106 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 6928 | Only that which can be an object of religion is an object of philosophy [Feuerbach] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 1887 | You cannot divide anything into many parts, because after the first division you are no longer dividing the original [Sext.Empiricus] |
| 6918 | Philosophy should not focus on names, but on the determined nature of things [Feuerbach] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 6904 | Modern philosophy begins with Descartes' abstraction from sensation and matter [Feuerbach] |
| 6931 | Empiricism is right about ideas, but forgets man himself as one of our objects [Feuerbach] |
| 6933 | The laws of reality are also the laws of thought [Feuerbach] |
| 1885 | Proof moves from agreed premises to a non-evident inference [Sext.Empiricus] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 12196 | A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 1902 | Since Socrates either died when he was alive (a contradiction) or died when he was dead (meaningless), he didn't die [Sext.Empiricus] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 6919 | Absolute thought remains in another world from being [Feuerbach] |
| 19457 | Being is what is undetermined, and hence indistinguishable [Feuerbach] |
| 6920 | Being posits essence, and my essence is my being [Feuerbach] |
| 6921 | Particularity belongs to being, whereas generality belongs to thought [Feuerbach] |
| 6926 | The only true being is of the senses, perception, feeling and love [Feuerbach] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 1889 | If an argument has an absurd conclusion, we should not assent to the absurdity, but avoid the absurd argument [Sext.Empiricus] |
| 1871 | Whether honey is essentially sweet may be doubted, as it is a matter of judgement rather than appearance [Sext.Empiricus] |
| 6908 | Consciousness is absolute reality, and everything exists through consciousness [Feuerbach] |
| 6932 | Ideas arise through communication, and reason is reached through community [Feuerbach] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 1883 | How can the intellect know if sensation is reliable if it doesn't directly see external objects? [Sext.Empiricus] |
| 6935 | In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach] |
| 1890 | We distinguish ambiguities by seeing what is useful [Sext.Empiricus] |
| 1870 | The basis of scepticism is the claim that every proposition has an equal opposing proposition [Sext.Empiricus] |
| 1882 | The necks of doves appear different in colour depending on the angle of viewing [Sext.Empiricus] |
| 1881 | The same oar seems bent in water and straight when out of it [Sext.Empiricus] |
| 1872 | The same tower appears round from a distance, but square close at hand [Sext.Empiricus] |
| 1873 | If we press the side of an eyeball, objects appear a different shape [Sext.Empiricus] |
| 1874 | How can we judge between our impressions and those of other animals, when we ourselves are involved? [Sext.Empiricus] |
| 1878 | Water that seems lukewarm can seem very hot on inflamed skin [Sext.Empiricus] |
| 1880 | Some actions seem shameful when sober but not when drunk [Sext.Empiricus] |
| 1877 | If we had no hearing or sight, we would assume no sound or sight exists, so there may be unsensed qualities [Sext.Empiricus] |
| 1879 | Sickness is perfectly natural to the sick, so their natural perceptions should carry some weight [Sext.Empiricus] |
| 1876 | If we enjoy different things, presumably we receive different impressions [Sext.Empiricus] |
| 1911 | Even if all known nations agree on a practice, there may be unknown nations which disagree [Sext.Empiricus] |
| 1910 | With us it is shameful for men to wear earrings, but among Syrians it is considered noble [Sext.Empiricus] |
| 1886 | If you don't view every particular, you may miss the one which disproves your universal induction [Sext.Empiricus] |
| 1884 | If we utter three steps of a logical argument, they never exist together [Sext.Empiricus] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 6925 | The new philosophy thinks of the concrete in a concrete (not a abstract) manner [Feuerbach] |
| 6924 | Plotinus was ashamed to have a body [Feuerbach] |
| 6927 | If you love nothing, it doesn't matter whether something exists or not [Feuerbach] |
| 6934 | Man is not a particular being, like animals, but a universal being [Feuerbach] |
| 6936 | The essence of man is in community, but with distinct individuals [Feuerbach] |
| 1894 | Some say that causes are physical, some say not [Sext.Empiricus] |
| 1897 | Knowing an effect results from a cause means knowing that the cause belongs with the effect, which is circular [Sext.Empiricus] |
| 1898 | Cause can't exist before effect, or exist at the same time, so it doesn't exist [Sext.Empiricus] |
| 1896 | If there were no causes then everything would have been randomly produced by everything [Sext.Empiricus] |
| 1895 | Causes are either equal to the effect, or they link equally with other causes, or they contribute slightly [Sext.Empiricus] |
| 1900 | If time and place are infinitely divided, it becomes impossible for movement ever to begin [Sext.Empiricus] |
| 1899 | Does the original self-mover push itself from behind, or pull itself from in front? [Sext.Empiricus] |
| 1901 | If all atoms, times and places are the same, everything should move with equal velocity [Sext.Empiricus] |
| 1903 | If motion and rest are abolished, so is time [Sext.Empiricus] |
| 1904 | Time must be unlimited, but past and present can't be non-existent, and can't be now, so time does not exist [Sext.Empiricus] |
| 1905 | How can time be divisible if we can't compare one length of time with another? [Sext.Empiricus] |
| 1891 | How can we agree on the concept of God, unless we agree on his substance or form or place? [Sext.Empiricus] |
| 6913 | God's existence cannot be separated from essence and concept, which can only be thought as existing [Feuerbach] |
| 1892 | The existence of God can't be self-evident or everyone would have agreed on it, so it needs demonstration [Sext.Empiricus] |
| 6903 | If God is only an object for man, then only the essence of man is revealed in God [Feuerbach] |
| 6923 | God is what man would like to be [Feuerbach] |
| 6911 | God is for us a mere empty idea, which we fill with our own ego and essence [Feuerbach] |
| 6902 | Catholicism concerns God in himself, Protestantism what God is for man [Feuerbach] |
| 6905 | Absolute idealism is the realized divine mind of Leibnizian theism [Feuerbach] |
| 1893 | If God foresaw evil he would presumably prevent it, and if he only foresees some things, why those things? [Sext.Empiricus] |