99 ideas
| 14888 | Wisdom prevents us from being ruled by the moment [Nietzsche] |
| 14863 | Unlike science, true wisdom involves good taste [Nietzsche] |
| 14890 | Suffering is the meaning of existence [Nietzsche] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 14861 | Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche] |
| 14887 | You should only develop a philosophy if you are willing to live by it [Nietzsche] |
| 14885 | The first aim of a philosopher is a life, not some works [Nietzsche] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 14889 | Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche] |
| 14862 | Philosophy is more valuable than much of science, because of its beauty [Nietzsche] |
| 14878 | It would better if there was no thought [Nietzsche] |
| 14881 | Why do people want philosophers? [Nietzsche] |
| 14876 | Philosophy is always secondary, because it cannot support a popular culture [Nietzsche] |
| 14860 | Kant has undermined our belief in metaphysics [Nietzsche] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 14859 | If philosophy controls science, then it has to determine its scope, and its value [Nietzsche] |
| 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] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [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] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [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] |
| 14880 | Logic is just slavery to language [Nietzsche] |
| 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] |
| 14869 | If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 14308 | We can bring dispositions into existence, as in creating an identifier [Dennett, by Mumford] |
| 7384 | Words are fixed by being attached to similarity clusters, without mention of 'essences' [Dennett] |
| 14875 | Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche] |
| 14866 | It always remains possible that the world just is the way it appears [Nietzsche] |
| 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] |
| 7374 | Light wavelengths entering the eye are only indirectly related to object colours [Dennett] |
| 14872 | Our knowledge is illogical, because it rests on false identities between things [Nietzsche] |
| 14879 | The most extreme scepticism is when you even give up logic [Nietzsche] |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| 14873 | If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche] |
| 7393 | We can't draw a clear line between conscious and unconscious [Dennett] |
| 7367 | Perhaps the brain doesn't 'fill in' gaps in consciousness if no one is looking. [Dennett] |
| 7394 | Conscious events can only be explained in terms of unconscious events [Dennett] |
| 7391 | We can know a lot of what it is like to be a bat, and nothing important is unknown [Dennett] |
| 7387 | "Qualia" can be replaced by complex dispositional brain states [Dennett] |
| 7376 | We can't assume that dispositions will remain normal when qualia have been inverted [Dennett] |
| 7372 | In peripheral vision we see objects without their details, so blindsight is not that special [Dennett] |
| 7373 | Blindsight subjects glean very paltry information [Dennett] |
| 14868 | Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche] |
| 14870 | We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche] |
| 7385 | People accept blurred boundaries in many things, but insist self is All or Nothing [Dennett] |
| 7383 | The psychological self is an abstraction, not a thing in the brain [Dennett] |
| 7386 | Selves are not soul-pearls, but artefacts of social processes [Dennett] |
| 7381 | We tell stories about ourselves, to protect, control and define who we are [Dennett] |
| 7382 | We spin narratives about ourselves, and the audience posits a centre of gravity for them [Dennett] |
| 7370 | The brain is controlled by shifting coalitions, guided by good purposeful habits [Dennett] |
| 7379 | If an epiphenomenon has no physical effects, it has to be undetectable [Dennett] |
| 14867 | It is just madness to think that the mind is supernatural (or even divine!) [Nietzsche] |
| 7365 | Dualism wallows in mystery, and to accept it is to give up [Dennett] |
| 7371 | All functionalism is 'homuncular', of one grain size or another [Dennett] |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [Dennett] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 14884 | The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche] |
| 14886 | Education is contrary to human nature [Nietzsche] |
| 14883 | We should evaluate the past morally [Nietzsche] |
| 14882 | Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche] |
| 7368 | Originally there were no reasons, purposes or functions; since there were no interests, there were only causes [Dennett] |
| 14865 | We do not know the nature of one single causality [Nietzsche] |
| 14871 | Laws of nature are merely complex networks of relations [Nietzsche] |
| 14864 | The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche] |