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| In a message dated 10/10/2002 5:02:00 PM Central Daylight Time, cowan@hidden.email writes: << Try "the amount of things in the bag", then: more concrete, easier to >> I wondered how this was going to work. Yet another disanalogy. Take the clear cases of abstractions (let's suppose they are clear, since no one is disputing them at the moment). {du'u koa broda} refers to a proposition/set of propositions {du'u ce'u broda} refers to a propositonal function/property {nu ko'a broda} refers to an event/ set of events {jei koa broda} refers to the truth value of {ko'a broda} (on a certain assignment) Taking the {du'u} case as a model, we get that {jei ce'u broda} is a function from names/things to truth values, that is, the Zadeh (early fuzzy logic) membership function for lo'i broda, the quantitative scale of du'u ce'u broda. Moving that along, {nu ce'u broda} ought to be the function from names/things to events, a function that doesn't have a useful name that I can think of at the moment, although it amounts to the application principle, the extensional analog of {du'u} as intension. Suppose, then, that {ni ko'a broda} is the value of the degree of brodaness on whatever scale is appropriated (x2) -- different for different properties, obviously. Then {ni ce'u broda} is the function from names/objects to degrees -- the scale itself, in short, and so a useful concept (and, yes, the connection with {jei} does become more apparent -- but the differences also come more clearly to light: {jei} has a limited range of values, {ni} does not; however much any set of {ni} values can be represented within [0,1], they often are not so represented and the move to so represent them can be seen as a step toward truth values, a usually separate notion. {jei} gives truth values immediately (that is how it is defined), whereas {ni} is at most mediately related to truth values, for a range of {ni} values may correspond to a single truth value, and the relation can be decided quite separately from the {ni} values -- which might remain the same over a range of truth-value assignments. None of this helps with {ka}, however. In the established usage, {ka ce'u broda} is the same as the (relatively) newly found {du'u ce'u broda}, which leads to the notion that {ka ko'a broda} ought to be a proposition -- which no one seems to have seriously suggested. On the other hand, the suggested alternative for {ka ko'a broda}, that it refers to a set of properties of le nu ko'a broda, leaves {ka ce'u broda} as a function from names/objects to properties of events, a notion which makes sense but doesn't have any obvious uses nor history of such, that I can think of. |