74 ideas
| 19250 | Everything interesting should be recorded, with records that can be rearranged [Peirce] |
| 19228 | Sciences concern existence, but philosophy also concerns potential existence [Peirce] |
| 19241 | An idea on its own isn't an idea, because they are continuous systems [Peirce] |
| 19227 | Philosophy is a search for real truth [Peirce] |
| 19218 | Metaphysics is pointless without exact modern logic [Peirce] |
| 19229 | Metaphysics is the science of both experience, and its general laws and types [Peirce] |
| 19219 | Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce] |
| 19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
| 19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
| 19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
| 19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| 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] |
| 19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
| 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] |
| 19240 | Realism is the belief that there is something in the being of things corresponding to our reasoning [Peirce] |
| 19239 | There may be no reality; it's just our one desperate hope of knowing anything [Peirce] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 19252 | Objective chance is the property of a distribution [Peirce] |
| 19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
| 19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
| 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] |
| 19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
| 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] |
| 19224 | Scientists will give up any conclusion, if experience opposes it [Peirce] |
| 19243 | If each inference slightly reduced our certainty, science would soon be in trouble [Peirce] |
| 19225 | I classify science by level of abstraction; principles derive from above, and data from below [Peirce] |
| 19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce] |
| 19235 | How does induction get started? [Peirce] |
| 19236 | Induction can never prove that laws have no exceptions [Peirce] |
| 19251 | The worst fallacy in induction is generalising one recondite property from a sample [Peirce] |
| 19222 | Men often answer inner 'whys' by treating unconscious instincts as if they were reasons [Peirce] |
| 19220 | We may think animals reason very little, but they hardly ever make mistakes! [Peirce] |
| 19255 | Generalisation is the great law of mind [Peirce] |
| 19242 | Generalization is the true end of life [Peirce] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 19249 | 'Know yourself' is not introspection; it is grasping how others see you [Peirce] |
| 19257 | Whatever is First must be sentient [Peirce] |
| 19248 | Reasoning involves observation, experiment, and habituation [Peirce] |
| 19221 | Everybody overrates their own reasoning, so it is clearly superficial [Peirce] |
| 19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
| 19230 | People should follow what lies before them, and is within their power [Peirce] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 19245 | We are not inspired by other people's knowledge; a sense of our ignorance motivates study [Peirce] |
| 19244 | Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce] |
| 19254 | Our laws of nature may be the result of evolution [Peirce] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |