48 ideas
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] |
22427 | To explain object qualities, primary qualities must be more than mere sources of experience [McGinn] |
4444 | One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong] |
4445 | If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong] |
4448 | Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong] |
4446 | It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong] |
4440 | 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong] |
4439 | 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong] |
4431 | 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong] |
4433 | Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong] |
4432 | 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong] |
4436 | 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong] |
4434 | 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong] |
4435 | 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong] |
4437 | 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong] |
4438 | 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong] |
22413 | Being red simply consists in looking red [McGinn] |
22415 | Relativity means differing secondary perceptions are not real disagreements [McGinn] |
22416 | Phenomenalism is correct for secondary qualities, so scepticism is there impossible [McGinn] |
22422 | Maybe all possible sense experience must involve both secondary and primary qualities [McGinn] |
22428 | You understood being red if you know the experience involved; not so with thngs being square [McGinn] |
22414 | You don't need to know how a square thing looks or feels to understand squareness [McGinn] |
22423 | Touch doesn't provide direct experience of primary qualities, because touch feels temperature [McGinn] |
22426 | We can perceive objectively, because primary qualities are not mind-created [McGinn] |
22412 | Lockean secondary qualities (unlike primaries) produce particular sensory experiences [McGinn] |
22421 | Could there be a mind which lacked secondary quality perception? [McGinn] |
22424 | Secondary qualities contain information; their variety would be superfluous otherwise [McGinn] |
22425 | The utility theory says secondary qualities give information useful to human beings [McGinn] |
7629 | We see objects 'directly' by representing them [McGinn] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22420 | The indexical perspective is subjective, incorrigible and constant [McGinn] |
18410 | Indexical thought is in relation to my self-consciousness [McGinn] |
22417 | Indexicals do not figure in theories of physics, because they are not explanatory causes [McGinn] |
18402 | Indexical concepts are indispensable, as we need them for the power to act [McGinn] |
22418 | I can know indexical truths a priori, unlike their non-indexical paraphrases [McGinn] |