101 ideas
| 13310 | Wisdom does not lie in books, and unread people can also become wise [Seneca] |
| 13295 | Wise people escape necessity by willing it [Seneca] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 13317 | Philosophy aims at happiness [Seneca] |
| 13293 | What philosophy offers humanity is guidance [Seneca] |
| 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] |
| 13309 | That something is a necessary condition of something else doesn't mean it caused it [Seneca] |
| 13313 | Even philosophers have got bogged down in analysing tiny bits of language [Seneca] |
| 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] |
| 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] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [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] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [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] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [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] |
| 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] |
| 6935 | In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach] |
| 13297 | To the four causes Plato adds a fifth, the idea which guided the event [Seneca] |
| 13307 | If everything can be measured, try measuring the size of a man's soul [Seneca] |
| 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] |
| 21399 | Referring to a person, and speaking about him, are very different [Seneca] |
| 6924 | Plotinus was ashamed to have a body [Feuerbach] |
| 13325 | Trouble in life comes from copying other people, which is following convention instead of reason [Seneca] |
| 22239 | Humans acquired the concept of virtue from an analogy with bodily health and strength [Seneca, by Allen] |
| 13294 | We know death, which is like before birth; ceasing to be and never beginning are the same [Seneca] |
| 13299 | Living is nothing wonderful; what matters is to die well [Seneca] |
| 13300 | It is as silly to lament ceasing to be as to lament not having lived in the remote past [Seneca] |
| 13321 | Is anything sweeter than valuing yourself more when you find you are loved? [Seneca] |
| 6927 | If you love nothing, it doesn't matter whether something exists or not [Feuerbach] |
| 13292 | Selfishness does not produce happiness; to live for yourself, live for others [Seneca] |
| 13303 | A man is as unhappy as he has convinced himself he is [Seneca] |
| 13302 | Life is like a play - it is the quality that matters, not the length [Seneca] |
| 13301 | We are scared of death - except when we are immersed in pleasure! [Seneca] |
| 13323 | The whole point of pleasure-seeking is novelty, and abandoning established ways [Seneca] |
| 13318 | Nature doesn't give us virtue; we must unremittingly pursue it, as a training and an art [Seneca] |
| 13324 | Living contrary to nature is like rowing against the stream [Seneca] |
| 13305 | Character is ruined by not looking back over our pasts, since the future rests on the past [Seneca] |
| 13312 | Excessive curiosity is a form of intemperance [Seneca] |
| 13308 | It's no good winning lots of fights, if you are then conquered by your own temper [Seneca] |
| 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] |
| 13315 | To govern used to mean to serve, not to rule; rulers did not test their powers over those who bestowed it [Seneca] |
| 13290 | One joy of learning is making teaching possible [Seneca] |
| 13322 | Both teachers and pupils should aim at one thing - the improvement of the pupil [Seneca] |
| 13298 | Suicide may be appropriate even when it is not urgent, if there are few reasons against it [Seneca] |
| 13320 | Sometimes we have a duty not to commit suicide, for those we love [Seneca] |
| 13319 | If we control our own death, no one has power over us [Seneca] |
| 13311 | Does time exist on its own? Did anything precede it? Did it pre-exist the cosmos? [Seneca] |
| 6913 | God's existence cannot be separated from essence and concept, which can only be thought as existing [Feuerbach] |
| 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] |