52 ideas
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
| 23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
| 23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
| 23128 | The opposite of liberalism is dogmatism [Gopnik] |
| 23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
| 23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
| 23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
| 23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
| 23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
| 23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
| 23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
| 23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
| 23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
| 23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
| 23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
| 23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
| 23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
| 23136 | Liberal free speech is actually paid speech [Gopnik] |
| 23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |