Combining Texts

All the ideas for 'First-order Logic, 2nd-order, Completeness', 'Change in View: Principles of Reasoning' and 'Attack Upon Christendom'

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21 ideas

2. Reason / A. Nature of Reason / 1. On Reason
19306 It is a principle of reasoning not to clutter your mind with trivialities [Harman]
19304 The rules of reasoning are not the rules of logic [Harman]
19307 If there is a great cost to avoiding inconsistency, we learn to reason our way around it [Harman]
19309 Logic has little relevance to reasoning, except when logical conclusions are immediate [Harman]
2. Reason / A. Nature of Reason / 4. Aims of Reason
19303 Implication just accumulates conclusions, but inference may also revise our views [Harman]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
10. Modality / B. Possibility / 6. Probability
19305 The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman]
19310 High probability premises need not imply high probability conclusions [Harman]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
19308 We strongly desire to believe what is true, even though logic does not require it [Harman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
19311 In revision of belief, we need to keep track of justifications for foundations, but not for coherence [Harman]
19312 Coherence is intelligible connections, especially one element explaining another [Harman]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
16009 When we seek our own 'freedom' we are just trying to avoid responsibility [Kierkegaard]