53 ideas
| 3099 | Inference is never a conscious process [Harman] |
| 3077 | Reasoning might be defined in terms of its functional role, which is to produce knowledge [Harman] |
| 3092 | If you believe that some of your beliefs are false, then at least one of your beliefs IS false [Harman] |
| 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] |
| 3093 | Any two states are logically linked, by being entailed by their conjunction [Harman] |
| 3098 | Deductive logic is the only logic there is [Harman] |
| 3094 | You don't have to accept the conclusion of a valid argument [Harman] |
| 3081 | A theory of truth in a language must involve a theory of logical form [Harman] |
| 3080 | Logical form is the part of a sentence structure which involves logical elements [Harman] |
| 3084 | Our underlying predicates represent words in the language, not universal concepts [Harman] |
| 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] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 3100 | You have to reaffirm all your beliefs when you make a logical inference [Harman] |
| 3089 | Only lack of imagination makes us think that 'cats are animals' is analytic [Harman] |
| 3088 | Analyticity is postulated because we can't imagine some things being true, but we may just lack imagination [Harman] |
| 3101 | Memories are not just preserved, they are constantly reinferred [Harman] |
| 3074 | People's reasons for belief are rarely conscious [Harman] |
| 3097 | We don't distinguish between accepting, and accepting as evidence [Harman] |
| 6369 | In negative coherence theories, beliefs are prima facie justified, and don't need initial reasons [Harman, by Pollock/Cruz] |
| 3096 | Coherence avoids scepticism, because it doesn't rely on unprovable foundations [Harman] |
| 3095 | Induction is an attempt to increase the coherence of our explanations [Harman] |
| 3073 | We see ourselves in the world as a map [Harman] |
| 3076 | Defining dispositions is circular [Harman] |
| 3075 | Could a cloud have a headache if its particles formed into the right pattern? [Harman] |
| 3086 | Are there any meanings apart from in a language? [Harman] |
| 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] |
| 3078 | Speech acts, communication, representation and truth form a single theory [Harman] |
| 3090 | There is only similarity in meaning, never sameness in meaning [Harman] |
| 3082 | Ambiguity is when different underlying truth-conditional structures have the same surface form [Harman] |
| 3079 | Truth in a language is explained by how the structural elements of a sentence contribute to its truth conditions [Harman] |
| 3085 | Sentences are different from propositions, since two sentences can express one proposition [Harman] |
| 3087 | The analytic/synthetic distinction is a silly division of thought into encyclopaedia and dictionary [Harman] |
| 3083 | Many predicates totally resist translation, so a universal underlying structure to languages is unlikely [Harman] |
| 467 | A virtue is a combination of intelligence, strength and luck [Ion] |