History: lo'ei

Source of version: 2 (current)

''lo'ei'' is ((xorxes)) definition of ''((lo'e))'', used by him for as the definition of ''lo'e'', and used by others to refer to his usage of ''lo'e''. (((Adam|I)) have changed the original ''lo'e''s to ''lo'ei''s for the sake of clarity in the meta-discussion.) ---- ''From [http://groups.yahoo.com/group/jboske/message/398|jboske 398]:'' I present here my definition of {[[lo'ei]} (nothing new, but maybe better formulated). I don't think it is incompatible with And's, though the approach is different. I define it for a very specific case in a specific context, and then I generalize it. We start from the official definition of {sisku}: sisku: x1 seeks/searches/looks for property x2 among set x3 We define a new predicate, {buska}, as follows: DEF1: tu'o ka ce'u goi ko'a ce'u goi ko'e ce'u goi ko'i zo'u ko'a buska ko'e ko'i cu du tu'o ka ce'u goi ko'a ce'u goi ko'e ce'u goi ko'i zo'u ko'a sisku tu'o ka ce'u du ko'e kei ko'i Now we define a particular use of {lo'ei broda} as follows: DEF2: buska [[lo'ei] broda = sisku tu'o ka ce'u broda Notice that from DEF1 we know that: buska [[lo'ei] broda = sisku tu'o ka ce'u du [[lo'ei] broda * This does not follow directly from DEF1, as pc pointed out during the discussion. The equivalence is still true, but it requires using DEF2 and its generalization to any other selbri. In any case, this is just an illustrative step and not a part of the definition of ''lo'ei''. --((xorxes)) and from DEF2 we know that: buska [[lo'ei] broda = sisku tu'o ka ce'u du lo broda So we have that: tu'o ka ce'u du [[lo'ei] broda = tu'o ka ce'u du lo broda which does not in any way entail that {[[lo'ei] broda} can be replaced by {lo broda} in other contexts. In particular, we have: buska [[lo'ei] broda = sisku tu'o ka da poi broda zo'u ce'u du da buska lo broda = da poi broda zo'u sisku tu'o ka ce'u du da which are clearly different. So we have defined {[[lo'ei] broda} when it appears in the x2 of {buska}. To generalize for any context {brode [[lo'ei] broda}, we need a predicate that is to {brode} as {sisku} is to {buska}. This protopredicate is simply {kairbrode}. It takes a property in x2 instead of the x2 of brode. mu'o mi'e ((xorxes)) ---- ''sisku'' is defined by the ((gi'uste)) as ''x1 looks for something with property x2''. In principle the most natural definition would be ''x1 looks for object x2'', but the actual definition allows searches for non-existent entities, and treats them identically to existent entities. ''buska'', as defined above, is just this second definition ''x1 looks for object x2''. ''kairbroda'' is the predicate parallel to ''sisku'' for regular predicates; e.g. ''kaircitka'' is ''x1 eats things with property x2''. ---- ((pycyn)) has objected (at least at one point or another) to several points about this definition. The ones ((Adam|I)) can fathom are: # The definition requires that ''le ka ce'u du lo broda'' be the same as ''le ka ce'u du lo'ei broda''. pycyn claimed that, since ''lo broda cu ckaji le ka ce'u du lo broda'' and hence ''lo broda cu ckaji le ka ce'u du lo'ei broda'', therefore ''lo broda cu du lo'ei broda'', to which ((xorxes)) strenuously objected. It is clear that ''ro da zo'u da ckaji le ka ce'u du da''; ((Adam|I)) think that pycyn was trying to claim that moving in the opposite direction is also possible; i.e. ''ro da ro de zo'u ganai da ckaji le ka ce'u du de gi da du de''. As I understand it, ((xorxes)) objects to this because he takes properties as intensional objects, and the inner form of the sub-bridi is not important, as long as it has the same meaning. **In fact, ''lo broda cu du lo'ei broda'' is true. What I object to is that this means that ''lo'ei broda'' can be substituted in general by ''lo broda''. This is as wrong as saying that because ''ro broda du lo broda'' is true (which it is) then ''ro broda'' could be substituted by ''lo broda''. --((xorxes)) **To see that ''lo broda cu du lo'ei broda'' is true, we just apply the definition: ''lo broda cu du lo'ei broda'' == ''lo broda cu kairdu'o le ka ce'u broda'' == ''lo broda cu ckaji le ka ce'u broda'', since ''kairdu'o'' means "x1 is identical to something with property x2", i.e. it is just ''ckaji''.--((xorxes)) # The definition ultimately has that ''broda lo'ei brode'' is defined as ''kairbroda le ka ce'u du lo'ei brode'' whereas ''broda lo brode'', in terms of ''kairbroda'', is ''da poi brode zo'u kairbroda le ka ce'u du da''. So ''lo brode'' remains bound in the main bridi, whereas ''lo'ei brode'' moves into the sub-bridi and gets bound there. In other words ''broda lo'ei brode'' should be ''ko'a goi lo'ei brode zo'u kairbroda le ka ce'u du ko'a''. ((Adam|I)) think that one could say either that binding ''lo'ei brode'' in the main bridi's prenex is acceptable, since ''lo'ei brod'' does not claim that there is any ''lo brode'', or that it doesn't matter where ''lo'ei brode'' is bound; since it is a singular, intensional term, it can move across term and scope boundaries without affecting the meaning. ** I think what you say is correct, but I'm not sure this was one of pc's objections. --((xorxes)) ---- This definition of ''lo'ei'' is equivalent in meaning to the second definition of ''((tu'o))'' as a quantifier given on that page (though it may or may not be exactly equivalent in the algebraic formulae that can be applied to it). In other words, in both ''broda lo'ei brode'' and ''broda tu'o brode'', there is no quantification over the set ''lo'i brode''; the (intensional) meaning of ''brode'' is added to the meaning of ''broda'' without actually going and picking out individual ''brode''s (or masses of ''brode''s, etc.) ---- ((xorxes)) has also defined a parallel ''((le'ei))'', which is his use of ''((le'e))''.