67 ideas
| 21887 | Derrida focuses on other philosophers, rather than on science [Derrida] |
| 21888 | Philosophy is just a linguistic display [Derrida] |
| 21896 | Philosophy aims to build foundations for thought [Derrida, by May] |
| 21893 | Philosophy is necessarily metaphorical, and its writing is aesthetic [Derrida] |
| 21892 | Interpretations can be interpreted, so there is no original 'meaning' available [Derrida] |
| 20925 | Hermeneutics blunts truth, by conforming it to the interpreter [Derrida, by Zimmermann,J] |
| 20934 | Hermeneutics is hostile, trying to overcome the other person's difference [Derrida, by Zimmermann,J] |
| 21895 | Structuralism destroys awareness of dynamic meaning [Derrida] |
| 21934 | The idea of being as persistent presence, and meaning as conscious intelligibility, are self-destructive [Derrida, by Glendinning] |
| 21883 | Sincerity can't be verified, so fiction infuses speech, and hence reality also [Derrida] |
| 21882 | Sentences are contradictory, as they have opposite meanings in some contexts [Derrida] |
| 21881 | We aim to explore the limits of expression (as in Mallarmé's poetry) [Derrida] |
| 4756 | Derrida says that all truth-talk is merely metaphor [Derrida, by Engel] |
| 21877 | True thoughts are inaccessible, in the subconscious, prior to speech or writing [Derrida] |
| 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] |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| 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] |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| 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] |
| 21878 | Names have a subjective aspect, especially the role of our own name [Derrida] |
| 21889 | 'I' is the perfect name, because it denotes without description [Derrida] |
| 21879 | Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| 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] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [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] |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| 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] |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 21890 | Heidegger showed that passing time is the key to consciousness [Derrida] |
| 21880 | 'Tacit theory' controls our thinking (which is why Freud is important) [Derrida] |
| 21886 | Meanings depend on differences and contrasts [Derrida] |
| 21930 | For Aristotle all proper nouns must have a single sense, which is the purpose of language [Derrida] |
| 21884 | Capacity for repetitions is the hallmark of language [Derrida] |
| 21935 | The sign is only conceivable as a movement between elusive presences [Derrida] |
| 21933 | Writing functions even if the sender or the receiver are absent [Derrida, by Glendinning] |
| 21894 | Madness and instability ('the demonic hyperbole') lurks in all language [Derrida] |
| 21931 | 'Dissemination' is opposed to polysemia, since that is irreducible, because of multiple understandings [Derrida, by Glendinning] |
| 21885 | Words exist in 'spacing', so meanings are never synchronic except in writing [Derrida] |
| 21891 | The good is implicitly violent (against evil), so there is no pure good [Derrida] |