Subject: Re: [lojban] fancu

From: [email-masked]
Date: Tue, 2 Oct 2001 21:51:34 EDT

In a message dated 10/2/2001 6:29:44 PM Central Daylight Time, 
[email-masked] writes:

> Your assumption is that to refer to a function we must use something
> that looks like one of its values. Is there a justification for that?
Not my assumption, just the usual way of doing it; how would you like to do 
it? A set of ordered pairs (but you hate sets) with the condition that for 
each first member there is only one second member? That is not what you have 
presented. You have presented a proposition or a function to propositions; 
that is what {du'u} does, le du'u bridi is by definition something we want to 
call the propsotition that bridi. Putting two variables in makes it a 
property, i.e., a function from (in this case) an ordered pair to a 
proposition. That is a perfectly good way to talk about taht kind of 
property/function, but that is not the kind of function we have here. I 
don't have a good third idea at the moment, except of course to use names and 
fill in the last place of {fancu} -- la mamfanc fancu lo'i danlu lo'i fetsi 
le nu roda mapti le mamta da.

> 
> In my view {makau} stands for the value that the relationship gives
> when the ce'u place is filled. {makau} will take a value from x3
> for each value taken from x2 and placed in {ce'u}.
Ahah! I have accused you of that view several times and you have almost as 
often denied it, swearing that you believed that the answer to a question was 
a proposition not a thing. Now, to make a point you will go back to your 
true view. OK. But notice that will make {la djan djuno le du'u makau mamta 
la bil) into perfect nonsense (of a highly forbidden kind: we can't use 
{djuno} for people).

Ah, but maybe what you mean is that somehow it is built into the operation of 
indirect questions that they generate the proposition with the right critter 
in for the {kau}. But then, of course, it is impossible to get the answer 
wrong, which, alas, goes against our experience: {mi jinvi le du'u maku mamta 
la bil} guarantees I get it right (so only essay questions from now on). 
And's view -- if I have it somewhat right -- at least misses that problem and 
only runs into all the intensionality or interchange problems -- as well as 
missing several good answers. The set-of-answers theory (not mine, by the 
way) was not arrived at without looking at these kinds of problems but was 
rather what people were forced to to deal with them.

> Why would its values be more representative of a function than the
> relationship that gives rise to it?

"Is mother of," {le ka/du'u ce'u mamta ce'u}, is a relation and, indeed, a 
function, as a set of ordered pairs --though the order is reversed here, so 
{le du'u ce'u se mamta ce'u} . There are many functions for which it is 
somewhat unnatural to think of the corresponding relation (sum, product, and 
the like, for example) and, indeed, the relations can usually be expressed 
only by an equation between the function with an argument and its value for 
that argument (though one way of doing Logic does take this notion as basic, 
to simplify some kinds of metatheoretical proofs). However, the shift from 
relation to function IN PRACTICE does require some indication that the 
relation IS a function and the {le ka ce'u... ce'u} does not show that, while 
value-description form does (well, almost -- Lojban has this singular / 
plural problem, as you know, but that can be handled in a variety of ways). 
It is that information that makes the value-description form better.