36 ideas
4262 | If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
4045 | Children may have three innate principles which enable them to learn to count [Goldman] |
4044 | Rat behaviour reveals a considerable ability to count [Goldman] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
4048 | Infant brains appear to have inbuilt ontological categories [Goldman] |
4043 | Elephants can be correctly identified from as few as three primitive shapes [Goldman] |
4049 | The way in which colour experiences are evoked is physically odd and unpredictable [Goldman] |
4047 | Gestalt psychology proposes inbuilt proximity, similarity, smoothness and closure principles [Goldman] |
8830 | A belief can be justified when the person has forgotten the evidence for it [Goldman] |
6871 | We can't only believe things if we are currently conscious of their justification - there are too many [Goldman] |
6872 | Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman] |
6874 | Internal justification needs both mental stability and time to compute coherence [Goldman] |
8832 | If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman] |
6873 | Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman] |
8829 | Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman] |
6875 | Reliability involves truth, and truth is external [Goldman] |
8831 | Introspection is really retrospection; my pain is justified by a brief causal history [Goldman] |