On 4/3/13 11:46 PM, Albert Y. C. Lai wrote: > On 13-04-03 07:39 PM, Alexander Solla wrote: >> There's your problem. Mathematicians do this specifically because it is >> helpful. If anything, explicit quantifiers and their interpretations >> are more complicated. People seem to naturally get how scoping works in >> mathematics until they have to figure out free and bound variables. > > Quantifiers are complicated, but I don't see how explicit is more so > than implicit.
When the quantifiers are implicit, we can rely on the unique human ability to DWIM. This is a tremendous advantage when first teaching people about mathematical concerns from a logical perspective. However, once people move beyond the basics of quantification (i.e., schemata, rank-1 polymorphism, etc), things get really hairy and this has lead to no end of quibbles in philosophy and semantics, where people seem perversely attached to ill-specified and outdated logics. On the other hand, with explicit quantification you can't rely on DWIM and must teach people all the gritty details up front--- since the application of those details is being made explicit. This is an extremely difficult task for people who are new to symbolic reasoning/manipulation in the first place. In my experience, it's better to get people fluently comfortable with symbolic manipulations before even mentioning quantifiers. -- Live well, ~wren _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
