Combining Texts

All the ideas for 'A Structural Account of Mathematics', 'reports' and 'Specimen inventorum'

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42 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is a more powerful persuader than gold [Democritus (attr)]
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]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
The cause of a change is not the real influence, but whatever gives a reason for the change [Leibniz]
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]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty is merely animal without intelligence [Democritus (attr)]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Behave well when alone, and feel shame in you own eyes [Democritus (attr)]
22. Metaethics / B. Value / 2. Values / d. Health
Good breeding in men means having a good character [Democritus (attr)]
22. Metaethics / B. Value / 2. Values / g. Love
Virtuous love consists of decorous desire for the beautiful [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
We should only choose pleasures which are concerned with the beautiful [Democritus (attr)]
Good and true are the same for everyone, but pleasures differ [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Only accept beneficial pleasures [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
The great pleasures come from the contemplation of noble works [Democritus (attr)]
Moderation brings more pleasures, and so increases pleasure [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Immoderate desire is the mark of a child, not an adult [Democritus (attr)]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
It is as brave to master pleasure as to overcome the enemy [Democritus (attr)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)]
A bad life is just a drawn-out death [Democritus (attr)]
Be virtuous from duty, not from fear [Democritus (attr)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Repentance of shameful deeds is salvation [Democritus (attr)]
Virtue comes more from practice than from nature [Democritus (attr)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / i. Absolute virtues
One must avoid even speaking of evil deeds [Democritus (attr)]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
The wrongdoer is more unfortunate than the person wronged [Democritus (attr)]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
The endless desire for money is a crueller slavery than poverty [Democritus (attr)]
Small appetite makes poverty equal to wealth [Democritus (attr)]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
It is better to have one intelligent friend than many unintelligent [Democritus (attr)]
23. Ethics / D. Deontological Ethics / 2. Duty
It is a great thing, when one is in adversity, to think of duty [Democritus (attr)]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
It is better to be poor in a democracy than be rich without freedom [Democritus (attr)]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]