Combining Texts

All the ideas for 'Introduction to Mathematical Logic', 'Does moral phil rest on a mistake?' and 'Prcis of 'Ruling Passions''

expand these ideas     |    start again     |     specify just one area for these texts

25 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
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
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]
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]
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 / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
9261 The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
11911 Some philosophers always want more from morality; for others, nature is enough [Blackburn]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
9262 The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
9260 Virtues won't generate an obligation, so it isn't a basis for morality [Prichard]
23. Ethics / D. Deontological Ethics / 2. Duty
9259 We feel obligations to overcome our own failings, and these are not relations to other people [Prichard]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
9258 If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard]