61 ideas
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 12430 | Classical logic is our preconditions for assessing empirical evidence [Kitcher] |
| 12431 | I believe classical logic because I was taught it and use it, but it could be undermined [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] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [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] |
| 16661 | There are two sorts of category - referring to things, and to circumstances of things [Boethius] |
| 15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 12428 | Many necessities are inexpressible, and unknowable a priori [Kitcher] |
| 12429 | Knowing our own existence is a priori, but not necessary [Kitcher] |
| 23308 | Reasoning relates to understanding as time does to eternity [Boethius, by Sorabji] |
| 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] |
| 5771 | Knowledge of present events doesn't make them necessary, so future events are no different [Boethius] |
| 5767 | Rational natures require free will, in order to have power of judgement [Boethius] |
| 5769 | Does foreknowledge cause necessity, or necessity cause foreknowledge? [Boethius] |
| 5768 | God's universal foreknowledge seems opposed to free will [Boethius] |
| 5762 | The wicked want goodness, so they would not be wicked if they obtained it [Boethius] |
| 5770 | Rewards and punishments are not deserved if they don't arise from free movement of the mind [Boethius] |
| 5764 | When people fall into wickedness they lose their human nature [Boethius] |
| 5756 | Happiness is a good which once obtained leaves nothing more to be desired [Boethius] |
| 5763 | The bad seek the good through desire, but the good through virtue, which is more natural [Boethius] |
| 5759 | Varied aims cannot be good because they differ, but only become good when they unify [Boethius] |
| 5754 | You can't control someone's free mind, only their body and possessions [Boethius] |
| 16692 | Divine eternity is the all-at-once and complete possession of unending life [Boethius] |
| 5752 | Where does evil come from if there is a god; where does good come from if there isn't? [Boethius] |
| 5757 | God is the supreme good, so no source of goodness could take precedence over God [Boethius] |
| 5758 | God is the good [Boethius] |
| 5760 | The power through which creation remains in existence and motion I call 'God' [Boethius] |
| 5753 | The regular events of this life could never be due to chance [Boethius] |
| 5765 | The reward of the good is to become gods [Boethius] |
| 5761 | God can do anything, but he cannot do evil, so evil must be nothing [Boethius] |
| 5766 | If you could see the plan of Providence, you would not think there was evil anywhere [Boethius] |