20 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
5078 | Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R] |
5067 | Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R] |
5079 | Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R] |
5068 | 'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R] |
5076 | To Greeks it seemed obvious that the virtue of anything is the perfection of its function [Taylor,R] |
5077 | The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R] |
5066 | If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R] |
5065 | The ethics of duty requires a religious framework [Taylor,R] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |