37 ideas
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
16185 | Causality indicates which properties are real [Cartwright,N] |
16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |
16178 | There are few laws for when one theory meets another [Cartwright,N] |