24 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
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] |
10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
10011 | Identity is a level one relation with a second-order definition [Hodes] |
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] |
10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
10027 | Mathematics is higher-order modal logic [Hodes] |
10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
3916 | Hopi consistently prefers verbs and events to nouns and things [Whorf] |
3917 | Scientific thought is essentially a specialised part of Indo-European languages [Whorf] |
3915 | The Hopi have no concept of time as something flowing from past to future [Whorf] |