Combining Texts

All the ideas for 'Truth and the Past', 'Infinity: Quest to Think the Unthinkable' and 'Clarification and Defense of Grounding'

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43 ideas

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 / D. Assumptions for Logic / 1. Bivalence
8195 Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
8194 Surely there is no exact single grain that brings a heap into existence [Dummett]
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]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8190 Intuitionists rely on the proof of mathematical statements, not their truth [Dummett]
7. Existence / B. Change in Existence / 1. Nature of Change
8198 A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17292 Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P]
17295 Ground relations depend on the properties [Audi,P]
17297 A ball's being spherical non-causally determines its power to roll [Audi,P]
17302 Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P]
17303 The best critique of grounding says it is actually either identity or elimination [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17294 Grounding is a singular relation between worldly facts [Audi,P]
17300 If grounding relates facts, properties must be included, as well as objects [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17296 We must accept grounding, for our important explanations [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / d. Grounding and reduction
17301 Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P]
7. Existence / D. Theories of Reality / 4. Anti-realism
8192 I no longer think what a statement about the past says is just what can justify it [Dummett]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
17293 Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
8199 The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17298 Two things being identical (like water and H2O) is not an explanation [Audi,P]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
17299 There are plenty of examples of non-causal explanation [Audi,P]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
8193 Verification is not an individual but a collective activity [Dummett]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
8189 Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett]
8191 The truth-conditions theory must get agreement on a conception of truth [Dummett]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
8197 Maybe past (which affects us) and future (which we can affect) are both real [Dummett]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
8196 The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett]