[lojban] Re: importing ro

[pycyn@aol.com]

In a message dated 11/6/2002 8:16:22 PM Central Standard Time, a.rosta@lycos.co.uk writes:
<<

pc,
the main instigator and advocate of the Yes answer to Q1, bases
his reasons on the way things work in logic, but we do not have
to agree that {da poi} is restricted quantification; we can decree
that it is not. Anybody who really wants restricted quantification
and Option B can create appropriate experimental cmavo for it.

>>
Since so many peple have been kind enough to tell me what I think and have universally gotten it wrong, allow me to say what I really do think. 
1.  There are four fundamental quantifiers in Lojban: {ro, su'o, no, me'i[ro]} (I intend to make sure that the default origin for {me'i} is {ro}, if it is not already).
2.  They are related as follows
subalterns: ro => su'o
             no => me'i
contraries: ro => naku no (and so, if you can't do the numbers, no => naku ro)
subcontraries: naku su'o => me'i (and so naku me'i => su'o)
contradictories: naku ro <=> me'i
                   naku su'o <=> no
(and so            naku no <=> su'o
                   naku me'i <=> ro)
When there is a guarantee that the subject term is non-empty, 
                   no => ro naku
                   me'i => su'o naku
I assume the universe is non-empy.
Consequently:
             naku ro da broda <=> me'i da broda <=> su'o da naku broda
             naku su'o da broda <=> no da broda <=> ro da naku broda
(typically, {broda} will in fact be complex -- a conditional with {ro}, a conjunction with {su'o} -- ordinary DeMorgan then applies to bring {naku} ti its smallest scope).
             naku ro broda cu brode <=>  me'i broda cu brode
and so on, as in contraries above.  The further move to, in this case, {su'o broda naku brode} requires the addition of implicit or explicit evidence that lo'i broda is not null.
{ro} imports as always (for the universe or a subject), {no} and {me'i} do not.  The usual formalae of formal logic continue to operate as usual, but are not the only -- or even usual -- ways to say "All S is P" or "Some S is P" etc. 

The system with {da} and connectives is definable within the system with only predications and conversely, but no particular advantage derives from such definitions once the basic rules are in place.

Sentences of the form {Q da poi broda cu brode} occupy an intermediate position, since {poi} can be read either as a restrictor on the range of the quantifier (the most natural, I think, but I don't insist on it) or as a part of the predicate to a universal subject -- that is as {ganai gi} or {ge gi} depending on the quantifier.  This seems to me the only question left to settle.
            
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