41 ideas
| 3695 | Philosophy is a priori if it is anything [Bonjour] |
| 3651 | Perceiving necessary connections is the essence of reasoning [Bonjour] |
| 3700 | Coherence can't be validated by appeal to coherence [Bonjour] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 19400 | Possibles demand existence, so as many of them as possible must actually exist [Leibniz] |
| 19401 | God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 3697 | The concept of possibility is prior to that of necessity [Bonjour] |
| 19402 | The actual universe is the richest composite of what is possible [Leibniz] |
| 3707 | Our rules of thought can only be judged by pure rational insight [Bonjour] |
| 3704 | Moderate rationalists believe in fallible a priori justification [Bonjour] |
| 3696 | A priori justification requires understanding but no experience [Bonjour] |
| 3703 | You can't explain away a priori justification as analyticity, and you can't totally give it up [Bonjour] |
| 3706 | A priori justification can vary in degree [Bonjour] |
| 3699 | The induction problem blocks any attempted proof of physical statements [Bonjour] |
| 3701 | Externalist theories of justification don't require believers to have reasons for their beliefs [Bonjour] |
| 3702 | Externalism means we have no reason to believe, which is strong scepticism [Bonjour] |
| 3709 | Induction must go beyond the evidence, in order to explain why the evidence occurred [Bonjour] |
| 3708 | All thought represents either properties or indexicals [Bonjour] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 3698 | Indeterminacy of translation is actually indeterminacy of meaning and belief [Bonjour] |