27 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] |
| 18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
| 1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
| 5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
| 1512 | Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea] |
| 1508 | Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea] |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| 4483 | If abstract terms are sets of tropes, 'being a unicorn' and 'being a griffin' turn out identical [Loux] |
| 4481 | Austere nominalists insist that the realist's universals lack the requisite independent identifiability [Loux] |
| 4477 | Universals come in hierarchies of generality [Loux] |
| 18957 | Nominalism only makes sense if it is materialist [Putnam] |
| 4482 | Austere nominalism has to take a host of things (like being red, or human) as primitive [Loux] |
| 4478 | Nominalism needs to account for abstract singular terms like 'circularity'. [Loux] |
| 18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
| 4480 | Times and places are identified by objects, so cannot be used in a theory of object-identity [Loux] |
| 18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
| 454 | If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea] |
| 455 | That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea] |
| 1511 | If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius] |