Combining Texts

All the ideas for 'A Structural Account of Mathematics', 'The Reality of Numbers' and 'Just and Unjust Wars'

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43 ideas

3. Truth / B. Truthmakers / 1. For Truthmakers
Truth and falsehood must track what does or doesn't exist [Bigelow]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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]
Realists about sets say there exists a null set in the real world, with no members [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]
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 / 4. Responsibility for Actions
Criminal responsibility can be fully assigned to each member of a group [Walzer]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
Double Effect needs a double intention - to achieve the good, and minimise the evil [Walzer]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Deep ethical theory is very controversial, but we have to live with higher ethical practice [Walzer]
25. Social Practice / C. Rights / 1. Basis of Rights
If whole states possess rights, there can be social relations between states [Walzer]
25. Social Practice / E. Policies / 1. War / a. Just wars
Just wars are self-defence, or a rightful intercession in another's troubles [Walzer]
Nuclear bombs are not for normal war; they undermine the 'just war', with a new morality [Walzer]
The aim of reprisals is to enforce the rules of war [Walzer]
Even non-violent intrusive acts between states count as aggression, if they justify resistance [Walzer]
The only good reason for fighting is in defence of rights [Walzer]
States can rightly pre-empt real and serious threats [Walzer]
Reprisal is defensible, as an alternative to war [Walzer]
States need not endure attacks passively, and successful reprisals are legitimate [Walzer]
With nuclear weapons we have a permanent supreme emergency (which is unstable) [Walzer]
25. Social Practice / E. Policies / 1. War / b. Justice in war
Jus ad bellum and Jus in bello are independent; unjust wars can be fought in a just way [Walzer]
For moral reasons, a just war must be a limited war [Walzer]
Napoleon said 'I don't care about the deaths of a million men' [Walzer]
25. Social Practice / E. Policies / 1. War / c. Combatants
Kidnapped sailors and volunteers have different obligations to the passengers [Walzer]
Even aggressor soldiers are not criminals, so they have equal rights with their opponents [Walzer]
The duties and moral status of loyal and obedient soldiers is the same in defence and aggression [Walzer]
We can't blame soldiers for anything they do which clearly promotes victory [Walzer]
Rejecting Combatant Equality allows just soldiers to be harsher, even to the extreme [Walzer]
25. Social Practice / E. Policies / 1. War / d. Non-combatants
Soldiers will only protect civilians if they feel safe from them [Walzer]
What matters in war is unacceptable targets, not unacceptable weapons [Walzer]
If the oppressor is cruel, nonviolence is either surrender, or a mere gesture [Walzer]
25. Social Practice / E. Policies / 1. War / e. Peace
We can only lead war towards peace if we firmly enforce the rules of war [Walzer]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]