 Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9874 Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
5. Theory of Logic / L. Paradox / 1. Paradox
13334 Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18252 Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18271 We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10623 Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
9975 Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18165 My Basic Law V is a law of pure logic [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13426 Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
13425 Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
3570 Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
22328 I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
22325 A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
2748 A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9190 A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
13665 Frege took the study of concepts to be part of logic [Frege, by Shapiro]