tech:logic matters

[ucleaar <ucleaar@UCL.AC.UK>]

> &: I have thought that {ro da poi kea broda cu brode} and {ro broda cu
> brode} both give "Ax: broda(x) -> brode(x)" - with neither entailing
> "Ex broda(x)". I assumed that it is in emulation of nat lang syntax
> rather than predicate logic that these forms are used in preference to a
> form with logical connectives (ganai...gi).
> pc: Well, _ro broda cu brode_ is both natural language and traditional
> logic (and more advanced modern logic) form for a quantifier which
> regularly in both those areas has existential import (implies there are
> brodas) but is generally agreed not to be existentially importing in
> Lojban. _ro da poi broda cu brode_  was devised to give a form with
> exstential import and fits nicely into the pattern of restricting the
> possibilities of what the sumti modified by _poi_ can be used for.
> However, its official status is now in some doubt and at least xorxes
> regularly asserted that it had no existential import.  In any case,
> Ex:Fx => Gx does not imply ExFx (nor ExGx).
> &: It would be helpful if you would indicate what logical form
> corresponds to {ro da poi kea broda} and {ro broda}.
> pc: Like so much of logical form representation, that for restricted
> (or binary) quantifiers is not standardized. The basic idea is apparent
> in (Ax: x broda)x, a quantifier on x, restricted for values to brodas,
> and what I take _ro da poi broda_ to represent.

This is maybe the source of the problem. I, and evidently most
others among us, but not you, have believed that "all men are mortal"
(and its jbobau equivalents, {ro prenu}, {ro da poi kea prenu})
means "Ax if x is a man then x is mortal", whereas for you it
means something like "In a subworld containing only men, everything
is mortal", "restricting our attention to individuals that are men,
every individual is mortal".

In summary: The real dispute between you & the rest of lojbania
is not about whether "(Ax Fx) -> (Ex Fx)" is true (I am willing to
accept that it is). Rather, the dispute is about whether lojban
quantification is restricted or unrestricted: you say it is
restricted, and the rest of lojbania says it is unrestricted.

Why you are not happy with unrestricted quantification, I don't know.
(It's not as though there was no way to do universal with existential
import - {ro lo suo} does that.)

> &: If you don't get your way, it's more likely due to people not
> understanding you than to them not deferring to you. (But,
> undeferentially I opine that I'm glad you didn't get your way on
> the matter you rue so.)
> pc: I have no evidence that anyone failed to understand my point
> about the universal quantifier -- a matter that they could check in
> a couple of minutes with a logic book -- yet in over two years you
> are the first person to admit that I was right (if that is what you
> did, rather than just stop arguing but going on as before).

I think it's likely that people who thought they were arguing with
you about existential import were in reality arguing about restricted
quantifiers. - That is, there really was a communication failure.

coo, mie and