133 ideas
| 2196 | The observation of human blindness and weakness is the result of all philosophy [Hume] |
| 2187 | If we suspect that a philosophical term is meaningless, we should ask what impression it derives from [Hume] |
| 2200 | All experimental conclusions assume that the future will be like the past [Hume] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 4636 | All reasoning concerning matters of fact is based on analogy (with similar results of similar causes) [Hume] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 2197 | Reason assists experience in discovering laws, and in measuring their application [Hume] |
| 7700 | We can't think about the abstract idea of triangles, but only of particular triangles [Hume] |
| 13602 | We cannot form an idea of a 'power', and the word is without meaning [Hume] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 2216 | We transfer the frequency of past observations to our future predictions [Hume] |
| 2215 | There is no such thing as chance [Hume] |
| 2209 | Belief is stronger, clearer and steadier than imagination [Hume] |
| 2207 | Belief can't be a concept plus an idea, or we could add the idea to fictions [Hume] |
| 2208 | Belief is just a particular feeling attached to ideas of objects [Hume] |
| 2213 | Beliefs are built up by resemblance, contiguity and causation [Hume] |
| 3661 | 'Natural beliefs' are unavoidable, whatever our judgements [Hume, by Strawson,G] |
| 2191 | Relations of ideas are known by thought, independently from the world [Hume] |
| 2239 | If secondary qualities (e.g. hardness) are in the mind, so are primary qualities like extension [Hume] |
| 2237 | It never occurs to people that they only experience representations, not the real objects [Hume] |
| 2192 | All reasoning about facts is causal; nothing else goes beyond memory and senses [Hume] |
| 2184 | All ideas are copies of impressions [Hume] |
| 23631 | Hume is loose when he says perceptions of different strength are different species [Reid on Hume] |
| 2182 | Impressions are our livelier perceptions, Ideas the less lively ones [Hume] |
| 2190 | All objects of enquiry are Relations of Ideas, or Matters of Fact [Hume] |
| 2246 | If books don't relate ideas or explain facts, commit them to the flames [Hume] |
| 2189 | All ideas are connected by Resemblance, Contiguity in time or place, and Cause and Effect [Hume] |
| 2186 | We cannot form the idea of something we haven't experienced [Hume] |
| 2702 | Only madmen dispute the authority of experience [Hume] |
| 2217 | When definitions are pushed to the limit, only experience can make them precise [Hume] |
| 2194 | How could Adam predict he would drown in water or burn in fire? [Hume] |
| 2183 | We can only invent a golden mountain by combining experiences [Hume] |
| 2205 | You couldn't reason at all if you lacked experience [Hume] |
| 3902 | Hume mistakenly lumps sensations and perceptions together as 'impressions' [Scruton on Hume] |
| 23421 | If a person had a gap in their experience of blue shades, they could imaginatively fill it in [Hume] |
| 2206 | Reasons for belief must eventually terminate in experience, or they are without foundation [Hume] |
| 2235 | There is no certain supreme principle, or infallible rule of inference [Hume] |
| 10328 | We think testimony matches reality because of experience, not some a priori connection [Hume] |
| 2230 | Good testimony needs education, integrity, motive and agreement [Hume, by PG] |
| 2238 | Reason can never show that experiences are connected to external objects [Hume] |
| 2242 | Mitigated scepticism draws attention to the limitations of human reason, and encourages modesty [Hume] |
| 2243 | Mitigated scepticism sensibly confines our enquiries to the narrow capacity of human understanding [Hume] |
| 2236 | Examples of illusion only show that sense experience needs correction by reason [Hume] |
| 2241 | The main objection to scepticism is that no good can come of it [Hume] |
| 2240 | It is a very extravagant aim of the sceptics to destroy reason and argument by means of reason and argument [Hume] |
| 2198 | We assume similar secret powers behind similar experiences, such as the nourishment of bread [Hume] |
| 2201 | Induction can't prove that the future will be like the past, since induction assumes this [Hume] |
| 2203 | If we infer causes from repetition, this explains why we infer from a thousand objects what we couldn't infer from one [Hume] |
| 2199 | Reason cannot show why reliable past experience should extend to future times and remote places [Hume] |
| 2202 | Fools, children and animals all learn from experience [Hume] |
| 2204 | All inferences from experience are effects of custom, not reasoning [Hume] |
| 6350 | Premises can support an argument without entailing it [Pollock/Cruz on Hume] |
| 3598 | Hume just shows induction isn't deduction [Williams,M on Hume] |
| 2210 | A picture of a friend strengthens our idea of him, by resemblance [Hume] |
| 17712 | General ideas are the connection by resemblance to some particular [Hume] |
| 8544 | Hume does not distinguish real resemblances among degrees of resemblance [Shoemaker on Hume] |
| 2211 | When I am close to (contiguous with) home, I feel its presence more nearly [Hume] |
| 2212 | An object made by a saint is the best way to produce thoughts of him [Hume] |
| 2214 | Our awareness of patterns of causation is too important to be left to slow and uncertain reasoning [Hume] |
| 2222 | The doctrine of free will arises from a false sensation we have of freedom in many actions [Hume] |
| 2223 | Liberty is merely acting according to the will, which anyone can do if they are not in chains [Hume] |
| 3655 | Hume makes determinism less rigid by removing the necessity from causation [Trusted on Hume] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 2220 | Only experience teaches us about our wills [Hume] |
| 2224 | Praise and blame can only be given if an action proceeds from a person's character and disposition [Hume] |
| 2225 | If you deny all necessity and causation, then our character is not responsible for our crime [Hume] |
| 2226 | Repentance gets rid of guilt, which shows that responsibility arose from the criminal principles in the mind [Hume] |
| 7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
| 7214 | Ethics rests on utility, which is the permanent progressive interests of people [Mill] |
| 7212 | Individuals have sovereignty over their own bodies and minds [Mill] |
| 7210 | The will of the people is that of the largest or most active part of the people [Mill] |
| 7227 | It is evil to give a government any more power than is necessary [Mill] |
| 7228 | Individuals often do things better than governments [Mill] |
| 7230 | Aim for the maximum dissemination of power consistent with efficiency [Mill] |
| 20515 | Maximise happiness by an area of strict privacy, and an area of utilitarian interventions [Mill, by Wolff,J] |
| 7229 | People who transact their own business will also have the initiative to control their government [Mill] |
| 7211 | Prevention of harm to others is the only justification for exercising power over people [Mill] |
| 7231 | The worth of a State, in the long run, is the worth of the individuals composing it [Mill] |
| 7217 | The main argument for freedom is that interference with it is usually misguided [Mill] |
| 2233 | No government has ever suffered by being too tolerant of philosophy [Hume] |
| 7213 | Liberty arises at the point where people can freely and equally discuss things [Mill] |
| 20517 | Utilitarianism values liberty, but guides us on which ones we should have or not have [Mill, by Wolff,J] |
| 20516 | Mill defends freedom as increasing happiness, but maybe it is an intrinsic good [Wolff,J on Mill] |
| 7215 | True freedom is pursuing our own good, while not impeding others [Mill] |
| 7218 | Individuals are not accountable for actions which only concern themselves [Mill] |
| 7221 | Blocking entry to an unsafe bridge does not infringe liberty, since no one wants unsafe bridges [Mill] |
| 7223 | Pimping and running a gambling-house are on the border between toleration and restraint [Mill] |
| 7220 | Restraint for its own sake is an evil [Mill] |
| 7219 | Society can punish actions which it believes to be prejudicial to others [Mill] |
| 7226 | Benefits performed by individuals, not by government, help also to educate them [Mill] |
| 7224 | We need individual opinions and conduct, and State education is a means to prevent that [Mill] |
| 7225 | It is a crime to create a being who lacks the ordinary chances of a desirable existence [Mill] |
| 2195 | We can discover some laws of nature, but never its ultimate principles and causes [Hume] |
| 2245 | A priori it looks as if a cause could have absolutely any effect [Hume] |
| 4772 | If a singular effect is studied, its cause can only be inferred from the types of events involved [Hume] |
| 8341 | Hume never even suggests that there is no such thing as causation [Hume, by Strawson,G] |
| 8344 | At first Hume said qualities are the causal entities, but later he said events [Hume, by Davidson] |
| 3662 | Hume says we can only know constant conjunctions, not that that's what causation IS [Hume, by Strawson,G] |
| 4771 | In both of Hume's definitions, causation is extrinsic to the sequence of events [Psillos on Hume] |
| 5194 | Hume's definition of cause as constantly joined thoughts can't cover undiscovered laws [Ayer on Hume] |
| 2221 | A cause is either similar events following one another, or an experience always suggesting a second experience [Hume] |
| 2193 | No causes can be known a priori, but only from experience of constant conjunctions [Hume] |
| 2234 | It is only when two species of thing are constantly conjoined that we can infer one from the other [Hume] |
| 8422 | Cause is where if the first object had not been, the second had not existed [Hume] |
| 2218 | In observing causes we can never observe any necessary connections or binding qualities [Hume] |
| 15249 | Hume never shows how a strong habit could generate the concept of necessity [Harré/Madden on Hume] |
| 8339 | Hume's regularity theory of causation is epistemological; he believed in some sort of natural necessity [Hume, by Strawson,G] |
| 2244 | It can never be a logical contradiction to assert the non-existence of something thought to exist [Hume] |
| 2232 | You can't infer the cause to be any greater than its effect [Hume] |
| 2228 | All experience must be against a supposed miracle, or it wouldn't be called 'a miracle' [Hume] |
| 2229 | To establish a miracle the falseness of the evidence must be a greater miracle than the claimed miraculous event [Hume] |
| 2227 | A miracle violates laws which have been established by continuous unchanging experience, so should be ignored [Hume] |
| 2185 | The idea of an infinite, intelligent, wise and good God arises from augmenting the best qualities of our own minds [Hume] |
| 7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |