Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Investigations in the Foundations of Set Theory I' and 'Truthmakers, Realism and Ontology'

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29 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
Moral realism doesn't seem to entail the existence of any things [Cameron]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Surely if some propositions are grounded in existence, they all are? [Cameron]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Orthodox Truthmaker applies to all propositions, and necessitates their truth [Cameron]
God fixes all the truths of the world by fixing what exists [Cameron]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
What the proposition says may not be its truthmaker [Cameron]
Rather than what exists, some claim that the truthmakers are ways of existence, dispositions, modalities etc [Cameron]
Truthmaking doesn't require realism, because we can be anti-realist about truthmakers [Cameron]
3. Truth / B. Truthmakers / 6. Making Negative Truths
Without truthmakers, negative truths must be ungrounded [Cameron]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
Maybe truthmaking and correspondence stand together, and are interdefinable [Cameron]
I support the correspondence theory because I believe in truthmakers [Cameron]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
7. Existence / D. Theories of Reality / 2. Realism
For realists it is analytic that truths are grounded in the world [Cameron]
Realism says a discourse is true or false, and some of it is true [Cameron]
Realism says truths rest on mind-independent reality; truthmaking theories are about which features [Cameron]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
We should reject distinct but indiscernible worlds [Cameron]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]