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Re: [lojban] Individuals and xorlo


On Mon, May 19, 2014 at 10:04 AM, guskant <gusni.kantu@gmail.com> wrote:

I have finished English translation of my commentary on gadri from a logical point of view:

Very nice. Here are some comments from me:


(1)<<
argument (sumti)
Symbol that refers to a referent, or that another argument can be substituted for.
>>

Your definition of "sumti" implies that "zi'o" is not a sumti. This is fine, but perhaps it's worth pointing out in a note this odd word, which is also called a "sumti" in a wider, merely syntactic sense,  Also things like "no da", "ci lo gerku", "mi .e do" and so on are called "sumti" in our formal grammars, although they only contain sumti by the semantic definition. Two other words that deserve special mention in this context are "ko" and "ma", which can arguably be said to fall under your definition, although they also are illocutionary force indicating devices, which ordinary sumti are not. 

(2)<<
When each of X and Y is an individual, {X jo'u Y} is called individuals. 
>>

I think you need to add "and X is not equal to Y" if you want to be more strict.
 
(3)<<
A plural constant that is an individual is called singular constant.

>>

I'd rephrase that as: "A plural constant that refers to a single individual is called a singular constant". I think it's worth keeping the distinction between the words or symbols, (constants and variables) and the referents of those symbols (things, people, trees, mountains, numbers, and so on). A constant can be singular or plural, and it can refer to an individual, but the constant is not the individual. The individual is the person, the tree or the house that the constant refers to. So if "X" is a singular constant, then X is an indifidual. 

(4)<<

No matter whether each of X and Y is plural or singular, {X jo'u Y} is not a singular constant. 

>>

Unless X=Y and X is an individual. But linguistically that would be odd indeed. "jo'u" should not be generally used to join something with itself, although theoretically it can be.


(5)<<

ro da    ro'oi da poi ro'oi de poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me de

su'o da    su'oi da poi ro'oi de poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me de

>>

When "poi" is used to restrict the domain for da/de/di, it is not necessary to use "ke'a", and indeed it's more clear to not use "ke'a". "ke'a" is needed when there is no explicit variable bound by the quantifier, but here your definitions are much more clear as:

ro da    ro'oi da poi ro'oi de poi de me da zo'u da me de

su'o da    su'oi da poi ro'oi de poi de me da zo'u da me de

(6)<<
For example, a plural constant {A jo'u B} can be in a domain of a bound plural variable, but it cannot be in a domain of a bound singular variable because it is not an individual.
>>

Constants are not in the domain of variables, it's their referents that are in the domain. And plural and singular quantifiers can share the same domain. I think what you want to say is that a variable bound by a singular quantifier cannot take more than one individual value at a time.

(7)<<
lo (LE)
It is prefixed to selbri, and forms a plural constant that refers to what satisfies x1, the first place of the selbri. If a quantifier follows {lo}, the quantifier represents the sum of all the referents of the plural constant. In the case that a quantifier follows {lo}, a sumti may follow it, and the quantifier represents the sum of all the referents of the sumti.
>>

I think "number", "count" or "quantity" would be better than "sum" there. To take an extreme example: "lo ci namcu" has three referents, three numbers. But "ci" is not (necessarily) the sum of the three numbers. The three numbers could be 1, 2 and 3. Their sum is 6, while their number is 3.

That nitpick aside, the second part is at least unclear. In "lo ci ko'a", "ci" is the number of referents of "lo ci ko'a", but "ko'a" could have more than three referents. If you want to express that three is the number of referents of the inner sumti as well you need "lo ro ci ko'a". "lo ci lo mu gerku" has three referents, but the inner sumti has five.

 (8)<<
An empty set is {lo selcmi be no da}, and an _expression_ {lo no broda} is officially meaningless (see Section 3.1Edit Plugin:alink. This implies that an empty set cannot be expressed with {lo'i/le'i/la'i}.
>>

Arguably, lots of things can be described as "lo selcmi be no da", not just the empty set.  A spoon, for example, or anything else that is not a set, will satisfy "ke'a selcmi no da". "lo selcmi be no da" works well as a description of the empty set in a universe of discourse in which there are only sets. (But then that is really the only universe of discourse in which one should mention sets at all, in my opinion.)

There's another problem with the "lo'i" definition. Can "lo selcmi be lo broda" be any set that has lo broda among its members, or is it the one and only set that has lo broda as its sole members? "cmima" only says that x1 is/are among the members of x2, does "selcmi" say that its x2 are all the members of its x1? Open question.

mu'o mi'e xorxes


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