80 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] |
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] |
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] |
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] |
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] |
21686 | Sense-data are dubious abstractions, with none of the plausibility of tables [Quine] |
20749 | Perceived objects always appear in a context [Heidegger] |
21685 | Empiricism says evidence rests on the senses, but that insight is derived from science [Quine] |
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] |
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] |
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] |