89 ideas
| 15586 | When philosophy makes itself intelligible, it commits suicide [Heidegger] |
| 15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
| 15582 | Perhaps the aim of philosophy is to abolish sham problems [Heidegger] |
| 22223 | Being-in-the-world is projection to possibilities, thrownness among them, and fallenness within them [Heidegger, by Caputo] |
| 22158 | Pheomenology seeks things themselves, without empty theories, problems and concepts [Heidegger] |
| 15574 | 'Logos' really means 'making something manifest' [Heidegger, by Polt] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 21953 | For Heidegger there is 'ontic' truth or 'uncoveredness', as in "he is a true friend" [Heidegger, by Wrathall] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 15569 | Heidegger says truth is historical, and never absolute [Heidegger, by Polt] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 15571 | The idea of an atemporal realm of validity is as implausible as medieval theology [Heidegger] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 21897 | Reducing being to the study of beings too readily accepts the modern scientific view [Heidegger, by May] |
| 15573 | For us, Being is constituted by awareness of other sorts of Being [Heidegger] |
| 9273 | Heidegger turns to 'Being' to affirm the uniqueness of humans in the world [Heidegger, by Gray] |
| 22157 | Dasein is a mode of Being distinguished by concern for its own Being [Heidegger] |
| 8137 | Dasein is ahead of itself in the world, and alongside encountered entities [Heidegger] |
| 21951 | In company with others one's Dasein dissolves, and even the others themselves dissolve [Heidegger] |
| 20745 | 'Dasein' expresses not 'what' the entity is, but its being [Heidegger] |
| 8134 | The word 'dasein' is used to mean 'the manner of Being which man possesses', and also the human creature [Heidegger, by Cooper,DE] |
| 8135 | 'Dasein' is Being which is laid claim to, and which matters to its owner [Heidegger, by Cooper,DE] |
| 21948 | Dasein is being which can understand itself, and possess itself in a way allowing authenticity [Heidegger] |
| 15584 | I say the manifestation of Being needs humans, and humans only exist as reflected in Being [Heidegger] |
| 7680 | Ontology is possible only as phenomenology [Heidegger] |
| 22161 | Readiness-to-hand defines things in themselves ontologically [Heidegger] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 15576 | Heidegger seeks a non-traditional concept of essence as 'essential unfolding' [Heidegger, by Polt] |
| 15578 | Propositions don't provide understanding, because the understanding must come first [Heidegger, by Polt] |
| 22159 | If we posit 'I' as the starting point, we miss the mind's phenomenal content [Heidegger] |
| 22160 | Our relationship to a hammer strengthens when we use [Heidegger] |
| 15580 | There are no raw sense-data - our experiences are of the sound or colour of something [Heidegger] |
| 20749 | Perceived objects always appear in a context [Heidegger] |
| 22163 | The scandal of philosophy is expecting to prove reality when the prover's Being is vague [Heidegger] |
| 21949 | Having thoughts and feelings need engagement in the world [Heidegger, by Wrathall] |
| 22222 | Dasein finds itself already amongst others [Heidegger, by Caputo] |
| 8136 | If we work and play with other people, they are bound to be 'Dasein', intelligent agents [Heidegger, by Cooper,DE] |
| 22164 | When Dasein grasps something it exists externally alongside the thing [Heidegger] |
| 15579 | My active existence is defined by being able to say 'I can' [Heidegger] |
| 15583 | Certainty that I will die is more basic to my existence than the Cogito [Heidegger] |
| 22162 | There is an everyday self, and an authentic self, when it is grasped in its own way [Heidegger] |
| 20114 | Everyone is other, and no one is himself [Heidegger] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 15577 | Moods are more fundamentally revealing than theories - as when fear reveals a threat [Heidegger, by Polt] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 20748 | We do not add value to naked things; its involvement is disclosed in understanding it [Heidegger] |
| 22166 | Dasein has the potential to be itself, but must be shown this in the midst of ordinariness [Heidegger] |
| 22165 | Anxiety reveals the possibility and individuality of Dasein [Heidegger] |
| 21952 | Anxiety about death frees me to live my own life [Heidegger, by Wrathall] |
| 22224 | Anxiety is the uncanniness felt when constantly fleeing from asserting one's own freedom [Heidegger, by Caputo] |
| 20767 | Culture is now dominated by boredom, so universal it is unnoticed [Heidegger, by Aho] |
| 15572 | Being what it is (essentia) must be conceived in terms of Being (existence) [Heidegger] |
| 20453 | Heidegger says we must either choose an inauthentic hero, or choose yourself as hero [Heidegger, by Critchley] |
| 15581 | Dasein is always only that which it has chosen to be [Heidegger] |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |