36 ideas
16943 | Philosophy is continuous with science, and has no external vantage point [Quine] |
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] |
16949 | Klein summarised geometry as grouped together by transformations [Quine] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
16939 | Mass terms just concern spread, but other terms involve both spread and individuation [Quine] |
16948 | Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine] |
16945 | We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine] |
16944 | Science is common sense, with a sophisticated method [Quine] |
16941 | Induction relies on similar effects following from each cause [Quine] |
16940 | Induction is just more of the same: animal expectations [Quine] |
16933 | Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine] |
16934 | General terms depend on similarities among things [Quine] |
16938 | To learn yellow by observation, must we be told to look at the colour? [Quine] |
16947 | Similarity is just interchangeability in the cosmic machine [Quine] |
8486 | Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine] |
16932 | Projectible predicates can be universalised about the kind to which they refer [Quine] |
7375 | Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett] |
16935 | If similarity has no degrees, kinds cannot be contained within one another [Quine] |
16936 | Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine] |
16937 | You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine] |
16942 | It is hard to see how regularities could be explained [Quine] |