114 ideas
| 21979 | Wisdom emerges at the end of a process [Hegel] |
| 22766 | Philosophy is exploration of the rational [Hegel] |
| 13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
| 13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
| 22768 | Subjective and objective are not firmly opposed, but merge into one another [Hegel] |
| 13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
| 13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
| 13747 | Supervenience is just modal correlation [Schaffer,J] |
| 13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
| 13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
| 13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
| 13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
| 13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
| 13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |
| 22780 | It is a rejection of intellectual dignity to say that we cannot know the truth [Hegel] |
| 22770 | A person is a being which is aware of its own self-directed and free subjectivity [Hegel] |
| 22788 | A human only become a somebody as a member of a social estate [Hegel] |
| 22792 | Individuals attain their right by discovering their self-consciousness in institutions [Hegel] |
| 21780 | A free will primarily wills its own freedoom [Hegel, by Houlgate] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 22769 | The concept of the will is the free will which wills its freedom [Hegel] |
| 21787 | Evil enters a good will when we believe we are doing right, but allow no criticism of our choice [Hegel, by Houlgate] |
| 21786 | Conscience is the right of the self to know what is right and obligatory, and thus make them true [Hegel] |
| 22784 | Love is ethical life in its natural form [Hegel] |
| 8029 | You can't have a morality which is supplied by the individual, but is also genuinely universal [Hegel, by MacIntyre] |
| 22771 | Be a person, and respect other persons [Hegel] |
| 22051 | The categorical imperative lacks roots in a historical culture [Hegel, by Bowie] |
| 22781 | The categorical imperative is fine if you already have a set of moral principles [Hegel] |
| 22779 | The good is realised freedom [Hegel] |
| 22787 | The family is the first basis of the state, but estates are a necessary second [Hegel] |
| 22790 | We cannot assert rights which are unnatural [Hegel] |
| 22767 | I aim to portray the state as a rational entity [Hegel] |
| 22789 | Society draws people, and requires their work, making them wholly dependent on it [Hegel] |
| 22791 | The state is the march of God in the world [Hegel] |
| 22778 | Individuals can't leave the state, because they are natural citizens, and humans require a state [Hegel] |
| 22794 | A fully developed state is conscious and knows what it wills [Hegel] |
| 22799 | The people do not have the ability to know the general will [Hegel] |
| 22801 | The great man of the ages is the one who reveals and accomplishes the will of his time [Hegel] |
| 22796 | A constitution embodies a nation's rights and condition [Hegel] |
| 22777 | Individuals must dedicate themselves to the ethical whole, and give their lives when asked [Hegel] |
| 21791 | Social groups must focus on the state, which must in turn respect their inclusion and their will [Hegel] |
| 22795 | People can achieve respect for their state by insight into its essence [Hegel] |
| 21988 | In the 1840s Hegel seemed to defend society being right as it is, as a manifestation of Mind [Hegel, by Singer] |
| 22800 | Majority rule means obligations can be imposed on me [Hegel] |
| 21792 | The state should reflect all interests, and not just popular will, or a popular party [Hegel, by Houlgate] |
| 22797 | In modern states an individual's actions should be their choice [Hegel] |
| 21790 | Moral individuals become ethical when they see the social aspect of a matter [Hegel, by Houlgate] |
| 8030 | For Hegel, the moral life can only be led within a certain type of community [Hegel, by MacIntyre] |
| 22785 | Even educated women are unsuited to science, philosophy, art and government [Hegel] |
| 21789 | Slaves have no duties because they have no rights [Hegel] |
| 22776 | Slaves are partly responsible for their own condition [Hegel] |
| 21778 | True liberal freedom is to pursue something, while being free to cease the pursuit [Hegel, by Houlgate] |
| 21779 | People assume they are free, but the options available are not under their control [Hegel] |
| 22085 | Freedom requires us to submit to a family, or a corporation, or a state [Hegel, by Houlgate] |
| 22798 | Money is the best way to achieve just equality [Hegel] |
| 22783 | Rights imply duties, and duties imply rights [Hegel] |
| 21782 | Man has an absolute right to appropriate things [Hegel] |
| 22773 | Because only human beings can own property, everything else can become our property [Hegel] |
| 22774 | A community does not have the property-owning rights that a person has [Hegel] |
| 22775 | The owner of a thing is obviously the first person to freely take possession of it [Hegel] |
| 22802 | Wars add strength to a nation, and cure internal dissension [Hegel] |
| 22786 | Children need discipline, to break their self-will and eradicate sensuousness [Hegel] |
| 22782 | To have pagan beliefs and be a pagan are quite different [Hegel] |
| 22793 | Some religions lead to harsh servitude and the debasement of human beings [Hegel] |