Combining Texts

All the ideas for 'Conditionals', 'The Epistemology of Essence (draft)' and 'What is Cantor's Continuum Problem?'

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14 ideas

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]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
There are many different conditional mental states, and different conditional speech acts [Edgington]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
If conceivability is a priori coherence, that implies possibility [Tahko]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Essences are used to explain natural kinds, modality, and causal powers [Tahko]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko]