64 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
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] |
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
3697 | The concept of possibility is prior to that of necessity [Bonjour] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
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] |
3696 | A priori justification requires understanding but no experience [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] |
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] |
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] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |