71 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] |
8893 | For any given area, there seem to be a huge number of possible coherent systems of beliefs [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] |
4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
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] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
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] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [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] |
3697 | The concept of possibility is prior to that of necessity [Bonjour] |
8888 | The concept of knowledge is so confused that it is best avoided [Bonjour] |
8887 | It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour] |
8897 | The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour] |
3704 | Moderate rationalists believe in fallible a priori justification [Bonjour] |
3707 | Our rules of thought can only be judged by pure rational insight [Bonjour] |
4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
8896 | Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [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] |
4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
3699 | The induction problem blocks any attempted proof of physical statements [Bonjour] |
21506 | A coherence theory of justification can combine with a correspondence theory of truth [Bonjour] |
21509 | There will always be a vast number of equally coherent but rival systems [Bonjour] |
21503 | Empirical coherence must attribute reliability to spontaneous experience [Bonjour] |
21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
21505 | A coherent system can be justified with initial beliefs lacking all credibility [Bonjour] |
21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
8891 | My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour] |
8892 | Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour] |
8894 | Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour] |
4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
3701 | Externalist theories of justification don't require believers to have reasons for their beliefs [Bonjour] |
8889 | Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour] |
4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
8890 | If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour] |
4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
3702 | Externalism means we have no reason to believe, which is strong scepticism [Bonjour] |
21508 | Anomalies challenge the claim that the basic explanations are actually basic [Bonjour] |
3709 | Induction must go beyond the evidence, in order to explain why the evidence occurred [Bonjour] |
6027 | From the fact that some men die, we cannot infer that they all do [Philodemus] |
8895 | If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [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] |
22241 | Don't fear god or worry about death; the good is easily got and the terrible easily cured [Philodemus] |