Combining Texts

All the ideas for 'Wiener Logik', 'The Foundations of Mathematics' and 'Preface to 'Principles of Philosophy''

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15 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics is the roots of the tree of science [Descartes]
2. Reason / D. Definition / 2. Aims of Definition
A simplification which is complete constitutes a definition [Kant]
2. Reason / F. Fallacies / 4. Circularity
I know the truth that God exists and is the author of truth [Descartes]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives us the necessary rules which show us how we ought to think [Kant]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
I just confront the evidence, and let it act on me [Ramsey]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Understanding, not the senses, gives certainty [Descartes]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If we knew what we know, we would be astonished [Kant]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
28. God / C. Attitudes to God / 5. Atheism
Atheism arises from empiricism, because God is intangible [Descartes]