20 ideas
14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
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] |
14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
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] |
14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
15666 | To understand language is to know how to use it to reach shared understandings [Habermas] |
14784 | Ethics is the science of aims [Peirce] |