Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'An Introduction to Modal Logic' and 'The Anti-Christ'

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36 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
2922 All intelligent Romans were Epicureans [Nietzsche]
3. Truth / A. Truth Problems / 3. Value of Truth
23520 Truth has had to be fought for, and normal life must be sacrificed to achieve it [Nietzsche]
2914 One must never ask whether truth is useful [Nietzsche]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
9540 A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
9541 The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell]
4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
9543 The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
9544 A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
2921 Philosophy grasps the limits of human reason, and values are beyond it [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
20138 Christianity is at war with the higher type of man, and excommunicates his basic instincts [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
20375 Virtues must be highly personal; if not, it is merely respect for a concept [Nietzsche]
23. Ethics / D. Deontological Ethics / 1. Deontology
2915 Each person should devise his own virtues and categorical imperative [Nietzsche]
28. God / A. Divine Nature / 4. Divine Contradictions
2920 A God who cures us of a head cold at the right moment is a total absurdity [Nietzsche]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
2917 Christianity is a revolt of things crawling on the ground against elevated things [Nietzsche]
29. Religion / B. Monotheistic Religion / 5. Bible
2918 The story in Genesis is the story of God's fear of science [Nietzsche]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
2919 'Faith' means not wanting to know what is true [Nietzsche]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
2916 The great lie of immortality destroys rationality and natural instinct [Nietzsche]