73 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] |
4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
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] |
3707 | Our rules of thought can only be judged by pure rational insight [Bonjour] |
3704 | Moderate rationalists believe in fallible a priori justification [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] |
3706 | A priori justification can vary in degree [Bonjour] |
3703 | You can't explain away a priori justification as analyticity, and you can't totally give it up [Bonjour] |
3696 | A priori justification requires understanding but no experience [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] |
21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
21505 | A coherent system can be justified with initial beliefs lacking all credibility [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] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
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] |
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] |
3698 | Indeterminacy of translation is actually indeterminacy of meaning and belief [Bonjour] |