Re: [lojban] Individuals and xorlo

On Sat, Feb 15, 2014 at 10:45 AM, guskant <gusni.kantu@gmail.com> wrote:

Le samedi 15 février 2014 10:55:19 UTC+9, xorxes a écrit :

On Fri, Feb 14, 2014 at 8:36 PM, guskant <gusni...@gmail.com> wrote:

It is because the following proposition is given as an axiom in the universe of discourse (UD1) on the current topic.
P1:
ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

From P1 I get "no da me lo sidbo".

If another axiom that is equivalent to P3 were given on UD1, yes, we would get "no da me lo sidbo". However, we did not give P3 or the equivalent as an axiom on UD1.

Why doesn't "no da me lo sidbo" follow directly from just P1?

Suppose "no da me lo sidbo" is false. Then "su'o da me lo sidbo" is true. Then "su'oi da poi ke'a me lo sidbo ku'o no'oi de zo'u de me da ijenai da me de", which contradicts P1. So under P1, "no da me lo sidbo" must be true.

Here is the proof of P2.

Yes, sorry, P2 does follow from P1. I was confused about something else. P2 says that lo sidbo is not a single individual. But from P1 you can derive a stronger theorem, not just that lo sidbo is not one individual, but also that there are no individuals at all among lo sidbo.

Moreover, it is also proved that {lo sidbo} is not individuals using a property of jo'u:

Indeed, that follows from P1, but not just from P2. I was slightly confused because P2 is too weak for what I thought you were saying, which is that lo sidbo is not one or more individuals.

I understand that giving an axiom
{ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da}

(for all X there is Y such that Y is individual and Y {me} X)
is very useful, and also necessary for conforming to mereology with atoms.

Still, we cannot assert this proposition to be a common axiom to all the universes of discourse, because

"Something that needs to be noted in general: we, the BPFK, made a consensus decision that we do not make rulings on ontological or metaphysical issues."
http://www.lojban.org/tiki/How+to+use+xorlo

(That page has a few of strange assertions, so I would take it with a grain of salt, but I agree about not making rulings on ontological or metaphysical issues.)

Asserting "ro'oi da su'oi de" as a common axiom is indeed an ontological commitment, and violates the principle of xorlo.

I'm not necessarily disagreeing with you. I'm just curious about what are the things you could say that don't involve individuals. What type of discourse would you analyse as taking place in a universe without individuals?

mu'o mi'e xorxes