Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'Resemblance Nominalism: a solution to universals' and 'Sapiens: brief history of humankind'

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44 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
The Scientific Revolution was the discovery of our own ignorance [Harari]
For millenia people didn't know how to convert one type of energy into another [Harari]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is a set consisting entirely of ordered pairs [Potter]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Entities are truthmakers for their resemblances, so no extra entities or 'resemblances' are needed [Rodriquez-Pereyra]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
Priority is a modality, arising from collections and members [Potter]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
Money does produce happiness, but only up to a point [Harari]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
If a group is bound by gossip, the natural size is 150 people [Harari]
24. Political Theory / A. Basis of a State / 2. Population / a. Human population
Since 1500 human population has increased fourteenfold, and consumption far more [Harari]
People 300m tons; domesticated animals 700m tons; larger wild animals 100m tons [Harari]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The Nazi aim was to encourage progressive evolution, and avoid degeneration [Harari]
24. Political Theory / B. Nature of a State / 5. Culture
We stabilise societies with dogmas, either of dubious science, or of non-scientific values [Harari]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
The state fostered individualism, to break the power of family and community [Harari]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
In 1750 losing your family and community meant death [Harari]
24. Political Theory / D. Ideologies / 11. Capitalism
The sacred command of capitalism is that profits must be used to increase production [Harari]
The main rule of capitalism is that all other goods depend on economic growth [Harari]
The progress of capitalism depends entirely on the new discoveries and gadgets of science [Harari]
In capitalism the rich invest, and the rest of us go shopping [Harari]
25. Social Practice / A. Freedoms / 4. Free market
No market is free of political bias, and markets need protection of their freedoms [Harari]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Freedom may work against us, as individuals can choose to leave, and make fewer commitments [Harari]
25. Social Practice / E. Policies / 1. War / e. Peace
Real peace is the implausibility of war (and not just its absence) [Harari]
25. Social Practice / E. Policies / 4. Taxation
Financing is increasingly through credit rather than taxes; people prefer investing to taxation [Harari]
25. Social Practice / E. Policies / 5. Education / d. Study of history
The more you know about history, the harder it becomes to explain [Harari]
History teaches us that the present was not inevitable, and shows us the possibilities [Harari]
28. God / C. Attitudes to God / 1. Monotheism
In order to explain both order and evil, a single evil creator is best, but no one favours that [Harari]
29. Religion / A. Polytheistic Religion / 1. Animism
Animism is belief that every part of nature is aware and feeling, and can communicate [Harari]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
Most polytheist recognise one supreme power or law, behind the various gods [Harari]
Polytheism is open-minded, and rarely persecutes opponents [Harari]
Mythologies are usual contracts with the gods, exchanging devotion for control of nature [Harari]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
Dualist religions see everything as a battleground of good and evil forces [Harari]
Dualist religions say the cosmos is a battleground, so can’t explain its order [Harari]
Manichaeans and Gnostics: good made spirit, evil made flesh [Harari]
29. Religion / B. Monotheistic Religion / 1. Monotheistic Religion
Monotheism appeared in Egypt in 1350 BCE, when the god Aten was declared supreme [Harari]