25 ideas
| 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] |
| 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] |
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| 18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
| 18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| 18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| 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] |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| 18957 | Nominalism only makes sense if it is materialist [Putnam] |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
| 18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| 18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
| 20062 | If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm] |
| 20054 | There has to be a brain event which is not caused by another event, but by the agent [Chisholm] |