Combining Texts

All the ideas for 'fragments/reports', 'Principle Doctrines ('Kuriai Doxai') (frags)' and 'Introduction to Mathematical Logic'

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36 ideas

1. Philosophy / A. Wisdom / 2. Wise People
14519 It is a great good to show reverence for a wise man [Epicurus]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
14518 In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1815 Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]
1812 All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]
1811 Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]
1813 All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]
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]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
14524 Bodies are combinations of shape, size, resistance and weight [Epicurus]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
8850 Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]
13. Knowledge Criteria / E. Relativism / 1. Relativism
1814 Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
14521 If everything is by necessity, then even denials of necessity are by necessity [Epicurus]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
14522 What happens to me if I obtain all my desires, and what if I fail? [Epicurus]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
3563 Pleasure and virtue entail one another [Epicurus]
23. Ethics / B. Contract Ethics / 1. Contractarianism
3560 Justice is merely a contract about not harming or being harmed [Epicurus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
14517 We value our own character, whatever it is, and we should respect the characters of others [Epicurus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
14513 Justice is a pledge of mutual protection [Epicurus]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
14515 A law is not just if it is not useful in mutual associations [Epicurus]
25. Social Practice / F. Life Issues / 4. Suicide
14520 It is small-minded to find many good reasons for suicide [Epicurus]