149 ideas
| 5361 | Philosophers must get used to absurdities [Russell] |
| 5368 | Philosophy verifies that our hierarchy of instinctive beliefs is harmonious and consistent [Russell] |
| 5432 | Metaphysics cannot give knowledge of the universe as a whole [Russell] |
| 5434 | Philosophy is similar to science, and has no special source of wisdom [Russell] |
| 5396 | Three Laws of Thought: identity, contradiction, and excluded middle [Russell] |
| 5405 | The law of contradiction is not a 'law of thought', but a belief about things [Russell] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 5420 | Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell] |
| 5419 | Truth and falsehood are properties of beliefs and statements [Russell] |
| 5417 | A good theory of truth must make falsehood possible [Russell] |
| 7395 | Truth as congruence may work for complex beliefs, but not for simple beliefs about existence [Joslin on Russell] |
| 5428 | Beliefs are true if they have corresponding facts, and false if they don't [Russell] |
| 5421 | The coherence theory says falsehood is failure to cohere, and truth is fitting into a complete system of Truth [Russell] |
| 5422 | More than one coherent body of beliefs seems possible [Russell] |
| 5423 | If we suspend the law of contradiction, nothing will appear to be incoherent [Russell] |
| 5424 | Coherence is not the meaning of truth, but an important test for truth [Russell] |
| 5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 5395 | Demonstration always relies on the rule that anything implied by a truth is true [Russell] |
| 5386 | Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell] |
| 5385 | The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 5370 | Space is neutral between touch and sight, so it cannot really be either of them [Russell] |
| 5418 | In a world of mere matter there might be 'facts', but no truths [Russell] |
| 5371 | Because we depend on correspondence, we know relations better than we know the items that relate [Russell] |
| 5407 | That Edinburgh is north of London is a non-mental fact, so relations are independent universals [Russell] |
| 5383 | Every complete sentence must contain at least one word (a verb) which stands for a universal [Russell] |
| 4428 | Propositions express relations (prepositions and verbs) as well as properties (nouns and adjectives) [Russell] |
| 5406 | Confused views of reality result from thinking that only nouns and adjectives represent universals [Russell] |
| 4479 | All universals are like the relation "is north of", in having no physical location at all [Russell, by Loux] |
| 4427 | Every sentence contains at least one word denoting a universal, so we need universals to know truth [Russell] |
| 4030 | Russell claims that universals are needed to explain a priori knowledge (as their relations) [Russell, by Mellor/Oliver] |
| 5409 | Normal existence is in time, so we must say that universals 'subsist' [Russell] |
| 5408 | If we identify whiteness with a thought, we can never think of it twice; whiteness is the object of a thought [Russell] |
| 4441 | 'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal [Russell] |
| 4429 | If we consider whiteness to be merely a mental 'idea', we rob it of its universality [Russell] |
| 5400 | In any possible world we feel that two and two would be four [Russell] |
| 5431 | Knowledge cannot be precisely defined, as it merges into 'probable opinion' [Russell] |
| 5426 | Belief relates a mind to several things other than itself [Russell] |
| 5366 | We have an 'instinctive' belief in the external world, prior to all reflection [Russell] |
| 5359 | Descartes showed that subjective things are the most certain [Russell] |
| 5377 | 'Acquaintance' is direct awareness, without inferences or judgements [Russell] |
| 6510 | Russell (1912) said phenomena only resemble reality in abstract structure [Russell, by Robinson,H] |
| 5372 | There is no reason to think that objects have colours [Russell] |
| 5373 | 'Idealism' says that everything which exists is in some sense mental [Russell] |
| 5362 | It is not illogical to think that only myself and my mental events exist [Russell] |
| 5412 | Some propositions are self-evident, but their implications may also be self-evident [Russell] |
| 5413 | Particular instances are more clearly self-evident than any general principles [Russell] |
| 5415 | As shown by memory, self-evidence comes in degrees [Russell] |
| 5416 | If self-evidence has degrees, we should accept the more self-evident as correct [Russell] |
| 5397 | The rationalists were right, because we know logical principles without experience [Russell] |
| 4430 | All a priori knowledge deals with the relations of universals [Russell] |
| 5411 | We can know some general propositions by universals, when no instance can be given [Russell] |
| 6514 | Russell's representationalism says primary qualities only show the structure of reality [Russell, by Robinson,H] |
| 6415 | After 1912, Russell said sense-data are last in analysis, not first in experience [Russell, by Grayling] |
| 5358 | 'Sense-data' are what are immediately known in sensation, such as colours or roughnesses [Russell] |
| 7290 | If Russell rejects innate ideas and direct a priori knowledge, he is left with a tabula rasa [Russell, by Thompson] |
| 5357 | It is natural to begin from experience, and presumably that is the basis of knowledge [Russell] |
| 5382 | We are acquainted with outer and inner sensation, memory, Self, and universals [Russell, by PG] |
| 5389 | Knowledge by descriptions enables us to transcend private experience [Russell] |
| 5376 | I can know the existence of something with which nobody is acquainted [Russell] |
| 5414 | Images are not memory, because they are present, and memories are of the past [Russell] |
| 5430 | A true belief is not knowledge if it is reached by bad reasoning [Russell] |
| 5429 | True belief is not knowledge when it is deduced from false belief [Russell] |
| 5378 | All knowledge (of things and of truths) rests on the foundations of acquaintance [Russell] |
| 5365 | Dreams can be explained fairly scientifically if we assume a physical world [Russell] |
| 5391 | Science aims to find uniformities to which (within the limits of experience) there are no exceptions [Russell] |
| 5394 | We can't prove induction from experience without begging the question [Russell] |
| 5390 | Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell] |
| 5392 | It doesn't follow that because the future has always resembled the past, that it always will [Russell] |
| 5363 | If the cat reappears in a new position, presumably it has passed through the intermediate positions [Russell] |
| 5367 | Belief in real objects makes our account of experience simpler and more systematic [Russell] |
| 5364 | It is hard not to believe that speaking humans are expressing thoughts, just as we do ourselves [Russell] |
| 5379 | If we didn't know our own minds by introspection, we couldn't know that other people have minds [Russell] |
| 2584 | Lobotomised patients can cease to care about a pain [Block] |
| 2582 | A brain looks no more likely than anything else to cause qualia [Block] |
| 5410 | I learn the universal 'resemblance' by seeing two shades of green, and their contrast with red [Russell] |
| 5381 | In seeing the sun, we are acquainted with our self, but not as a permanent person [Russell] |
| 5380 | In perceiving the sun, I am aware of sun sense-data, and of the perceiver of the data [Russell] |
| 2574 | Behaviour requires knowledge as well as dispositions [Block] |
| 2576 | In functionalism, desires are internal states with causal relations [Block] |
| 2575 | Functionalism is behaviourism, but with mental states as intermediaries [Block] |
| 2583 | You might invert colours, but you can't invert beliefs [Block] |
| 2578 | Could a creature without a brain be in the right functional state for pain? [Block] |
| 2585 | Not just any old functional network will have mental states [Block] |
| 2586 | In functionalism, what are the special inputs and outputs of conscious creatures? [Block] |
| 2579 | Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block] |
| 5369 | It is rational to believe in reality, despite the lack of demonstrative reasons for it [Russell] |
| 5375 | Knowledge of truths applies to judgements; knowledge by acquaintance applies to sensations and things [Russell] |
| 21711 | Russell's 'multiple relations' theory says beliefs attach to ingredients, not to propositions [Russell, by Linsky,B] |
| 5427 | Truth is when a mental state corresponds to a complex unity of external constituents [Russell] |
| 5425 | In order to explain falsehood, a belief must involve several terms, not two [Russell] |
| 2577 | Simple machine-functionalism says mind just is a Turing machine [Block] |
| 2580 | A Turing machine, given a state and input, specifies an output and the next state [Block] |
| 5384 | A universal of which we are aware is called a 'concept' [Russell] |
| 13468 | Russell started philosophy of language, by declaring some plausible sentences to be meaningless [Russell, by Hart,WD] |
| 5388 | Every understood proposition is composed of constituents with which we are acquainted [Russell] |
| 5387 | It is pure chance which descriptions in a person's mind make a name apply to an individual [Russell] |
| 2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |
| 21724 | The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 5398 | Judgements of usefulness depend on judgements of value [Russell] |
| 5393 | We can't know that our laws are exceptionless, or even that there are any laws [Russell] |