Combining Texts

All the ideas for 'Theory of Knowledge (2nd edn)', 'works' and 'Grundlagen (Foundations of Theory of Manifolds)'

unexpand these ideas     |    start again     |     specify just one area for these texts

5 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
2945 Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]
     Full Idea: Some philosophers (e.g Plato) begin with an account of reality, and then appended an account of how we can know it, ..but Descartes turned the tables, insisting that we must first decide what we can know.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.2)
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
2946 You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]
     Full Idea: An analysis is always relative to some objective. It makes no sense to simply demand an analysis of goodness, knowledge, beauty or truth, without some indication of the purpose of the analysis.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.7)
     A reaction: Your dismantling of a car will go better if you know what a car is for, but you can still take it apart in ignorance.
1. Philosophy / H. Continental Philosophy / 5. Critical Theory
15661 Horkheimer's critical theory was interdisciplinary, and aware of its own context and function [Horkheimer, by Finlayson]
     Full Idea: Horkheimer was chiefly responsible for developing 'critical theory' during the 1930s. ...It was interdisciplinary, reflective, dialectical, and critical. It reflected on the social context that gave rise to it, and its own function within that society.
     From: report of Max Horkheimer (works [1950]) by James Gordon Finlayson - Habermas Ch.1:02
4. Formal Logic / F. Set Theory ST / 1. Set Theory
15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
     Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞.....
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
     Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence).
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4