52 ideas
| 17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
| 17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
| 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] |
| 17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [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] |
| 17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
| 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] |
| 17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
| 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] |
| 17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
| 17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
| 17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
| 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] |
| 17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
| 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] |
| 17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
| 8724 | The meaning of 'know' does not change from courtroom to living room [Unger] |
| 8722 | No one knows anything, and no one is ever justified or reasonable [Unger] |
| 8723 | An evil scientist may give you a momentary life, with totally false memories [Unger] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
| 17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
| 17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
| 17732 | Success semantics explains representation in terms of success in action [Jenkins] |
| 17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |