14 ideas
20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
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] |
6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
3193 | Turing showed that logical rules can be specified computationally and mechanically [Turing, by Rey] |
3979 | The Turing Machine is the best idea yet about how the mind works [Fodor on Turing] |
5321 | In 50 years computers will successfully imitate humans with a 70% success rate [Turing] |
5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |