Combining Texts

All the ideas for 'fragments/reports', 'Democracy in America (abr Renshaw)' and 'A Structural Account of Mathematics'

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34 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]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
Wherever there is a small community, the association of the people is natural [Tocqueville]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
The people are just individuals, and only present themselves as united to foreigners [Tocqueville]
24. Political Theory / A. Basis of a State / 2. Population / b. State population
Vast empires are bad for well-being and freedom, though they may promote glory [Tocqueville]
People would be much happier and freer in small nations [Tocqueville]
24. Political Theory / B. Nature of a State / 3. Constitutions
In American judges rule according to the Constitution, not the law [Tocqueville]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
A monarchical family is always deeply concerned with the interests of the state [Tocqueville]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
Despots like to see their own regulations ignored, by themselves and their agents [Tocqueville]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Aristocracy is constituted by inherited landed property [Tocqueville]
24. Political Theory / C. Ruling a State / 4. Changing the State / a. Centralisation
In Europe it is thought that local government is best handled centrally [Tocqueville]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
An election, and its lead up time, are always a national crisis [Tocqueville]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Universal suffrage is no guarantee of wise choices [Tocqueville]
25. Social Practice / A. Freedoms / 1. Slavery
Slavery undermines the morals and energy of a society [Tocqueville]
25. Social Practice / A. Freedoms / 3. Free speech
The liberty of the press is more valuable for what it prevents than what it promotes [Tocqueville]
25. Social Practice / B. Equalities / 1. Grounds of equality
It is admirable to elevate the humble to the level of the great, but the opposite is depraved [Tocqueville]
25. Social Practice / B. Equalities / 2. Political equality
Equality can only be established by equal rights for all (or no rights for anyone) [Tocqueville]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]