39 ideas
12596 | Reasoning aims at increasing explanatory coherence [Harman] |
12599 | Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman] |
8368 | A correct definition is what can be substituted without loss of meaning [Ducasse] |
12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
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] |
12598 | Reality is the overlap of true complete theories [Harman] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12602 | There is no natural border between inner and outer [Harman] |
12603 | We can only describe mental attitudes in relation to the external world [Harman] |
12601 | The way things look is a relational matter, not an intrinsic matter [Harman] |
12592 | Concepts in thought have content, but not meaning, which requires communication [Harman] |
12590 | Take meaning to be use in calculation with concepts, rather than in communication [Harman] |
12593 | The use theory attaches meanings to words, not to sentences [Harman] |
12588 | Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman] |
12589 | Some regard conceptual role semantics as an entirely internal matter [Harman] |
12600 | The content of thought is relations, between mental states, things in the world, and contexts [Harman] |
12594 | If one proposition negates the other, which is the negative one? [Harman] |
12591 | Mastery of a language requires thinking, and not just communication [Harman] |
8367 | Causation is defined in terms of a single sequence, and constant conjunction is no part of it [Ducasse] |
8372 | We see what is in common between causes to assign names to them, not to perceive them [Ducasse] |
8369 | Causes are either sufficient, or necessary, or necessitated, or contingent upon [Ducasse] |
8373 | When a brick and a canary-song hit a window, we ignore the canary if we are interested in the breakage [Ducasse] |
8370 | A cause is a change which occurs close to the effect and just before it [Ducasse] |
8371 | Recurrence is only relevant to the meaning of law, not to the meaning of cause [Ducasse] |
8374 | We are interested in generalising about causes and effects purely for practical purposes [Ducasse] |