116 ideas
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
19917 | Without reason and human help, human life is misery [Spinoza] |
232 | Opposites are as unlike as possible [Plato] |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
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] |
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] |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [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] |
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] |
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] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
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] |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
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] |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
227 | You must always mean the same thing when you utter the same name [Plato] |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
220 | The concept of a master includes the concept of a slave [Plato] |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
19922 | People are only free if they are guided entirely by reason [Spinoza] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
19935 | Peoples are created by individuals, not by nature, and only distinguished by language and law [Spinoza] |
19914 | In nature everything has an absolute right to do anything it is capable of doing [Spinoza] |
19915 | Natural rights are determined by desire and power, not by reason [Spinoza] |
7487 | Society exists to extend human awareness [Spinoza, by Watson] |
19943 | The state aims to allow personal development, so its main purpose is freedom [Spinoza] |
19930 | Sovereignty must include the power to make people submit to it [Spinoza] |
19936 | Kings tend to fight wars for glory, rather than for peace and liberty [Spinoza] |
19937 | Monarchs are always proud, and can't back down [Spinoza] |
19940 | Deposing a monarch is dangerous, because the people are used to royal authority [Spinoza] |
19931 | Every state is more frightened of its own citizens than of external enemies [Spinoza] |
19920 | Democracy is a legitimate gathering of people who do whatever they can do [Spinoza] |
19933 | If religion is law, then piety is justice, impiety is crime, and non-believers must leave [Spinoza] |
19938 | Allowing religious ministers any control of the state is bad for both parties [Spinoza] |
19923 | Slavery is not just obedience, but acting only in the interests of the master [Spinoza] |
19939 | Government is oppressive if opinions can be crimes, because people can't give them up [Spinoza] |
19944 | Without liberty of thought there is no trust in the state, and corruption follows [Spinoza] |
19942 | Treason may be committed as much by words as by deeds [Spinoza] |
19924 | The freest state is a rational one, where people can submit themselves to reason [Spinoza] |
7827 | Spinoza wanted democracy based on individual rights, and is thus the first modern political philosopher [Stewart,M on Spinoza] |
19926 | The sovereignty has absolute power over citizens [Spinoza] |
19918 | Forming a society meant following reason, and giving up dangerous appetites and mutual harm [Spinoza] |
19919 | People only give up their rights, and keep promises, if they hope for some greater good [Spinoza] |
19921 | Once you have given up your rights, there is no going back [Spinoza] |
19925 | In democracy we don't abandon our rights, but transfer them to the majority of us [Spinoza] |
19928 | No one, in giving up their power and right, ceases to be a human being [Spinoza] |
19929 | Everyone who gives up their rights must fear the recipients of them [Spinoza] |
19932 | The early Hebrews, following Moses, gave up their rights to God alone [Spinoza] |
19916 | The order of nature does not prohibit anything, and allows whatever appetite produces [Spinoza] |
19927 | State and religious law can clash, so the state must make decisions about religion [Spinoza] |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
225 | The unlimited has no shape and is endless [Plato] |
233 | Some things do not partake of the One [Plato] |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
231 | Everything partakes of the One in some way [Plato] |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
19934 | Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza] |
4300 | The Bible has nothing in common with reasoning and philosophy [Spinoza] |