Combining Texts

All the ideas for 'Necessary Existents', 'A Structural Account of Mathematics' and 'True in Theory, but not in Practice'

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32 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]
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]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
General rules of action also need a judgement about when to apply them [Kant]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant]
23. Ethics / D. Deontological Ethics / 2. Duty
It can't be a duty to strive after the impossible [Kant]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
There can be no restraints on freedom if reason does not reveal some basic rights [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Personal contracts are for some end, but a civil state contract involves a duty to share [Kant]
There must be a unanimous contract that citizens accept majority decisions [Kant]
A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
A law is unjust if the whole people could not possibly agree to it [Kant]
24. Political Theory / B. Nature of a State / 4. Citizenship
A citizen must control his own life, and possess property or an important skill [Kant]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
A lawful civil state must embody freedom, equality and independence for its members [Kant]
25. Social Practice / B. Equalities / 4. Economic equality
Citizens can rise to any rank that talent, effort and luck can achieve [Kant]
25. Social Practice / C. Rights / 3. Alienating rights
You can't make a contract renouncing your right to make contracts! [Kant]
25. Social Practice / E. Policies / 1. War / a. Just wars
The people (who have to fight) and not the head of state should declare a war [Kant]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]