72 ideas
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] |
15569 | Heidegger says truth is historical, and never absolute [Heidegger, by Polt] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
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] |
7680 | Ontology is possible only as phenomenology [Heidegger] |
22161 | Readiness-to-hand defines things in themselves ontologically [Heidegger] |
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] |
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] |
15577 | Moods are more fundamentally revealing than theories - as when fear reveals a threat [Heidegger, by Polt] |
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] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |