109 ideas
18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
18459 | Diversity arises from the power of unity [Porphyry] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
18464 | Justice is each person fulfilling his function [Porphyry] |
19956 | True goodness is political, and consists of love of and submission to the laws [Montesquieu] |
18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
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] |
19989 | The will of a despot is an enigma, so magistrates can only follow their own will [Montesquieu] |
19975 | Despots are always lazy and ignorant, so they always delegate their power to a vizier [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] |
18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
19958 | Laws are the necessary relations that derive from the nature of things [Montesquieu] |
18454 | Time is the circular movement of the soul [Porphyry] |
18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
18460 | God is nowhere, and hence everywhere [Porphyry] |
18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |