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Jordan: > On Wed, Jan 08, 2003 at 01:11:31AM -0000, And Rosta wrote: > > Lojbab: > > > At 12:19 AM 1/7/03 +0000, And Rosta wrote: > > > > > >A good logical language is one that is not only logically precise but > > > > > >also concise > > > > > > > > > > Why? > > > > > > > >Because a notation that is insufficiently concise is a deterrent to > > > >using it. If it takes ages to say what you want to say, then you > > > >are more likely to choose to say something shorter than what you > > > >had wanted to say > > > > > > > >Creating a logical language is a pretty trivial undertaking, because > > > >logic notations have already been invented. The challenge is to > > > >create a more concise (and hence more usable) notation > > > > > > If logicians haven't done it, what makes you think we could? > > > > 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 > > This book also argues that mathmatical expressions like '3 + 2' are > simply shorthand versions of (complex) logical expressions You are right. I have the (perhaps wrong) impression that Quine was unusually interested in notation, but yes, the notation does contain abbreviatory devices. > So, Quine is a logician. Quine is interested in concision. Therefore > at least some logicians are interested in concision (and I would > argue most are, because basically all employ shorthands such as ~ > and -> and such things) Concision is not the only reason for using abbreviatory devices. Another reason is that notation simply doesn't matter much (except to notation fetishists like us), and furthermore by using a traditional and somewhat ad hoc abbreviatory system one avoids being sidetracked by debates about which are the more fundamental logical elements. It's probably fair to say that standard notation is about as concise as it could be without being far more complicated and less perspicuous. > Thus if lojban/loglan/blah is supposed to be interesting, it is > *not* (only) as Concise Logic(tm) Not only, I'm sure, else there would be far fewer people interested in it, but I still stand by what I said. Okay, to be as concise as possible is not the only desideratum -- it is just one aspect of the general desideratum of being ergonomic. --And.