31 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
17867 | If a concept is not compact, it will not be presentable to finite minds [Almog] |
17877 | The number series is primitive, not the result of some set theoretic axioms [Almog] |
8915 | How we refer to abstractions is much less clear than how we refer to other things [Rosen] |
17871 | Fregean meanings are analogous to conceptual essence, defining a kind [Almog] |
17866 | Essential definition aims at existence conditions and structural truths [Almog] |
17868 | Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog] |
17872 | Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog] |
17870 | Alien 'tigers' can't be tigers if they are not related to our tigers [Almog] |
17869 | Kripke and Putnam offer an intermediary between real and nominal essences [Almog] |
17876 | Individual essences are just cobbled together classificatory predicates [Almog] |
17873 | Water must be related to water, just as tigers must be related to tigers [Almog] |
8917 | The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen] |
8912 | Nowadays abstractions are defined as non-spatial, causally inert things [Rosen] |
8913 | Chess may be abstract, but it has existed in specific space and time [Rosen] |
8914 | Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen] |
8916 | Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen] |
8918 | Functional terms can pick out abstractions by asserting an equivalence relation [Rosen] |
8919 | Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen] |
17864 | Defining an essence comes no where near giving a thing's nature [Almog] |
17863 | Essences promise to reveal reality, but actually drive us away from it [Almog] |