185 ideas
| 23350 | A wise philosophers uses reason to cautiously judge each aspect of living [Epictetus] |
| 23355 | The task of philosophy is to establish standards, as occurs with weights and measures [Epictetus] |
| 21394 | Philosophy is knowing each logos, how they fit together, and what follows from them [Epictetus] |
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| 20876 | Philosophy investigates the causes of disagreements, and seeks a standard for settling them [Epictetus] |
| 23344 | Reason itself must be compounded from some of our impressions [Epictetus] |
| 23343 | Because reason performs all analysis, we should analyse reason - but how? [Epictetus] |
| 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] |
| 8625 | What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill] |
| 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] |
| 17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill] |
| 10427 | All names are names of something, real or imaginary [Mill] |
| 4944 | Mill says names have denotation but not connotation [Mill, by Kripke] |
| 7762 | Proper names are just labels for persons or objects, and the meaning is the object [Mill, by Lycan] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [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] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [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] |
| 9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
| 8742 | The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill] |
| 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] |
| 5201 | Mill says logic and maths is induction based on a very large number of instances [Mill, by Ayer] |
| 9360 | If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI on Mill] |
| 9888 | Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett on Mill] |
| 9796 | Things possess the properties of numbers, as quantity, and as countable parts [Mill] |
| 9794 | There are no such things as numbers in the abstract [Mill] |
| 9795 | Numbers have generalised application to entities (such as bodies or sounds) [Mill] |
| 9798 | Different parcels made from three pebbles produce different actual sensations [Mill] |
| 9797 | '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill] |
| 9799 | 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill] |
| 9803 | We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious [Mill] |
| 9802 | Numbers denote physical properties of physical phenomena [Mill] |
| 9804 | Arithmetical results give a mode of formation of a given number [Mill] |
| 9805 | 12 is the cube of 1728 means pebbles can be aggregated a certain way [Mill] |
| 8741 | Numbers must be of something; they don't exist as abstractions [Mill] |
| 12411 | Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill] |
| 5656 | Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill] |
| 9624 | Numbers are a very general property of objects [Mill, by Brown,JR] |
| 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] |
| 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] |
| 9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
| 11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
| 12190 | Necessity is what will be, despite any alternative suppositions whatever [Mill] |
| 22623 | Necessity can only mean what must be, without conditions of any kind [Mill] |
| 23359 | We can't believe apparent falsehoods, or deny apparent truths [Epictetus] |
| 3583 | External objects are permanent possibilities of sensation [Mill] |
| 23356 | Self-evidence is most obvious when people who deny a proposition still have to use it [Epictetus] |
| 16859 | Most perception is one-tenth observation and nine-tenths inference [Mill] |
| 9082 | Clear concepts result from good observation, extensive experience, and accurate memory [Mill] |
| 16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill] |
| 16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
| 16845 | The whole theory of induction rests on causes [Mill] |
| 17086 | Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Mill, by Ruben] |
| 17091 | Explanation is fitting of facts into ever more general patterns of regularity [Mill, by Ruben] |
| 16805 | Causal inference is by spotting either Agreements or Differences [Mill, by Lipton] |
| 16835 | The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton] |
| 3537 | I judge others' feeling by analogy with my body and behaviour [Mill] |
| 9079 | We can focus our minds on what is common to a whole class, neglecting other aspects [Mill] |
| 9081 | We don't recognise comparisons by something in our minds; the concepts result from the comparisons [Mill] |
| 23330 | Freedom is making all things happen by choice, without constraint [Epictetus] |
| 23342 | Freedom is acting by choice, with no constraint possible [Epictetus] |
| 23329 | We make progress when we improve and naturalise our choices, asserting their freedom [Epictetus] |
| 23332 | Zeus gave me a nature which is free (like himself) from all compulsion [Epictetus] |
| 23331 | Not even Zeus can control what I choose [Epictetus] |
| 23338 | You can fetter my leg, but not even Zeus can control my power of choice [Epictetus] |
| 20875 | If we could foresee the future, we should collaborate with disease and death [Epictetus] |
| 23347 | If I know I am fated to be ill, I should want to be ill [Epictetus] |
| 9078 | The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill] |
| 9080 | General conceptions are a necessary preliminary to Induction [Mill] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 3772 | The will, in the beginning, is entirely produced by desire [Mill] |
| 23325 | Epictetus developed a notion of will as the source of our responsibility [Epictetus, by Frede,M] |
| 20873 | Tragedies are versified sufferings of people impressed by externals [Epictetus] |
| 23364 | Homer wrote to show that the most blessed men can be ruined by poor judgement [Epictetus] |
| 7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
| 3769 | With early training, any absurdity or evil may be given the power of conscience [Mill] |
| 23340 | We consist of animal bodies and god-like reason [Epictetus] |
| 23366 | We see nature's will in the ways all people are the same [Epictetus] |
| 23358 | Every species produces exceptional beings, and we must just accept their nature [Epictetus] |
| 23339 | I will die as becomes a person returning what he does not own [Epictetus] |
| 23345 | Don't be frightened of pain or death; only be frightened of fearing them [Epictetus] |
| 23357 | Knowledge of what is good leads to love; only the wise, who distinguish good from evil, can love [Epictetus] |
| 23363 | The evil for everything is what is contrary to its nature [Epictetus] |
| 23328 | The essences of good and evil are in dispositions to choose [Epictetus] |
| 3767 | Motive shows the worth of the agent, but not of the action [Mill] |
| 7076 | Mill wondered if he would be happy if all his aims were realised, and answered no [Mill, by Critchley] |
| 23362 | All human ills result from failure to apply preconceptions to particular cases [Epictetus] |
| 23353 | We have a natural sense of honour [Epictetus] |
| 23354 | If someone harms themselves in harming me, then I harm myself by returning the harm [Epictetus] |
| 3771 | Virtues only have value because they achieve some further end [Mill] |
| 23324 | In the Discourses choice [prohairesis] defines our character and behaviour [Epictetus, by Frede,M] |
| 4022 | Epictetus says we should console others for misfortune, but not be moved by pity [Epictetus, by Taylor,C] |
| 23365 | If someone is weeping, you should sympathise and help, but not share his suffering [Epictetus] |
| 23361 | Health is only a good when it is used well [Epictetus] |
| 3768 | Orthodox morality is the only one which feels obligatory [Mill] |
| 3764 | Actions are right if they promote pleasure, wrong if they promote pain [Mill] |
| 3776 | Utilitarianism only works if everybody has a totally equal right to happiness [Mill] |
| 7214 | Ethics rests on utility, which is the permanent progressive interests of people [Mill] |
| 7202 | The English believe in the task of annihilating evil for the victory of good [Nietzsche on Mill] |
| 5935 | Mill's qualities of pleasure is an admission that there are other good states of mind than pleasure [Ross on Mill] |
| 3766 | Better to be Socrates dissatisfied than a fool satisfied [Mill] |
| 3763 | Ultimate goods such as pleasure can never be proved to be good [Mill] |
| 3765 | Only pleasure and freedom from pain are desirable as ends [Mill] |
| 3770 | General happiness is only desirable because individuals desire their own happiness [Mill] |
| 6697 | Moral rules protecting human welfare are more vital than local maxims [Mill] |
| 23346 | A person is as naturally a part of a city as a foot is part of the body [Epictetus] |
| 23351 | We are citizens of the universe, and principal parts of it [Epictetus] |
| 7212 | Individuals have sovereignty over their own bodies and minds [Mill] |
| 3774 | Rights are a matter of justice, not of benevolence [Mill] |
| 3773 | No individual has the right to receive our benevolence [Mill] |
| 7210 | The will of the people is that of the largest or most active part of the people [Mill] |
| 23352 | A citizen should only consider what is good for the whole society [Epictetus] |
| 20874 | A citizen is committed to ignore private advantage, and seek communal good [Epictetus] |
| 7227 | It is evil to give a government any more power than is necessary [Mill] |
| 7228 | Individuals often do things better than governments [Mill] |
| 7230 | Aim for the maximum dissemination of power consistent with efficiency [Mill] |
| 20515 | Maximise happiness by an area of strict privacy, and an area of utilitarian interventions [Mill, by Wolff,J] |
| 7229 | People who transact their own business will also have the initiative to control their government [Mill] |
| 20508 | How people vote should be on public record, so they can be held accountable [Mill, by Wolff,J] |
| 20507 | Voting is a strict duty, like jury service, and must only be aimed at the public good [Mill] |
| 20505 | Direct democracy is inexperience judging experience, and ignorance judging knowledge [Mill] |
| 20504 | People can only participate in decisions in small communities, so representatives are needed [Mill] |
| 7211 | Prevention of harm to others is the only justification for exercising power over people [Mill] |
| 7231 | The worth of a State, in the long run, is the worth of the individuals composing it [Mill] |
| 7217 | The main argument for freedom is that interference with it is usually misguided [Mill] |
| 7213 | Liberty arises at the point where people can freely and equally discuss things [Mill] |
| 20517 | Utilitarianism values liberty, but guides us on which ones we should have or not have [Mill, by Wolff,J] |
| 20516 | Mill defends freedom as increasing happiness, but maybe it is an intrinsic good [Wolff,J on Mill] |
| 7215 | True freedom is pursuing our own good, while not impeding others [Mill] |
| 7218 | Individuals are not accountable for actions which only concern themselves [Mill] |
| 7221 | Blocking entry to an unsafe bridge does not infringe liberty, since no one wants unsafe bridges [Mill] |
| 7223 | Pimping and running a gambling-house are on the border between toleration and restraint [Mill] |
| 7220 | Restraint for its own sake is an evil [Mill] |
| 3775 | A right is a valid claim to society's protection [Mill] |
| 22604 | Punishing a criminal for moral ignorance is the same as punishing someone for being blind [Epictetus] |
| 23368 | Perhaps we should persuade culprits that their punishment is just? [Epictetus] |
| 7219 | Society can punish actions which it believes to be prejudicial to others [Mill] |
| 7226 | Benefits performed by individuals, not by government, help also to educate them [Mill] |
| 7224 | We need individual opinions and conduct, and State education is a means to prevent that [Mill] |
| 7225 | It is a crime to create a being who lacks the ordinary chances of a desirable existence [Mill] |
| 23349 | Asses are born to carry human burdens, not as ends in themselves [Epictetus] |
| 8345 | A cause is the total of all the conditions which inevitably produce the result [Mill] |
| 10391 | Causes and conditions are not distinct, because we select capriciously from among them [Mill] |
| 14547 | The strict cause is the total positive and negative conditions which ensure the consequent [Mill] |
| 8377 | Causation is just invariability of succession between every natural fact and a preceding fact [Mill] |
| 14545 | A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill] |
| 4773 | Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos] |
| 4775 | In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Mill, by Psillos] |
| 4776 | In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Mill, by Psillos] |
| 9417 | What are the fewest propositions from which all natural uniformities could be inferred? [Mill] |
| 23341 | God created humans as spectators and interpreters of God's works [Epictetus] |
| 23348 | Both god and the good bring benefits, so their true nature seems to be the same [Epictetus] |
| 21332 | We don't get a love of 'order' from nature - which is thoroughly chaotic [Mill] |
| 7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |
| 23360 | Each of the four elements in you is entirely scattered after death [Epictetus] |
| 21335 | Belief that an afterlife is required for justice is an admission that this life is very unjust [Mill] |
| 21334 | No necessity ties an omnipotent Creator, so he evidently wills human misery [Mill] |
| 21333 | Evil comes from good just as often as good comes from evil [Mill] |
| 21329 | Nature dispenses cruelty with no concern for either mercy or justice [Mill] |
| 21328 | Killing is a human crime, but nature kills everyone, and often with great tortures [Mill] |
| 21331 | Hurricanes, locusts, floods and blight can starve a million people to death [Mill] |
| 21330 | Nature makes childbirth a miserable experience, often leading to the death of the mother [Mill] |