52 ideas
| 23755 | Genius and love of truth are always accompanied by great humility [Weil] |
| 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] |
| 23747 | What is sacred is not a person, but the whole physical human being [Weil] |
| 23756 | The mind is imprisoned and limited by language, restricting our awareness of wider thoughts [Weil] |
| 23758 | Beauty is an attractive mystery, leaving nothing to be desired [Weil] |
| 23760 | All we need are the unity of justice, truth and beauty [Weil] |
| 23748 | The sacred in every human is their expectation of good rather than evil [Weil] |
| 23759 | Everything which originates in love is beautiful [Weil] |
| 23762 | Evil is transmitted by comforts and pleasures, but mostly by doing harm to people [Weil] |
| 23750 | It is not more money which the wretched members of society need [Weil] |
| 23749 | The problem of the collective is not suppression of persons, but persons erasing themselves [Weil] |
| 23753 | People absurdly claim an equal share of things which are essentially privileged [Weil] |
| 23751 | Rights are asserted contentiously, and need the backing of force [Weil] |
| 23752 | Giving centrality to rights stifles all impulses of charity [Weil] |
| 23757 | The spirit of justice needs the full attention of truth, and that attention is love [Weil] |
| 23761 | Justice (concerning harm) is distinct from rights (concerning inequality) [Weil] |
| 23764 | The only thing in society worse than crime is repressive justice [Weil] |
| 23763 | Punishment aims at the good for men who don't desire it [Weil] |
| 23754 | The only choice is between supernatural good, or evil [Weil] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |