[YG Conlang Archives] > [jboske group] > messages [Date Index] [Thread Index] >
On Tue, 7 Jan 2003, Jordan DeLong wrote: > On Tue, Jan 07, 2003 at 11:22:31PM -0500, Invent Yourself wrote: > > 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 > > In fact, Quine defines ratios in terms of integer multiplication, > which he defines in terms of integer addition. They all come down > to quantification, neither-nor and membership. > > How we think of it is beside the point. I think it's the only thing that matters. An abbreviation is an abbreviation only when the conversers know that it's an abbreviation for something else that they both know. Otherwise, it's simply an expansion. We have to call certain concepts reasonably primitive, and only the speakers are qualified to announce what they are using as primitives. > > the 5 pipes is stretching the point. Still, it should be pointed out that > > It is not stretching the point. Let me give a better (more drastic) > example, > |- (x)(y) (x = y) -> (x mem y & y mem x) > actually means > |- (x)(y) > ((z)((((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y)) | > (((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x))) | > (z)((((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y)) | > (((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x))) | > ((x mem y | x mem y) | (y mem x | y mem x)) | > (z)((((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y)) | > (((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x))) | > (z)((((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y) | > ((z mem x | z mem x) | z mem y)) | > (((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x) | > ((z mem y | z mem y) | z mem x))) | > ((x mem y | x mem y) | (y mem x | y mem x))) > > No bullshit. You made a mistake in the 9th line. Only kidding. I hope you used a script for that! > (Yes this took me a while, but fun to see how complicated it actually > is). > > > 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. > > My whole point is that the point of lojban is not "speakable logic". I believe that was one of the intents of JCB. -- // if (!terrorist) // ignore (); // else collect_data ();