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*To*: Erik Rauch <rauch>*Subject*: Re: Lean Lujvo and fat gismu*From*: Logical Language Group <lojbab@ACCESS.DIGEX.NET>*Date*: Tue, 12 Oct 1993 15:12:46 -0400*In-Reply-To*: <199310121800.AA24499@access.digex.net> from "Art Protin" at Oct 12, 93 01:57:00 pm*Reply-To*: Logical Language Group <lojbab@ACCESS.DIGEX.NET>*Sender*: Lojban list <LOJBAN%CUVMB.bitnet@YaleVM.YCC.YALE.EDU>

mi'e .djan. .i mi pu cusku di'e > > It is this sort of fuzziness which caused the Lojban engineers > > to remove the comparative places from many gismu. As Art Protin > > recently posted, Loglan "groda" historically meant "x1 is bigger > > than x2 by standard x3" and "x1 is big" was interpreted as "x1 > > is bigger than something-unspecified". (Institute Loglan has > > never had an equivalent of "zo'e"). > > > This gimmick breaks down in many cases, though: "x1 is not big" > > obviously cannot be so rewritten. la .art. cusku di'e > I am afraid I don't see this. Either of the two forms seem to > make sense: > > X [is] not bigger-than [something-unspecified] > > and > > X [is] reverse-relation bigger-than [something-unspecified]. > > (or reordered for English speakers "[something-unspecified] [is] > bigger-than X"). Doesn't work. To deny that something is big is not the same as to deny that there exists something else which it is bigger than. I deny that a mouse is big, but I affirm that a mouse is bigger than something (e.g. a fly). Similarly with the colors. Loglan "blanu" meant "x1 is bluer than x2", but Lojban blanu is just "x1 is blue", because "X is not blue" does not mean "There does not exist a Y such that X is bluer than Y", nor does it mean "For all Y, X is not bluer than Y". The latter (universal) reading would construe "The sky is not blue" as true, because it is not as blue as a color-chip displaying focal blue. The former (existential) reading would construe "Leaves are not blue" as false, because the color of leaves is closer to focal-blue than, say, the color of McIntosh apples. > Also, the "heap paradox" seems very lame. A heap is not precisely > defined and then a formal proof fails because of this imprecision > does not strike me as a really interesting paradox. The > proof/paradox falls apart if I define a heap as > > a gravitationally stable aggregate of items such that > there is no 2 available dimensional view that permits > precise counting of the constituent items. (I presume this means "available 2-dimensional view".) > Then the heap ceases to be a heap when the constituent items > can be counted either because enough have been removed or > those items have been rearranged to distinguish each item. Sorry, this definition is no more precise than the intuitive meaning. Consider the notion of being able to count N objects precisely just by looking at them. For values of N up to six, this is easy for anyone. If the objects are properly arrayed, N can be much larger; it is easy to count the 48 stars on the pre-1958 American flag because they are arranged in a 6 x 8 array. Zacharias Dase, the calculating prodigy, could accomplish the feat for N=43 (sheep in a field). Nonetheless, for N=10000, no one can count the objects. But nevertheless, there is no value k which represents the exact boundary between what is and what is not countable, such that a "pseudo-heap" of k objects is countable, whereas a "true heap" of k+1 objects is not. Therefore, the paradox returns. There simply is no lower limit on the size of a heap. (Reply to Dave: I was, of course, dealing with the intuitive notion of a heap, not any computer-science sense of the term. The CS heap has all sorts of properties which do not apply to the physical heap -- the terms represent at most polysemy, and probably full homonymy, like the algebraic vs. the physical uses of "ring".) > The cleanup of the definition of small is more difficult, > but again a precise proof with imprecise terms should always > be suspect. Any kind of nonsense can be shown with those. Exactly. The point is that a great many natural-language predicates are inherently vague, not subject to formal definition. -- John Cowan sharing account <lojbab@access.digex.net> for now e'osai ko sarji la lojban.

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