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] |
| 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] |
| 18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| 13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
| 9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
| 18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
| 18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| 18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
| 10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
| 9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
| 18165 | My Basic Law V is a law of pure logic [Frege] |
| 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] |
| 9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
| 13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |