Combining Texts

All the ideas for 'Can there be Vague Objects?', 'What is Cantor's Continuum Problem?' and 'Rules for the Direction of the Mind'

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13 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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe]
Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans]
Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis]
There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson]
9. Objects / F. Identity among Objects / 6. Identity between Objects
There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
In pursuing truth, anything less certain than mathematics is a waste of time [Descartes]