117 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] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
4636 | All reasoning concerning matters of fact is based on analogy (with similar results of similar causes) [Hume] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
2197 | Reason assists experience in discovering laws, and in measuring their application [Hume] |
21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
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] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
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] |
3661 | 'Natural beliefs' are unavoidable, whatever our judgements [Hume, by Strawson,G] |
2213 | Beliefs are built up by resemblance, contiguity and causation [Hume] |
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] |
2190 | All objects of enquiry are Relations of Ideas, or Matters of Fact [Hume] |
2184 | All ideas are copies of impressions [Hume] |
2192 | All reasoning about facts is causal; nothing else goes beyond memory and senses [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] |
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] |
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] |
2217 | When definitions are pushed to the limit, only experience can make them precise [Hume] |
2186 | We cannot form the idea of something we haven't experienced [Hume] |
2702 | Only madmen dispute the authority of 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] |
2199 | Reason cannot show why reliable past experience should extend to future times and remote places [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] |
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] |
17712 | General ideas are the connection by resemblance to some particular [Hume] |
2210 | A picture of a friend strengthens our idea of him, by resemblance [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] |
2214 | Our awareness of patterns of causation is too important to be left to slow and uncertain reasoning [Hume] |
2212 | An object made by a saint is the best way to produce thoughts of him [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] |
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] |
2233 | No government has ever suffered by being too tolerant of philosophy [Hume] |
2195 | We can discover some laws of nature, but never its ultimate principles and causes [Hume] |
4772 | If a singular effect is studied, its cause can only be inferred from the types of events involved [Hume] |
2245 | A priori it looks as if a cause could have absolutely any effect [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] |
2193 | No causes can be known a priori, but only from experience of constant conjunctions [Hume] |
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] |
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] |
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] |
2218 | In observing causes we can never observe any necessary connections or binding qualities [Hume] |
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] |