Combining Texts

All the ideas for 'Changes in Events and Changes in Things', 'Introduction to Mathematical Logic' and 'A Dictionary of Political Thought'

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29 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
17749 Post proved the consistency of propositional logic in 1921 [Walicki]
17765 Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
17752 The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
17753 The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
17759 Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17748 The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
15201 That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
7590 Consequentialism emphasises value rather than obligation in morality [Scruton]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
7589 Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
7595 The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton]
24. Political Theory / D. Ideologies / 3. Conservatism
7588 Allegiance is fundamental to the conservative view of society [Scruton]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
7594 Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
7593 Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
7592 For positivists law is a matter of form, for naturalists it is a matter of content [Scruton]
25. Social Practice / F. Life Issues / 3. Abortion
7587 The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
22899 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN]