142 ideas
5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
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] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
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] |
1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
16292 | An explicit definition enables the elimination of what is defined [Halbach] |
16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
5420 | Truth is a property of a belief, but dependent on its external relations, not its internal qualities [Russell] |
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [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] |
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] |
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] |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [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] |
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] |
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] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [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] |
16320 | Some say deflationism is axioms which are conservative over the base theory [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] |
5401 | The mortality of Socrates is more certain from induction than it is from deduction [Russell] |
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] |
5395 | Demonstration always relies on the rule that anything implied by a truth is true [Russell] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
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] |
16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [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] |
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] |
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] |
5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
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] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
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] |
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] |
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] |
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] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
21724 | The main aim of the multiple relations theory of judgement was to dispense with propositions [Russell, by Linsky,B] |
5398 | Judgements of usefulness depend on judgements of value [Russell] |
405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
5393 | We can't know that our laws are exceptionless, or even that there are any laws [Russell] |
1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |