lo'ei

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lo'ei is xorxe's 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 have changed the original lo'es to lo'eis for the sake of clarity in the meta-discussion.)


From 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 gimste 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 can fathom are:

  1. 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 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
  2. 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 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 brodes (or masses of brodes, etc.)


xorxes has also defined a parallel le'ei, which is his use of le'e.