Combining Texts

All the ideas for 'A Dictionary of Political Thought', 'Principle Doctrines ('Kuriai Doxai') (frags)' and 'Introduction to Mathematical Logic'

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38 ideas

1. Philosophy / A. Wisdom / 2. Wise People
It is a great good to show reverence for a wise man [Epicurus]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Post proved the consistency of propositional logic in 1921 [Walicki]
Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
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
The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
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
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
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
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
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
A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
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
Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
Two infinite ordinals can represent a single infinite cardinal [Walicki]
Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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
Inductive proof depends on the choice of the ordering [Walicki]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
Bodies are combinations of shape, size, resistance and weight [Epicurus]
10. Modality / A. Necessity / 2. Nature of Necessity
Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If everything is by necessity, then even denials of necessity are by necessity [Epicurus]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Consequentialism emphasises value rather than obligation in morality [Scruton]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
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
Pleasure and virtue entail one another [Epicurus]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Justice is merely a contract about not harming or being harmed [Epicurus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
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
Justice is a pledge of mutual protection [Epicurus]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
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
The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
A law is not just if it is not useful in mutual associations [Epicurus]
24. Political Theory / D. Ideologies / 3. Conservatism
Allegiance is fundamental to the conservative view of society [Scruton]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
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
Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
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
The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton]
25. Social Practice / F. Life Issues / 4. Suicide
It is small-minded to find many good reasons for suicide [Epicurus]