Combining Texts

All the ideas for 'Rationality', 'The History of Animals' and 'What is Cantor's Continuum Problem?'

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15 ideas

2. Reason / A. Nature of Reason / 1. On Reason
You can be rational with undetected or minor inconsistencies [Harman]
2. Reason / A. Nature of Reason / 6. Coherence
A coherent conceptual scheme contains best explanations of most of your beliefs [Harman]
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]
14. Science / C. Induction / 1. Induction
Enumerative induction is inference to the best explanation [Harman]
14. Science / C. Induction / 3. Limits of Induction
Induction is 'defeasible', since additional information can invalidate it [Harman]
14. Science / C. Induction / 4. Reason in Induction
All reasoning is inductive, and deduction only concerns implication [Harman]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Aristotelian explanation by essence may need to draw on knowledge of other essences [Aristotle, by Koslicki]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Ordinary rationality is conservative, starting from where your beliefs currently are [Harman]
27. Natural Reality / G. Biology / 2. Life
Plants have far less life than animals, but more life than other corporeal entities [Aristotle]
27. Natural Reality / G. Biology / 3. Evolution
There is a gradual proceeding from the inanimate to animals, with no clear borderlines [Aristotle]