77 ideas
21761 | If we start with indeterminate being, we arrive at being and nothing as a united pair [Hegel, by Houlgate] |
21764 | Thought about being leads to a string of other concepts, like becoming, quantity, specificity, causality... [Hegel, by Houlgate] |
21769 | We must start with absolute abstraction, with no presuppositions, so we start with pure being [Hegel] |
22037 | Objectivity is not by correspondence, but by the historical determined necessity of Geist [Hegel, by Pinkard] |
21983 | Being and nothing are the same and not the same, which is the identity of identity and non-identity [Hegel] |
21985 | The so-called world is filled with contradiction [Hegel] |
21766 | Dialectic is the instability of thoughts generating their opposite, and then new more complex thoughts [Hegel, by Houlgate] |
21978 | Hegel's dialectic is not thesis-antithesis-synthesis, but usually negation of negation of the negation [Hegel, by Moore,AW] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
21977 | Nothing exists, as thinkable and expressible [Hegel] |
21762 | To grasp an existence, we must consider its non-existence [Hegel, by Houlgate] |
21760 | Thinking of nothing is not the same as simply not thinking [Hegel, by Houlgate] |
21765 | The ground of a thing is not another thing, but the first thing's substance or rational concept [Hegel, by Houlgate] |
22059 | Kant's thing-in-itself is just an abstraction from our knowledge; things only exist for us [Hegel, by Bowie] |
22083 | Hegel believe that the genuine categories reveal things in themselves [Hegel, by Houlgate] |
22080 | The nature of each category relates itself to another [Hegel] |
21772 | In absolute knowing, the gap between object and oneself closes, producing certainty [Hegel] |
21972 | Hegel, unlike Kant, said how things appear is the same as how things are [Hegel, by Moore,AW] |
22038 | Hegel's non-subjective idealism is the unity of subjective and objective viewpoints [Hegel, by Pinkard] |
22044 | Hegel claimed his system was about the world, but it only mapped conceptual interdependence [Pinkard on Hegel] |
21464 | The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner] |
21975 | The absolute idea is being, imperishable life, self-knowing truth, and all truth [Hegel] |
21976 | The absolute idea is the great unity of the infinite system of concepts [Hegel, by Moore,AW] |
22084 | Authentic thinking and reality have the same content [Hegel] |
20954 | The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie] |
22058 | Hegel's 'absolute idea' is the interdependence of all truths to justify any of them [Hegel, by Bowie] |
6386 | In no important way can psychology be reduced to the physical sciences [Davidson] |
20953 | Every concept depends on the counter-concepts of what it is not [Hegel, by Bowie] |
21763 | When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |