24 ideas
8996 | If if time is money then if time is not money then time is money then if if if time is not money... [Quine] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
8995 | Definition by words is determinate but relative; fixing contexts could make it absolute [Quine] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
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] |
10064 | Quine quickly dismisses If-thenism [Quine, by Musgrave] |
20296 | Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey] |
8998 | Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine] |
8999 | Logic isn't conventional, because logic is needed to infer logic from conventions [Quine] |
9000 | If a convention cannot be communicated until after its adoption, what is its role? [Quine] |
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] |
8994 | If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine] |
8997 | There are four different possible conventional accounts of geometry [Quine] |
8993 | If mathematics follows from definitions, then it is conventional, and part of logic [Quine] |
14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce] |
14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |