46 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] |
| 14979 | Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider] |
| 15454 | Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 15455 | Total intrinsic properties give us what a thing is [Lewis] |
| 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] |
| 23814 | Every human yearns for an unattainable transcendent good [Weil] |
| 23824 | Where human needs are satisfied we find happiness, friendship and beauty [Weil] |
| 23815 | We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil] |
| 23823 | Life needs risks to avoid sickly boredom [Weil] |
| 23822 | We all need to partipate in public tasks, and take some initiative [Weil] |
| 23817 | We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil] |
| 23819 | Deliberate public lying should be punished [Weil] |
| 23818 | We have liberty in the space between nature and accepted authority [Weil] |
| 23820 | People need personal and collective property, and a social class lacking property is shameful [Weil] |
| 23821 | Crime should be punished, to bring the perpetrator freely back to morality [Weil] |
| 23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |