Combining Texts

All the ideas for 'The Roots of Reference', 'Draft Statement of Human Obligations' and 'A Structural Account of Mathematics'

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29 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]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
Every human yearns for an unattainable transcendent good [Weil]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Where human needs are satisfied we find happiness, friendship and beauty [Weil]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil]
23. Ethics / F. Existentialism / 4. Boredom
Life needs risks to avoid sickly boredom [Weil]
24. Political Theory / B. Nature of a State / 4. Citizenship
We all need to partipate in public tasks, and take some initiative [Weil]
24. Political Theory / D. Ideologies / 3. Conservatism
We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil]
25. Social Practice / A. Freedoms / 3. Free speech
Deliberate public lying should be punished [Weil]
25. Social Practice / A. Freedoms / 6. Political freedom
We have liberty in the space between nature and accepted authority [Weil]
25. Social Practice / C. Rights / 4. Property rights
People need personal and collective property, and a social class lacking property is shameful [Weil]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
Crime should be punished, to bring the perpetrator freely back to morality [Weil]
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 / c. God is the good
Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil]