Combining Texts

All the ideas for 'The Emperor's New 'Knows'', 'Maxims' and 'A Structural Account of Mathematics'

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28 ideas

1. Philosophy / A. Wisdom / 2. Wise People
To try to be wise all on one's own is folly [Rochefoucauld]
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]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
How could 'S knows he has hands' not have a fixed content? [Bach]
If contextualism is right, knowledge sentences are baffling out of their context [Bach]
Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
La Rochefoucauld's idea of disguised self-love implies an unconscious mind [Rochefoucauld, by Sartre]
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 / B. Value / 2. Values / g. Love
Judging by effects, love looks more like hatred than friendship [Rochefoucauld]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Supreme cleverness is knowledge of the real value of things [Rochefoucauld]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Realising our future misery is a kind of happiness [Rochefoucauld]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue doesn't go far without the support of vanity [Rochefoucauld]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
True friendship is even rarer than true love [Rochefoucauld]
23. Ethics / F. Existentialism / 4. Boredom
We are bored by people to whom we ourselves are boring [Rochefoucauld]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]