Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Mathematical Logic' and 'Natural Goodness'

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34 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22496 Wisdom only implies the knowledge achievable in any normal lifetime [Foot]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23367 Even pointing a finger should only be done for a reason [Epictetus]
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]
17757 Members of ordinals are ordinals, and also subsets of ordinals [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]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
23694 All criterions of practical rationality derive from goodness of will [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
23686 Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright]
23693 Practical rationality must weigh both what is morally and what is non-morally required [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23687 Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
22492 Virtues are as necessary to humans as stings are to bees [Foot]
22493 Sterility is a human defect, but the choice to be childless is not [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22491 Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
22497 Deep happiness usually comes from the basic things in life [Foot]
22498 Happiness is enjoying the pursuit and attainment of right ends [Foot]
23. Ethics / A. Egoism / 1. Ethical Egoism
23695 Good actions can never be justified by the good they brings to their agent [Foot]
23. Ethics / B. Contract Ethics / 5. Free Rider
22499 We all know that just pretending to be someone's friend is not the good life [Foot]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22495 Someone is a good person because of their rational will, not their body or memory [Foot]
23. Ethics / F. Existentialism / 7. Existential Action
22502 Refraining from murder is not made good by authenticity or self-fulfilment [Foot]