22 ideas
| 8525 | Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K] |
| 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] |
| 8518 | Events are trope-sequences, in which tropes replace one another [Campbell,K] |
| 8513 | Two red cloths are separate instances of redness, because you can dye one of them blue [Campbell,K] |
| 8514 | Red could only recur in a variety of objects if it was many, which makes them particulars [Campbell,K] |
| 8522 | Tropes solve the Companionship Difficulty, since the resemblance is only between abstract particulars [Campbell,K] |
| 8523 | Tropes solve the Imperfect Community problem, as they can only resemble in one respect [Campbell,K] |
| 8524 | Trope theory makes space central to reality, as tropes must have a shape and size [Campbell,K] |
| 8521 | Nominalism has the problem that without humans nothing would resemble anything else [Campbell,K] |
| 8515 | Tropes are basic particulars, so concrete particulars are collections of co-located tropes [Campbell,K] |
| 8519 | Bundles must be unique, so the Identity of Indiscernibles is a necessity - which it isn't! [Campbell,K] |
| 4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
| 8512 | Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 8516 | Davidson can't explain causation entirely by events, because conditions are also involved [Campbell,K] |
| 8517 | Causal conditions are particular abstract instances of properties, which makes them tropes [Campbell,K] |