Combining Texts

All the ideas for 'Conditionals', 'Aristotle on Essence and Explanation' and 'What is Cantor's Continuum Problem?'

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15 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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Jones may cease to exist without some simple property, but that doesn't make it essential [Kung]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
A property may belong essentially to one thing and contingently to another [Kung]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Aristotelian essences underlie a thing's existence, explain it, and must belong to it [Kung]
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]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Some peripheral properties are explained by essential ones, but don't themselves explain properties [Kung]
Some non-essential properties may explain more than essential-but-peripheral ones do [Kung]