54 ideas
| 22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
| 21238 | Later phenomenologists tried hard to incorporate social relationships [Bakewell] |
| 21237 | Phenomenology begins from the immediate, rather than from axioms and theories [Bakewell] |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| 4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
| 17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
| 16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
| 7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
| 7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
| 9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| 7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
| 7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| 13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
| 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] |
| 17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
| 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] |
| 10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
| 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] |
| 11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
| 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] |
| 22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
| 7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |