27 ideas
| 6782 | Realism is the only philosophy of science that doesn't make the success of science a miracle [Putnam] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
| 18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
| 18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
| 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] |
| 18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
| 18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
| 18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
| 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] |
| 18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
| 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] |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| 18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| 22181 | Putnam says anti-realism is a bad explanation of accurate predictions [Putnam, by Okasha] |
| 18957 | Nominalism only makes sense if it is materialist [Putnam] |
| 18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
| 18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |