Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Why Propositions cannot be concrete' and 'An essentialist approach to Truth-making'

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13 ideas

3. Truth / B. Truthmakers / 2. Truthmaker Relation
Propositions are made true, in virtue of something which explains its truth [Lowe]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Modes are beings that are related both to substances and to universals [Lowe]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
Tropes have existence independently of any entities [Lowe]
18. Thought / E. Abstraction / 1. Abstract Thought
The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction [Plantinga]
Theists may see abstract objects as really divine thoughts [Plantinga]
19. Language / D. Propositions / 3. Concrete Propositions
If propositions are concrete they don't have to exist, and so they can't be necessary truths [Plantinga]
19. Language / D. Propositions / 4. Mental Propositions
Propositions can't just be in brains, because 'there are no human beings' might be true [Plantinga]