159 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] |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| 2200 | All experimental conclusions assume that the future will be like the past [Hume] |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| 4636 | All reasoning concerning matters of fact is based on analogy (with similar results of similar causes) [Hume] |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| 16324 | Any definition of truth requires a metalanguage [Halbach] |
| 16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
| 16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
| 16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
| 16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
| 16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| 16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
| 16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
| 16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
| 16309 | Every attempt at formal rigour uses some set theory [Halbach] |
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| 9895 | A number is a multitude composed of units [Dummett] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
| 16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
| 16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| 2197 | Reason assists experience in discovering laws, and in measuring their application [Hume] |
| 16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| 7700 | We can't think about the abstract idea of triangles, but only of particular triangles [Hume] |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| 13602 | We cannot form an idea of a 'power', and the word is without meaning [Hume] |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| 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] |
| 2208 | Belief is just a particular feeling attached to ideas of objects [Hume] |
| 2207 | Belief can't be a concept plus an idea, or we could add the idea to fictions [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] |
| 2184 | All ideas are copies of impressions [Hume] |
| 2192 | All reasoning about facts is causal; nothing else goes beyond memory and senses [Hume] |
| 2246 | If books don't relate ideas or explain facts, commit them to the flames [Hume] |
| 2190 | All objects of enquiry are Relations of Ideas, or Matters of Fact [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] |
| 2189 | All ideas are connected by Resemblance, Contiguity in time or place, and Cause and Effect [Hume] |
| 2702 | Only madmen dispute the authority of experience [Hume] |
| 2183 | We can only invent a golden mountain by combining experiences [Hume] |
| 2186 | We cannot form the idea of something we haven't experienced [Hume] |
| 2194 | How could Adam predict he would drown in water or burn in fire? [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] |
| 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] |
| 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] |
| 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] |
| 3598 | Hume just shows induction isn't deduction [Williams,M on Hume] |
| 6350 | Premises can support an argument without entailing it [Pollock/Cruz 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] |
| 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] |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| 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] |
| 2234 | It is only when two species of thing are constantly conjoined that we can infer one from the other [Hume] |
| 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] |
| 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] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| 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] |
| 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] |
| 2228 | All experience must be against a supposed miracle, or it wouldn't be called 'a miracle' [Hume] |
| 2185 | The idea of an infinite, intelligent, wise and good God arises from augmenting the best qualities of our own minds [Hume] |