131 ideas
| 2196 | The observation of human blindness and weakness is the result of all philosophy [Hume] |
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| 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] |
| 4636 | All reasoning concerning matters of fact is based on analogy (with similar results of similar causes) [Hume] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 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] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 2216 | We transfer the frequency of past observations to our future predictions [Hume] |
| 2215 | There is no such thing as chance [Hume] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 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] |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| 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] |
| 2240 | It is a very extravagant aim of the sceptics to destroy reason and argument by means of reason and argument [Hume] |
| 2241 | The main objection to scepticism is that no good can come of it [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] |
| 2204 | All inferences from experience are effects of custom, not reasoning [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] |
| 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] |
| 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] |
| 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] |