46 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] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
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] |