61 ideas
| 14027 | If we are to use words in enquiry, we need their main, unambiguous and uncontested meanings [Epicurus] |
| 12801 | Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley] |
| 14040 | Observation and applied thought are always true [Epicurus] |
| 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] |
| 14028 | Nothing comes to be from what doesn't exist [Epicurus] |
| 14029 | If disappearing things went to nothingness, nothing could return, and it would all be gone by now [Epicurus] |
| 14030 | The totality is complete, so there is no room for it to change, and nothing extraneous to change it [Epicurus] |
| 14048 | Astronomical movements are blessed, but they don't need the help of the gods [Epicurus] |
| 14044 | The perceived accidental properties of bodies cannot be conceived of as independent natures [Epicurus] |
| 14045 | Accidental properties give a body its nature, but are not themselves bodies or parts of bodies [Epicurus] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 14046 | A 'body' is a conception of an aggregate, with properties defined by application conditions [Epicurus] |
| 14047 | Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus] |
| 14039 | Above and below us will never appear to be the same, because it is inconceivable [Epicurus] |
| 14050 | We aim to dissolve our fears, by understanding their causes [Epicurus] |
| 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] |
| 14037 | Atoms only have shape, weight and size, and the properties which accompany shape [Epicurus] |
| 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] |
| 12800 | Externalists want to understand knowledge, Internalists want to understand justification [Foley] |
| 12802 | We aren't directly pragmatic about belief, but pragmatic about the deliberation which precedes it [Foley] |
| 12803 | Justification comes from acceptable procedures, given practical constraints [Foley] |
| 6010 | Illusions are not false perceptions, as we accurately perceive the pattern of atoms [Epicurus, by Modrak] |
| 14041 | The soul is fine parts distributed through the body, resembling hot breath [Epicurus] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 14042 | The soul cannot be incorporeal, because then it could neither act nor be acted upon [Epicurus] |
| 14032 | Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus] |
| 14033 | Bodies are unlimited as well as void, since the two necessarily go together [Epicurus] |
| 14034 | There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus] |
| 14035 | Atoms just have shape, size and weight; colour results from their arrangement [Epicurus] |
| 14038 | There cannot be unlimited division, because it would reduce things to non-existence [Epicurus] |
| 14049 | We aim to know the natures which are observed in natural phenomena [Epicurus] |
| 14043 | The void cannot interact, but just gives the possibility of motion [Epicurus] |
| 14031 | Space must exist, since movement is obvious, and there must be somewhere to move in [Epicurus] |
| 14036 | There are endless cosmoi, some like and some unlike this one [Epicurus] |