14 ideas
6558 | A foolish consistency is the hobgoblin of little minds [Emerson] |
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] |
19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |