Once upon a time in the history of Logjam, it was carved in Silly-putty for all eternity that lo broda meant su'o lo ro broda, Like Manicheanism in Christianity, this heresy was quickly quelled and yet continues to affect many sects within the loglang community. It lingers in the cult that requires that lo broda always refers to the same thing, whether Mr. Broda or brodahood or just the solid lump of Broda. It is behind most of the other views as well, though usually with more emphasis on the su'o. The question is, do these different cliques have enough in common to make a language which is indifferent to their various claims. The general success of xorlo, which is based in one group, but whose basis is generally ignored (or not understood), suggests that it they have. This is an inquiry into whether there are any sentences which would be true on on ontology but not on some other. I needs must also take into account the kind of mental adjustments that each group has to make to accommodate the sayings of another group in the vulgar (i.e., not minutely accurate) form. In keeping with the times, I will attempt to do this in terms of emerging Xorban, in particular, taking the quantifier l, rather than the term-maker lo from the older languages.
From familiarity, I begin by considering a relatively conservative ontology in which the universe of discourse consists of discrete things, which are grouped by predicates into classes and relations and the like. Variables range over exactly these, but may be instantiated to several at once (or they range of L-sets of these -- the distinction does not make a formal difference, whatever it may mean materially). Since there are no terms but variables in this system, the question of truth comes down to whether values taken on by a variable in a context fall in the class assigned to the attached predicate. In the case of sa Ra Pa and la Ra Pa, it is enough that some such values work. For ra Ra Pa they all must. The difference between l and s is that the one requires the same values each time, the other does not, beyond certain syntactically defined limits.
The question of whether a value is in the set defined by a predicate is not an entirely straightforward matter. There are at least three cases to consider (using L-set language for simplicity): the value as a whole is in the set assigned the predicate, though not all its members are; all its members are (and perhaps the set as a whole as well); or some (but not necessarily) all its members are. This last includes cases where the some members for classes which are in as classes). Generally, these distinctions are ignored, since it is usually obvious from the nature of the predicate which is involved or it does not really matter. When it is an issue, however, devices are needed to indicate which is the appropriate sense of "satisfy" that is intended. As a rough rule, when precision begins to be an issue, l alone indicates the first case, a subordinate r the second and a subordinate s the third. I suppose more explicit modifiers might also be used, especially when the set is referred to several times in the following sentence and thus might be involved in different ways.
I cannot speak with confidence about the other ontologies. So far as I can see, the Mr. Broda story and the lump of Broda story do not different formally very much from the above plan. To be sure, the "class' is always the same on these views and the "members" are derivative from it rather than the other way around, but the way that sentences behave when total precision is not the issue seems not to differ much. To be sure, a powder puff tail may count as a rabbit in the lump Rabbit class, is unlikely to fare any differently in comparison to other ontologies: if it's all you see, it probably counts as a rabbit; if it's all you catch, it probably won't. Whether the same quantifier expansions would have th4e dsame effect (or even be intelligible) on these other views is unclear.
There are indications that the layers of concepts ontology also come down to the same formality. But I confess that I can't see how to fit myopic singulars in at all, mainly because I just do not understand the notion. My chief problem (though probably not the only one, if this were removed) is the claim that la Ra Pa entails ra Ra Pa <=> sa Ra Pa, that there is either only one or none at all Rs (or that they are totally uniform, at least with respect to P). This becomes puzzling, I think, because it appears from other things said that la Ra encompasses all Rs. If the expressions brings in only a portion of the Rs (or if P is very general) there does not seem to be a problem, though the insistence on the formula seems forced. I am sure there is something more here that I am missing but don't (obviously) see what it can be.
9/26/12
Some remarks today, though rather opaque, encouraged my belief that we are all about the same pattern with very different words and images. The short form seems to be:
The extension of a predicates is a thing which satisfies that predicate in some way
This thing is broken down using some form of the jest relation (variously interpreted according to the case, but formally the same), generating a join semi-lattice of things, each of which also satisfies the predicate in some way (maybe the same, maybe differently).
The quantifiers r, s, l indicate things in the lattice b In a particular case, Qa Ra Pa says that the selected thing in the R lattice also satisfies P in some way (is also a node in the P lattice).
The way of satisfaction may be spelled out but typically will not, as being obvious.
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