Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'The Limits of Communitarianism' and 'On the Question of Absolute Undecidability'

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14 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
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]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
I can't defend the view that the majority values of a community are thereby right [Sandel]
25. Social Practice / A. Freedoms / 3. Free speech
If persons define themselves by a group membership, insults to that group are a real harm [Sandel]
In the liberal view an insult to my group doesn't hurt me, since I'm defined by choices not groups [Sandel]
25. Social Practice / E. Policies / 2. Religion in Society
The case for religious liberty depends on the religion contributing to a morally good life [Sandel]