51 ideas
20678 | The Scientific Revolution was the discovery of our own ignorance [Harari] |
20686 | For millenia people didn't know how to convert one type of energy into another [Harari] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
16039 | Supervenience: No A-difference without a B-difference [Bennett,K] |
16043 | Supervenience is non-symmetric - sometimes it's symmetric, and sometimes it's one-way [Bennett,K] |
16047 | Weak supervenience is in one world, strong supervenience in all possible worlds [Bennett,K] |
16040 | Aesthetics, morality and mind supervene on the physical? Modal on non-modal? General on particular? [Bennett,K] |
16044 | Some entailments do not involve supervenience, as when brotherhood entails siblinghood [Bennett,K] |
16046 | Reduction requires supervenience, but does supervenience suffice for reduction? [Bennett,K] |
16049 | Definitions of physicalism are compatible with a necessary God [Bennett,K] |
16042 | The metaphysically and logically possible worlds are the same, so they are the same strength [Bennett,K] |
20692 | Money does produce happiness, but only up to a point [Harari] |
20663 | If a group is bound by gossip, the natural size is 150 people [Harari] |
20677 | Since 1500 human population has increased fourteenfold, and consumption far more [Harari] |
20688 | People 300m tons; domesticated animals 700m tons; larger wild animals 100m tons [Harari] |
20674 | The Nazi aim was to encourage progressive evolution, and avoid degeneration [Harari] |
20679 | We stabilise societies with dogmas, either of dubious science, or of non-scientific values [Harari] |
20690 | The state fostered individualism, to break the power of family and community [Harari] |
20689 | In 1750 losing your family and community meant death [Harari] |
20681 | The sacred command of capitalism is that profits must be used to increase production [Harari] |
20682 | The main rule of capitalism is that all other goods depend on economic growth [Harari] |
20683 | The progress of capitalism depends entirely on the new discoveries and gadgets of science [Harari] |
20687 | In capitalism the rich invest, and the rest of us go shopping [Harari] |
20685 | No market is free of political bias, and markets need protection of their freedoms [Harari] |
20693 | Freedom may work against us, as individuals can choose to leave, and make fewer commitments [Harari] |
20691 | Real peace is the implausibility of war (and not just its absence) [Harari] |
20684 | Financing is increasingly through credit rather than taxes; people prefer investing to taxation [Harari] |
20675 | The more you know about history, the harder it becomes to explain [Harari] |
20676 | History teaches us that the present was not inevitable, and shows us the possibilities [Harari] |
20671 | In order to explain both order and evil, a single evil creator is best, but no one favours that [Harari] |
20664 | Animism is belief that every part of nature is aware and feeling, and can communicate [Harari] |
20666 | Most polytheist recognise one supreme power or law, behind the various gods [Harari] |
20667 | Polytheism is open-minded, and rarely persecutes opponents [Harari] |
20665 | Mythologies are usual contracts with the gods, exchanging devotion for control of nature [Harari] |
20669 | Dualist religions see everything as a battleground of good and evil forces [Harari] |
20670 | Dualist religions say the cosmos is a battleground, so can’t explain its order [Harari] |
20673 | Manichaeans and Gnostics: good made spirit, evil made flesh [Harari] |
20668 | Monotheism appeared in Egypt in 1350 BCE, when the god Aten was declared supreme [Harari] |