50 ideas
12105 | Our knowledge starts in theology, passes through metaphysics, and ends in positivism [Comte] |
12104 | All ideas must be understood historically [Comte] |
12112 | Metaphysics is just the oversubtle qualification of abstract names for phenomena [Comte] |
12111 | Positivism is the final state of human intelligence [Comte] |
12106 | Positivism gives up absolute truth, and seeks phenomenal laws, by reason and observation [Comte] |
12114 | Science can drown in detail, so we need broad scientists (to keep out the metaphysicians) [Comte] |
12116 | Only positivist philosophy can terminate modern social crises [Comte] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
6346 | The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz] |
6351 | Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz] |
6374 | To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz] |
6355 | Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz] |
6359 | Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz] |
6366 | Perception causes beliefs in us, without inference or justification [Pollock/Cruz] |
6362 | Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12108 | All real knowledge rests on observed facts [Comte] |
6371 | Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz] |
6373 | Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz] |
6353 | People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz] |
6361 | Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz] |
6357 | Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz] |
6363 | Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz] |
6365 | Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz] |
6354 | Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz] |
6367 | Coherence theories isolate justification from the world [Pollock/Cruz] |
6370 | Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz] |
6358 | One belief may cause another, without being the basis for the second belief [Pollock/Cruz] |
6364 | We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz] |
12109 | We must observe in order to form theories, but connected observations need prior theories [Comte] |
6352 | Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz] |
6372 | Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz] |
12107 | Positivism explains facts by connecting particular phenomena with general facts [Comte] |
6360 | Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz] |
12115 | Introspection is pure illusion; we can obviously observe everything except ourselves [Comte] |
12113 | The search for first or final causes is futile [Comte] |
12110 | We can never know origins, purposes or inner natures [Comte] |