Combining Texts

All the ideas for 'Events', 'Higher-Order Logic' and 'The Fixation of Belief'

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28 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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
9413 An event is a change in or to an object [Lombard, by Mumford]
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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
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]
6943 A mere question does not stimulate a struggle for belief; there must be a real doubt [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]
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]