Combining Texts

All the ideas for 'fragments/reports', 'What is Cantor's Continuum Problem?' and 'Intro to 'Modality and Tense''

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17 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophers with a new concept are like children with a new toy [Fine,K]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K]
7. Existence / D. Theories of Reality / 3. Reality
A non-standard realism, with no privileged standpoint, might challenge its absoluteness or coherence [Fine,K]
9. Objects / A. Existence of Objects / 3. Objects in Thought
Objects, as well as sentences, can have logical form [Fine,K]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
We must distinguish between the identity or essence of an object, and its necessary features [Fine,K]
10. Modality / A. Necessity / 3. Types of Necessity
The three basic types of necessity are metaphysical, natural and normative [Fine,K]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances' [Fine,K]
10. Modality / A. Necessity / 11. Denial of Necessity
Empiricists suspect modal notions: either it happens or it doesn't; it is just regularities. [Fine,K]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
If sentence content is all worlds where it is true, all necessary truths have the same content! [Fine,K]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero]