Combining Texts

All the ideas for 'General Draft', 'A Structural Account of Mathematics' and 'Db (ideas)'

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35 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy is homesickness - the urge to be at home everywhere [Novalis]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Note that "is" can assert existence, or predication, or identity, or classification [PG]
2. Reason / F. Fallacies / 1. Fallacy
Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG]
2. Reason / F. Fallacies / 3. Question Begging
Question-begging assumes the proposition which is being challenged [PG]
2. Reason / F. Fallacies / 6. Fallacy of Division
What is true of a set is also true of its members [PG]
2. Reason / F. Fallacies / 7. Ad Hominem
The Ad Hominem Fallacy criticises the speaker rather than the argument [PG]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG]
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]
5. Theory of Logic / L. Paradox / 1. Paradox
Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG]
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]
10. Modality / B. Possibility / 6. Probability
Everything has a probability, something will happen, and probabilities add up [PG]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
If reality is just what we perceive, we would have no need for a sixth sense [PG]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Desire for perfection is an illness, if it turns against what is imperfect [Novalis]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG]
Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG]
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]
23. Ethics / E. Utilitarianism / 4. Unfairness
Utilitarianism seems to justify the discreet murder of unhappy people [PG]
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 / 2. Life
Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG]
28. God / A. Divine Nature / 4. Divine Contradictions
An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG]
How could God know there wasn't an unknown force controlling his 'free' will? [PG]