26 ideas
21489 | Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin] |
19095 | Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak] |
19097 | Peirce did not think a belief was true if it was useful [Peirce, by Misak] |
21494 | If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
10352 | The real is the idea in which the community ultimately settles down [Peirce] |
13498 | Peirce and others began the mapping out of relations [Peirce, by Hart,WD] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
21491 | Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
16376 | The possible can only be general, and the force of actuality is needed to produce a particular [Peirce] |
19107 | Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce] |
20618 | Persons must be conscious, reasoning, motivated, communicative, self-aware [Warren, by Tuckness/Wolf] |