Combining Texts

All the ideas for 'The Fixation of Belief', 'Speeches in Elberfeld' and 'On Second-Order Logic'

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23 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
6947 Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce]
2. Reason / A. Nature of Reason / 4. Aims of Reason
6937 Reason aims to discover the unknown by thinking about the known [Peirce]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
7. Existence / D. Theories of Reality / 2. Realism
21492 Realism is basic to the scientific method [Peirce]
7. Existence / D. Theories of Reality / 4. Anti-realism
6949 If someone doubted reality, they would not actually feel dissatisfaction [Peirce]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
6940 The feeling of belief shows a habit which will determine our actions [Peirce]
6941 We are entirely satisfied with a firm belief, even if it is false [Peirce]
6942 We want true beliefs, but obviously we think our beliefs are true [Peirce]
6943 A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
6598 We need our beliefs to be determined by some external inhuman permanency [Peirce]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
6944 Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce]
13. Knowledge Criteria / C. External Justification / 1. External Justification
6948 Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
6945 Once doubt ceases, there is no point in continuing to argue [Peirce]
24. Political Theory / D. Ideologies / 11. Capitalism
20525 Free markets lead to boom and bust, pointless middlemen, and alienated workers [Engels]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
6939 What is true of one piece of copper is true of another (unlike brass) [Peirce]
27. Natural Reality / G. Biology / 3. Evolution
6938 Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce]
28. God / B. Proving God / 2. Proofs of Reason / d. Pascal's Wager
6946 If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce]