57 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] |
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] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
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] |
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] |
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] |
7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |
19254 | Our laws of nature may be the result of evolution [Peirce] |