Combining Texts

All the ideas for 'fragments/reports', 'The Fixation of Belief' and 'Model Theory'

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24 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]
2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
6019 If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
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]
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]