Combining Texts

All the ideas for 'A Structural Account of Mathematics', 'On the Law of War and Peace' and 'Defeasibility Theory'

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33 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Realists about sets say there exists a null set in the real world, with no members [Chihara]
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
A pack of wolves doesn't cease when one member dies [Chihara]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
Indefeasibility does not imply infallibility [Grundmann]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
Can a defeater itself be defeated? [Grundmann]
Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann]
You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann]
Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann]
Knowledge requires that there are no facts which would defeat its justification [Grundmann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
'Moderate' foundationalism has basic justification which is defeasible [Grundmann]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius]
25. Social Practice / A. Freedoms / 7. Freedom to leave
A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD]
A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck]
25. Social Practice / E. Policies / 1. War / b. Justice in war
It is permissible in a just cause to capture a place in neutral territory [Grotius]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
Moral principles have some validity without a God commanding obedience [Grotius, by Mautner]