Combining Texts

All the ideas for 'works', 'Trees, Terms and Truth' and 'Infinity: Quest to Think the Unthinkable'

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35 ideas

3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18915 If facts are the truthmakers, they are not in the world [Engelbretsen]
18919 There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18913 Traditional term logic struggled to express relations [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
18907 Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
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 / A. Overview of Logic / 2. History of Logic
18912 Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18922 Logical syntax is actually close to surface linguistic form [Engelbretsen]
18905 Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18908 Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
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
10860 An ordinal number is defined by the set that comes before it [Clegg]
10861 Beyond infinity cardinals and ordinals can come apart [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]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18917 Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
18916 Facts are not in the world - they are properties of the world [Engelbretsen]
7. Existence / E. Categories / 4. Category Realism
18921 Individuals are arranged in inclusion categories that match our semantics [Engelbretsen]
19. Language / B. Reference / 2. Denoting
18918 Terms denote objects with properties, and statements denote the world with that property [Engelbretsen]
19. Language / D. Propositions / 1. Propositions
18920 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen]
19. Language / F. Communication / 3. Denial
18906 Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
20239 Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]