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On Tue, 7 Jan 2003, Jordan DeLong wrote: > On Wed, Jan 08, 2003 at 01:11:31AM -0000, And Rosta wrote: > > > > Because (i) it's blindingly obvious how to do it, (ii) I've done it > > in my own engelang, (iii) for the reasons I spelled out in my > > previous message, logicians aren't interested in concision. > > But they in fact *are* interested in concision, and they have done > it. In the book I have by Quine he defines a bunch of "macro" type > things which just shorten stuff, and serve no other purpose. The > expression (A -> B) is *shorthand* for (~A v B), (A v B) is shorthand > for ~(A | B) (where '|' is the neither-nor connective), ~A is > shorthand for (A | A). So the original (A -> B) actually is just > a short version of writing (((A | A) | B) | ((A | A) | B)). In > fact his system only has 3 truly fundamental things: quantification, > neither-nor, and the membership operator---but no logician would > want to write everything in terms of those. He even gives a whole > system of little dot thingies to avoid having to write parenthesis. We can perform division using addition and negation alone, but it doesn't make much sense to claim that division is actually a shorthand for addition, because we don't think of it that way. Your final formula with the 5 pipes is stretching the point. Still, it should be pointed out that your first example can't be done in Lojban. For A --> B we use ~A V B. To achieve logical rigor in Lojban usually is not significantly more concise than English. Lojban prenexes contain fewer syllables than their English counterparts, but the number of operators is the same order of magnitude. They wanted to create a speakable logic, but didn't give serious thought to very-alternative notations, so they mapped the classic "for every A, there exists a B" prenex Logician's English. I'd like to see what elegant solutions AndR came up with. -- // if (!terrorist) // ignore (); // else collect_data ();