97 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 14027 | If we are to use words in enquiry, we need their main, unambiguous and uncontested meanings [Epicurus] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 14040 | Observation and applied thought are always true [Epicurus] |
| 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] |
| 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] |
| 14028 | Nothing comes to be from what doesn't exist [Epicurus] |
| 14029 | If disappearing things went to nothingness, nothing could return, and it would all be gone by now [Epicurus] |
| 14030 | The totality is complete, so there is no room for it to change, and nothing extraneous to change it [Epicurus] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 14048 | Astronomical movements are blessed, but they don't need the help of the gods [Epicurus] |
| 14044 | The perceived accidental properties of bodies cannot be conceived of as independent natures [Epicurus] |
| 14045 | Accidental properties give a body its nature, but are not themselves bodies or parts of bodies [Epicurus] |
| 14046 | A 'body' is a conception of an aggregate, with properties defined by application conditions [Epicurus] |
| 14047 | Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus] |
| 20146 | 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes] |
| 14039 | Above and below us will never appear to be the same, because it is inconceivable [Epicurus] |
| 14050 | We aim to dissolve our fears, by understanding their causes [Epicurus] |
| 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] |
| 14037 | Atoms only have shape, weight and size, and the properties which accompany shape [Epicurus] |
| 6010 | Illusions are not false perceptions, as we accurately perceive the pattern of atoms [Epicurus, by Modrak] |
| 14041 | The soul is fine parts distributed through the body, resembling hot breath [Epicurus] |
| 14042 | The soul cannot be incorporeal, because then it could neither act nor be acted upon [Epicurus] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 20169 | An action may be intended under one description, but not under another [Kekes] |
| 20149 | To control our actions better, make them result from our attitudes, not from circumstances [Kekes] |
| 19738 | Values are an attempt to achieve well-being by bringing contingencies under control [Kekes] |
| 20145 | Values help us to control life, by connecting it to what is stable and manageable [Kekes] |
| 20170 | Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes] |
| 20165 | Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes] |
| 20171 | Practical reason is not universal and impersonal, because it depends on what success is [Kekes] |
| 20175 | If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes] |
| 20174 | Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes] |
| 20156 | We are bound to regret some values we never aspired to [Kekes] |
| 20150 | There are far more values than we can pursue, so they are optional possibilities [Kekes] |
| 20158 | Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes] |
| 20159 | Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes] |
| 20161 | The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes] |
| 20151 | Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes] |
| 20152 | Unconditional commitments are our most basic convictions, saying what must never be done [Kekes] |
| 20153 | Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes] |
| 20162 | Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes] |
| 20154 | Control is the key to well-being [Kekes] |
| 20157 | Well-being needs correct attitudes and well-ordered commitments to local values [Kekes] |
| 20172 | Boredom destroys our ability to evaluate [Kekes] |
| 20173 | Boredom is apathy and restlessness, yearning for something interesting [Kekes] |
| 20155 | Society is alienating if it lacks our values, and its values repel us [Kekes] |
| 20164 | The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes] |
| 20163 | Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes] |
| 20148 | Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes] |
| 14032 | Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus] |
| 14033 | Bodies are unlimited as well as void, since the two necessarily go together [Epicurus] |
| 14034 | There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus] |
| 14035 | Atoms just have shape, size and weight; colour results from their arrangement [Epicurus] |
| 14038 | There cannot be unlimited division, because it would reduce things to non-existence [Epicurus] |
| 14049 | We aim to know the natures which are observed in natural phenomena [Epicurus] |
| 14043 | The void cannot interact, but just gives the possibility of motion [Epicurus] |
| 14031 | Space must exist, since movement is obvious, and there must be somewhere to move in [Epicurus] |
| 14036 | There are endless cosmoi, some like and some unlike this one [Epicurus] |