133 ideas
23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
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] |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [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] |
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] |
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] |
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] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
11237 | Only universals have essence [Plato, by Politis] |
11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
19956 | True goodness is political, and consists of love of and submission to the laws [Montesquieu] |
9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
2912 | Plato is boring [Nietzsche on Plato] |
19961 | Primitive people would be too vulnerable and timid to attack anyone, so peace would reign [Montesquieu] |
19962 | Men do not desire to subjugate one another; domination is a complex and advanced idea [Montesquieu] |
19963 | People are drawn into society by needs, shared fears, pleasure, and knowledge [Montesquieu] |
20008 | People are guided by a multitude of influences, from which the spirit of a nation emerges [Montesquieu] |
19993 | In small republics citizens identify with the public good, and abuses are fewer [Montesquieu] |
19992 | In a large republic there is too much wealth for individuals to manage it [Montesquieu] |
20005 | The rich would never submit to a lottery deciding which part of their society should be slaves [Montesquieu] |
19995 | All states aim at preservation, and then have distinctive individual purposes [Montesquieu] |
19964 | The natural power of a father suggests rule by one person, but that authority can be spread [Montesquieu] |
19986 | Monarchies can act more quickly, because one person is in charge [Montesquieu] |
19972 | The nobility are an indispensable part of a monarchy [Montesquieu] |
19974 | Monarchs must not just have links to the people; they need a body which maintains the laws [Montesquieu] |
19976 | Ambition is good in a monarchy, because the monarch can always restrain it [Montesquieu] |
19978 | In monarchies, men's actions are judged by their grand appearance, not their virtues [Montesquieu] |
19985 | In a monarchy, the nobility must be hereditary, to bind them together [Montesquieu] |
19988 | A despot's agents must be given power, so they inevitably become corrupt [Montesquieu] |
19977 | Despotism and honour are incompatible, because honour scorns his power, and lives by rules [Montesquieu] |
20007 | Tyranny is either real violence, or the imposition of unpopular legislation [Montesquieu] |
19975 | Despots are always lazy and ignorant, so they always delegate their power to a vizier [Montesquieu] |
19989 | The will of a despot is an enigma, so magistrates can only follow their own will [Montesquieu] |
19970 | If the nobility is numerous, the senate is the artistocracy, and the nobles are a democracy [Montesquieu] |
19971 | Aristocracy is democratic if they resemble the people, but not if they resemble the monarch [Montesquieu] |
19984 | Great inequality between aristocrats and the rest is bad - and also among aristocrats themselves [Montesquieu] |
19980 | If a government is to be preserved, it must first be loved [Montesquieu] |
19996 | A government has a legislature, an international executive, and a domestic executive [Montesquieu] |
19997 | The judiciary must be separate from the legislature, to avoid arbitrary power [Montesquieu] |
19965 | The fundamental laws of a democracy decide who can vote [Montesquieu] |
19968 | It is basic to a democracy that the people themselves must name their ministers [Montesquieu] |
19969 | Voting should be public, so the lower classes can be influenced by the example of notable people [Montesquieu] |
19999 | All citizens (apart from the very humble poor) should choose their representatives [Montesquieu] |
19967 | In a democracy the people should manage themselves, and only delegate what they can't do [Montesquieu] |
19966 | A democratic assembly must have a fixed number, to see whether everyone has spoken [Montesquieu] |
19998 | If deputies represent people, they are accountable, but less so if they represent places [Montesquieu] |
20003 | Slaves are not members of the society, so no law can forbid them to run away [Montesquieu] |
20000 | Slavery is entirely bad; the master abandons the virtues, and they are pointless in the slave [Montesquieu] |
20006 | The demand for slavery is just the masters' demand for luxury [Montesquieu] |
20009 | Freedom of speech and writing, within the law, is essential to preserve liberty [Montesquieu] |
19994 | Freedom in society is ability to do what is right, and not having to do what is wrong [Montesquieu] |
19981 | No one even thinks of equality in monarchies and despotism; they all want superiority [Montesquieu] |
19991 | Equality is not command by everyone or no one, but command and obedience among equals [Montesquieu] |
19990 | Democracy is corrupted by lack of equality, or by extreme equality (between rulers and ruled) [Montesquieu] |
19982 | Some equality can be achieved by social categories, combined with taxes and poor relief [Montesquieu] |
19983 | Democracies may sometimes need to restrict equality [Montesquieu] |
19959 | Prior to positive laws there is natural equity, of obedience, gratitude, dependence and merit [Montesquieu] |
19960 | Sensation gives animals natural laws, but knowledge can make them break them [Montesquieu] |
20002 | The death penalty is permissible, because its victims enjoyed the protection of that law [Montesquieu] |
20010 | If religion teaches determinism, penalties must be severe; if free will, then that is different [Montesquieu] |
20001 | The only right victors have over captives is the protection of the former [Montesquieu] |
19973 | The clergy are essential to a monarchy, but dangerous in a republic [Montesquieu] |
19987 | Religion has the most influence in despotic states, and reinforces veneration for the ruler [Montesquieu] |
20011 | Religion can support the state when the law fails to do so [Montesquieu] |
20004 | French slavery was accepted because it was the best method of religious conversion [Montesquieu] |
19979 | In monarchies education ennobles people, and in despotisms it debases them [Montesquieu] |
19957 | Teaching is the best practice of the general virtue that leads us to love everyone [Montesquieu] |
19958 | Laws are the necessary relations that derive from the nature of things [Montesquieu] |
1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |