80 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] |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| 13643 | Aristotelian logic is complete [Shapiro] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| 21889 | 'I' is the perfect name, because it denotes without description [Derrida] |
| 21878 | Names have a subjective aspect, especially the role of our own name [Derrida] |
| 21879 | Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida] |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| 13628 | We can live well without completeness in logic [Shapiro] |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| 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] |
| 4053 | If it is desirable that a given patient die, then moral objections to killing them do not apply [Rachels] |
| 4052 | It has become normal to consider passive euthanasia while condemning active euthanasia [Rachels] |