115 ideas
| 1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
| 447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
| 449 | Being is not divisible, since it is all alike [Parmenides] |
| 1503 | There is no such thing as nothing [Parmenides] |
| 445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
| 21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
| 452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
| 444 | The first way of enquiry involves necessary existence [Parmenides] |
| 450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
| 451 | Thinking implies existence, because thinking depends on it [Parmenides] |
| 1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
| 3058 | Only reason can prove the truth of facts [Parmenides] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 19956 | True goodness is political, and consists of love of and submission to the laws [Montesquieu] |
| 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] |
| 19983 | Democracies may sometimes need to restrict equality [Montesquieu] |
| 19982 | Some equality can be achieved by social categories, combined with taxes and poor relief [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] |
| 5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
| 1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
| 20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
| 226 | The one is without any kind of motion [Parmenides] |
| 1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
| 453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
| 555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
| 1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
| 19958 | Laws are the necessary relations that derive from the nature of things [Montesquieu] |
| 5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
| 13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
| 22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
| 1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |
| 1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |