WikiDiscuss

> "-F" (and "F-") – distributive predication ("collective predication,"
> including personal predication for individuals, is the norm),
> "F*" – "participates in Fing."

I suppose you would also need to distinguish "*F" from "F*",
"participates in Fing" from "participates in being F-ed".

I think that would be the best way of marking distributivity. Marking
it on the sumti is not very convenient because we sometimes want
to use the same sumti filling a distributive place for one predicate
and a collective one for another, or because it is cnvenient for
anaphora to have as antecedent a sumti that is neutral with respect
to distributivity.

Unfortunately, in Lojban this way of marking distributivity is complicated,
because Lojban predicates don't normally have just two arguments, but
they can have any number of arguments. So where does one put the
mark?

Perhaps a practical solution would be to put the distributive mark
as a selbri-tcita when it corresponds to the x1, and on the corresponding
sumti in other cases. This is not the most elegant way of doing it, but
because the x1 is the most likely sumti to be shared by more than one
selbri, it would at least cover the most cases.

mu'o mi'e xorxes

Posted by pycyn on Mon 28 of Nov, 2005 04:49 GMT posts: 2388

> > "-F" (and "F-") – distributive predication
> ("collective predication,"
> > including personal predication for
> individuals, is the norm),
> > "F*" – "participates in Fing."
>
> I suppose you would also need to distinguish
> "*F" from "F*",
> "participates in Fing" from "participates in
> being F-ed".

Good point. If the second place is collective
then there must be participation notion there as
well. So, like dash, star goes more with the
argument than the predicate (though sometimes
with the predicate, apparently). Notation needs
some work here.

> I think that would be the best way of marking
> distributivity. Marking
> it on the sumti is not very convenient because
> we sometimes want
> to use the same sumti filling a distributive
> place for one predicate
> and a collective one for another, or because it
> is convenient for
> anaphora to have as antecedent a sumti that is
> neutral with respect
> to distributivity.

Well, sometimes we also want a predicate taking
one argument collectively and the other
distributively at the same place. As I said, the
notation needs some work here, lathough these are
actualy problems for applications, not for the
pure system, which lacks non-sentential
conjunctions.

> Unfortunately, in Lojban this way of marking
> distributivity is complicated,
> because Lojban predicates don't normally have
> just two arguments, but
> they can have any number of arguments. So where
> does one put the
> mark?

With the argument generally - except in the cases
noted. that is, after all how Lojban does it
(with {lV} vs. {lVi}. But it lacks devices for
the exception (and for the predication internal a
description). I want to get the formalism right
before I worry too much about any application to
Lojban.

> Perhaps a practical solution would be to put
> the distributive mark
> as a selbri-tcita when it corresponds to the
> x1, and on the corresponding
> sumti in other cases. This is not the most
> elegant way of doing it, but
> because the x1 is the most likely sumti to be
> shared by more than one
> selbri, it would at least cover the most cases.

As noted, Lojban already covers most cases quite
well. The remaining ones are going to take some
novel device in any case. As far as I can see,
some such device is going to be needed whatever
happens with this notion (It appears to have to
be UI or one of the other few "happen anywhere" groups.)

On 11/26/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> So, like dash, star goes more with the
> argument than the predicate (though sometimes
> with the predicate, apparently). Notation needs
> some work here.

I think one could say that it indicates the *manner* in which
an argument fills a place. It is not a property of a sumti
when not filling a place nor of a place when not being filled
by a sumti.

Another interesting system, similar to bunches but different in
one respect, is the system of kinds. Kinds, with the relation
"subkind" for "in", share all the same thesis as bunches except
for this one: "Every bunch breaks down completely into individuals".
For kinds, it is not the case that every kind breaks down completely
into ultimate kinds, where an ultimate kind is a kind that has only
itself as a subkind, i.e. the equivalent of "individual" for bunches.

mu'o mi'e xorxes

Posted by pycyn on Mon 28 of Nov, 2005 04:49 GMT posts: 2388

> On 11/26/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > So, like dash, star goes more with the
> > argument than the predicate (though sometimes
> > with the predicate, apparently). Notation
> needs
> > some work here.
>
> I think one could say that it indicates the
> *manner* in which
> an argument fills a place. It is not a property
> of a sumti
> when not filling a place nor of a place when
> not being filled
> by a sumti.

I'm not sure what the practical upshot of this is
for either the theory or Lojban but it is
essentially correct metaphysically. It seems to
suggest the detached (UIish)marker, part of
neither component. The fit of theory and Lojban
is not very good at present. In Lojban the
predication is neutral, with the differentiation
being only in the gadri, with {lV} also be
neutral except when differntiation is needed,
when it becomes distributive just by not being
{lVi}. In the thory the basic predication is
collective; neutral is achieved by disjunction.
But the bunch is the same whether predicated of
distributively or collectively.

> Another interesting system, similar to bunches
> but different in
> one respect, is the system of kinds. Kinds,
> with the relation
> "subkind" for "in", share all the same thesis
> as bunches except
> for this one: "Every bunch breaks down
> completely into individuals".
> For kinds, it is not the case that every kind
> breaks down completely
> into ultimate kinds, where an ultimate kind is
> a kind that has only
> itself as a subkind, i.e. the equivalent of
> "individual" for bunches.

I'm not sure that it will work out that there are
kinds that do not break down into subkinds. The
tendency to dichotomize is pretty strong after
all. I can't think of a real case, anyhow. Of
course, this does require in some cases, taking
individuals as infima species (a hallowed
practice).

On 11/27/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> I'm not sure that it will work out that there are
> kinds that do not break down into subkinds. The
> tendency to dichotomize is pretty strong after
> all. I can't think of a real case, anyhow.

I was thinking of special abstract things like the number seven.
Any kind of seven is seven, at least from some point
of view.

More normal kinds can be refined indefinitely:
dogs > fat dogs > fat ugly dogs > fat ugly dogs that bark > fat
ugly dogs that bark at trees > ...

> Of
> course, this does require in some cases, taking
> individuals as infima species (a hallowed
> practice).

Not sure what that means.

The natural numbers greater than one follow the same rules
as bunches, with "+" being the product and "in" being "is a divisor of".
Then the primes are the individuals and "every bunch breaks down
completely into individuals". Kinds are more like the real numbers.

mu'o mi'e xorxes

Posted by pycyn on Mon 28 of Nov, 2005 04:49 GMT posts: 2388

> On 11/27/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > I'm not sure that it will work out that there
> are
> > kinds that do not break down into subkinds.
> The
> > tendency to dichotomize is pretty strong
> after
> > all. I can't think of a real case, anyhow.
>
> I was thinking of special abstract things like
> the number seven.
> Any kind of seven is seven, at least from some
> point
> of view.

I don't think I follow this. The number seven is
a kind in that there is a natural seven and a
rational one and a real one and so on, but that
seems to be breaking down in ultimate kinds,
pretty much any way you extend the list. And of
course anything is some subkind is also a thing
of the kind itself. So I have missed the point
here.

> More normal kinds can be refined indefinitely:
> dogs > fat dogs > fat ugly dogs > fat ugly dogs
> that bark > fat
> ugly dogs that bark at trees > ...

No, at a certain point you get down to
individuals and, although they can be specified
in a variety of ways, it is not clear that they
are new kinds ("kind" is ambiguous between
intensional and extensional versions; I suppose
you mean this as inrtensional). In any case, the
fact that it can be divide indefinitely only
complicates the claim that we always get to the
bottom; it does not deny it.

> > Of
> > course, this does require in some cases,
> taking
> > individuals as infima species (a hallowed
> > practice).
>
> Not sure what that means.

At the bottom level, the next lowest kind has
only individuals as subkinds, each "one of a
kind." But some might object to taking
individuals as kinds. In that case the lowest
kinds would have no subkinds and so are the
sought lowest level into which the kind divides.
I gather I am still missing your point.

> The natural numbers greater than one follow the
> same rules
> as bunches, with "+" being the product and "in"
> being "is a divisor of".
> Then the primes are the individuals and "every
> bunch breaks down
> completely into individuals". Kinds are more
> like the real numbers.

I do hope this is true, relative consistency
proofs using set theory are always a bit chancey.
But I still don't get the kinds claim: it would
seem that every number is then "in" every other
and so there are no individuals. But the bit
about every number being in every number tells me
that the characterization of kinds is incomplete,
for it is not in any sense fitting that every
kind should be a subkind of every kind. At
least, I don't know of a notion of kinds in which
this would happen. Still missing the point?

On 11/27/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
> > I was thinking of special abstract things like
> > the number seven.
> > Any kind of seven is seven, at least from some
> > point
> > of view.
>
> I don't think I follow this. The number seven is
> a kind in that there is a natural seven and a
> rational one and a real one and so on,

That's why I hedged "at least from some point of view".
If natural sevens, rational sevens and real sevens are
different kinds of sevens, then obviously sevens are not
an ultimate kind.

> but that
> seems to be breaking down in ultimate kinds,
> pretty much any way you extend the list.

I'm not sure that if sevens can differ like that then
natural sevens won't in turn be able to differ in some other
way, but it doesn't really matter.

> And of
> course anything is some subkind is also a thing
> of the kind itself. So I have missed the point
> here.

The point was that the restriction "every bunch breaks down
completely into individuals" for the system of bunches is an
independent restriction of all the other thesis listed, it doesn't
follow from them but must be imposed. There are systems
where it need not hold.

(I said that whereas it may be the case that *some* kinds
might break down completely into ultimate kinds, not all kinds
do. "Sevens" or "naturals sevens" *might* be an example of
ultimate kinds, or perhaps there are no ultimate kinds, depending
on your point of view. But whether or not sevens or natural sevens
are ultimate kinds, not all kinds break down completely into ultimate
kinds.)

> ("kind" is ambiguous between
> intensional and extensional versions; I suppose
> you mean this as inrtensional).

Yes.

> In any case, the
> fact that it can be divide indefinitely only
> complicates the claim that we always get to the
> bottom; it does not deny it.

You can impose it as an additional condition, but it does
not follow from the rest of the thesis.

> At the bottom level, the next lowest kind has
> only individuals as subkinds, each "one of a
> kind."

That is, if you assume there is a bottom level.

> But some might object to taking
> individuals as kinds. In that case the lowest
> kinds would have no subkinds and so are the
> sought lowest level into which the kind divides.
> I gather I am still missing your point.

My point is that you need not assume a bottom level.

> > The natural numbers greater than one follow the
> > same rules
> > as bunches, with "+" being the product and "in"
> > being "is a divisor of".
> > Then the primes are the individuals and "every
> > bunch breaks down
> > completely into individuals". Kinds are more
> > like the real numbers.
>
> I do hope this is true, relative consistency
> proofs using set theory are always a bit chancey.
> But I still don't get the kinds claim: it would
> seem that every number is then "in" every other
> and so there are no individuals.

Well, I was keeping the "greater than one" restriction, so
every number is "in" every number greater than or equal to
itself. And indeed this is an example where there are no
individuals, there is no bottom level.

mu'o mi'e xorxes

Posted by pycyn on Mon 28 of Nov, 2005 19:38 GMT posts: 2388

> On 11/27/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge Llambías <jjllambias@gmail.com>
> wrote:
> > > I was thinking of special abstract things
> like
> > > the number seven.
> > > Any kind of seven is seven, at least from
> some
> > > point
> > > of view.
> >
> > I don't think I follow this. The number seven
> is
> > a kind in that there is a natural seven and a
> > rational one and a real one and so on,
>
> That's why I hedged "at least from some point
> of view".
> If natural sevens, rational sevens and real
> sevens are
> different kinds of sevens, then obviously
> sevens are not
> an ultimate kind.

But natural sevens, real sevens, and rational
sevens might be.

> > but that
> > seems to be breaking down in ultimate kinds,
> > pretty much any way you extend the list.
>
> I'm not sure that if sevens can differ like
> that then
> natural sevens won't in turn be able to differ
> in some other
> way, but it doesn't really matter.
>
> > And of
> > course anything is some subkind is also a
> thing
> > of the kind itself. So I have missed the
> point
> > here.
>
> The point was that the restriction "every bunch
> breaks down
> completely into individuals" for the system of
> bunches is an
> independent restriction of all the other thesis
> listed, it doesn't
> follow from them but must be imposed. There are
> systems
> where it need not hold.

Ahah! Yes, I think that that is true, though I
don't think your remarks prove it. And ordinary
system of intensional kinds might work for this
however, either a poset or some sort of nexus
(where a memger could fall under two or more
members which are not directly related) and then
the possibility of infinitely subdividing would
keep generating new sets. But that might also
mean that the set of individuals was infinite,
not empty. It doesn't quite work yet.

>
> > In any case, the
> > fact that it can be divide indefinitely only
> > complicates the claim that we always get to
> the
> > bottom; it does not deny it.
>
> You can impose it as an additional condition,
> but it does
> not follow from the rest of the thesis.

Well, of course, that is something one wants of
one's axioms (which I suppose this must be then):
that they are independent of other axioms. I
hope that turns out to be true for all of them
(if I ever get around to sorting out the theses
into various types.

> > At the bottom level, the next lowest kind has
> > only individuals as subkinds, each "one of a
> > kind."
>
> That is, if you assume there is a bottom level.

Well, it turns out I was taking extensional kinds
as my model and that does make a difference. The
bottom level is more obviously the case here --
though I think it always is for anything that
really might be called a kinds. I await a
contrary case, but won't be either surprised or
dismayed if one turns up, since my interest is
not in kinds (about whivh I haven't given much
thought) but about bunches, which I think I am
close to defining.

> > But some might object to taking
> > individuals as kinds. In that case the lowest
> > kinds would have no subkinds and so are the
> > sought lowest level into which the kind
> divides.
> > I gather I am still missing your point.
>
> My point is that you need not assume a bottom
> level.
>
> > > The natural numbers greater than one follow
> the
> > > same rules
> > > as bunches, with "+" being the product and
> "in"
> > > being "is a divisor of".
> > > Then the primes are the individuals and
> "every
> > > bunch breaks down
> > > completely into individuals".

Well, it turns out they aren't. The model
disconfirms a+a=a at least.

>>> Kinds are
> more
> > > like the real numbers.
> >
> > I do hope this is true, relative consistency
> > proofs using set theory are always a bit
> chancey.

But alas this does not help in that matter.

> > But I still don't get the kinds claim: it
> would
> > seem that every number is then "in" every
> other
> > and so there are no individuals.
>
> Well, I was keeping the "greater than one"
> restriction,

What restriction is that? We are looking only at
real numbers (strictly?) greater than 1. But
that does in no way take away from the fact that
every one divides every one. I suppose you mean
that the quotient in such a division has to be
greater than one (or, apparently, one or greater)
This will get an ordering and, of course, since
there are no least real greater than 1 (I think
this needs "strictly greater") there are no
individuals, but the result is not very plausibly
called a system of kinds, I don't think.
>so
> every number is "in" every number greater than
> or equal to
> itself. And indeed this is an example where
> there are no
> individuals, there is no bottom level.

But also no idempotence (is that the word I want?
a+a=a) and probably not asymmetry: a in b & b in
a => a=b, as this will dramatically reduce the
number of kinds (and, indeed, give individuals).
So it is still not the proof of independence that
is wanted.

On 11/28/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
> > The point was that the restriction "every bunch
> > breaks down
> > completely into individuals" for the system of
> > bunches is an
> > independent restriction of all the other thesis
> > listed, it doesn't
> > follow from them but must be imposed. There are
> > systems
> > where it need not hold.
>
> Ahah! Yes, I think that that is true, though I
> don't think your remarks prove it.

Well, I guess you would first need to present it as a fomal
thesis before a formal proof that it is not a theorem could
be given.

> > > > The natural numbers greater than one follow
> > the
> > > > same rules
> > > > as bunches, with "+" being the product and
> > "in"
> > > > being "is a divisor of".
> > > > Then the primes are the individuals and
> > "every
> > > > bunch breaks down
> > > > completely into individuals".
>
> Well, it turns out they aren't. The model
> disconfirms a+a=a at least.

Hmm, right. To have that property, take all the powers of a prime

For the case with no individuals you can take for example
the open sets on the real line, with union as "+".

mu'o mi'e xorxes

Posted by pycyn on Tue 29 of Nov, 2005 00:09 GMT posts: 2388

> On 11/28/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge Llambías <jjllambias@gmail.com>
> wrote:
> > > The point was that the restriction "every
> bunch
> > > breaks down
> > > completely into individuals" for the system
> of
> > > bunches is an
> > > independent restriction of all the other
> thesis
> > > listed, it doesn't
> > > follow from them but must be imposed. There
> are
> > > systems
> > > where it need not hold.
> >
> > Ahah! Yes, I think that that is true, though
> I
> > don't think your remarks prove it.
>
> Well, I guess you would first need to present
> it as a fomal
> thesis before a formal proof that it is not a
> theorem could
> be given.

My point is that the system presented differs
from mine in more than the one axiom and so can't
prove independence of that axiom.

> > > > > The natural numbers greater than one
> follow
> > > the
> > > > > same rules
> > > > > as bunches, with "+" being the product
> and
> > > "in"
> > > > > being "is a divisor of".
> > > > > Then the primes are the individuals and
> > > "every
> > > > > bunch breaks down
> > > > > completely into individuals".
> >
> > Well, it turns out they aren't. The model
> > disconfirms a+a=a at least.
>
> Hmm, right. To have that property, take all the
> powers of a prime

But your countercase is about the reals; what
would be the corresponding move there?

> For the case with no individuals you can take
> for example
> the open sets on the real line, with union as
> "+".

Nice; that does look to give a case that fits all
the theses so far developed except the foundation
one and what follows from it. But it still has
nothing to do with bunches which are conceptually
exactly founded in the way stated: a bunch is a
bunch of things and when you get down to the
things that is the end of the process (actually a
step before, since in some versions unit bunches
are the singleton of the thing, not the thing
itself — but the thing is a member, not in in
the relevant sense, which tends to be like
inclusion in these versions). Can you think if a
Lojbanically relevant use for kinds, those
unfounded critters?

On 11/28/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
> > For the case with no individuals you can take
> > for example
> > the open sets on the real line, with union as
> > "+".
>
> Nice; that does look to give a case that fits all
> the theses so far developed except the foundation
> one and what follows from it. But it still has
> nothing to do with bunches which are conceptually
> exactly founded in the way stated: a bunch is a
> bunch of things and when you get down to the
> things that is the end of the process (actually a
> step before, since in some versions unit bunches
> are the singleton of the thing, not the thing
> itself — but the thing is a member, not in in
> the relevant sense, which tends to be like
> inclusion in these versions).

That's clear, yes.

Can you think if a
> Lojbanically relevant use for kinds, those
> unfounded critters?

Certainly. (Intensional) kinds for example. Stages of individuals
would be another.

mu'o mi'e xorxes

Posted by pycyn on Wed 30 of Nov, 2005 00:34 GMT posts: 2388

> On 11/28/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:

>
> Can you think if a
> > Lojbanically relevant use for kinds, those
> > unfounded critters?
>
> Certainly. (Intensional) kinds for example.
> Stages of individuals
> would be another.

1. I don't see anything bpeculiarly or
immediately Lojbanic in these but it would be
intersting to see something along that line.

2. Neither kinds nor stages of individuals seems
to me to be like the real line in the relevant
ways. Kinds have infima species, complete
analytic heceities — individual concepts — in
one direction, and complete state descriptions in
the other, both of which become contradictory if
further modified (of course, you may want to
allow contradictory kinds, but even those have
lower bounds). These are, of course, infinitely
complex and so unlikely to be of much use, but
the theory does allow them (indeed, I suspect
that their existence can be proven in a usual
formal system). As for stages, that will only
work if time is really continuous, but it seems
that it is discrete (or is that discreet?) though
-- calculus being what it is — taking it as
continuous is usally a nice shortcut.

On 11/29/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> 2. Neither kinds nor stages of individuals seems
> to me to be like the real line in the relevant
> ways.

It depends on what you take to be *the* relevant ways, I suppose.
In the only way I claimed them to be alike is in their satisfying
all of the listed thesis except for the one about breaking down
completely into individuals.

...
> As for stages, that will only
> work if time is really continuous, but it seems
> that it is discrete (or is that discreet?) though
> — calculus being what it is — taking it as
> continuous is usally a nice shortcut.

Yes. Whether or not time is really continuous is not
important from the language point of view. All that
matters is that it can be taken as continuous. Lojban
certainly supports this view, implicit for example in the
word {ru'i}.

mu'o mi'e xorxes

Posted by pycyn on Wed 30 of Nov, 2005 14:48 GMT posts: 2388

> On 11/29/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > 2. Neither kinds nor stages of individuals
> seems
> > to me to be like the real line in the
> relevant
> > ways.
>
> It depends on what you take to be *the*
> relevant ways, I suppose.
> In the only way I claimed them to be alike is
> in their satisfying
> all of the listed thesis except for the one
> about breaking down
> completely into individuals.

Cases?

> ...
> > As for stages, that will only
> > work if time is really continuous, but it
> seems
> > that it is discrete (or is that discreet?)
> though
> > — calculus being what it is — taking it as
> > continuous is usally a nice shortcut.
>
> Yes. Whether or not time is really continuous
> is not
> important from the language point of view. All
> that
> matters is that it can be taken as continuous.
> Lojban
> certainly supports this view, implicit for
> example in the
> word {ru'i}.

Well, {ru'i} doesn't seem to have anything to do
with the cntinuum; it merely means "without
significant interruption" "whenever there is an
occasion" even.

On 11/30/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
>
> > On 11/29/05, John E Clifford
> > <clifford-j@sbcglobal.net> wrote:
> > > 2. Neither kinds nor stages of individuals
> > seems
> > > to me to be like the real line in the
> > relevant
> > > ways.
> >
> > It depends on what you take to be *the*
> > relevant ways, I suppose.
> > In the only way I claimed them to be alike is
> > in their satisfying
> > all of the listed thesis except for the one
> > about breaking down
> > completely into individuals.
>
> Cases?

Cases of what?

> Well, {ru'i} doesn't seem to have anything to do
> with the cntinuum; it merely means "without
> significant interruption" "whenever there is an
> occasion" even.

So you take time to be *linguistically* discrete? Interesting.

mu'o mi'e xorxes

Posted by pycyn on Wed 30 of Nov, 2005 17:03 GMT posts: 2388

> On 11/30/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge Llambías <jjllambias@gmail.com>
> wrote:
> >
> > > On 11/29/05, John E Clifford
> > > <clifford-j@sbcglobal.net> wrote:
> > > > 2. Neither kinds nor stages of
> individuals
> > > seems
> > > > to me to be like the real line in the
> > > relevant
> > > > ways.
> > >
> > > It depends on what you take to be *the*
> > > relevant ways, I suppose.
> > > In the only way I claimed them to be alike
> is
> > > in their satisfying
> > > all of the listed thesis except for the one
> > > about breaking down
> > > completely into individuals.
> >
> > Cases?
>
> Cases of what?

Things we might really use that satisfy all the
theses not tied with foundation.
>
> > Well, {ru'i} doesn't seem to have anything to
> do
> > with the continuum; it merely means "without
> > significant interruption" "whenever there is
> an
> > occasion" even.
>
> So you take time to be *linguistically*
> discrete? Interesting.

Well, I didn't say so; I just made a comment
about {ru'i}, which seems to me to say nothing
about the nature of time. But, so far as I can
tell, Lojban at least (but I think English too)
treats time as discrete in most situations --
other than certain kinds of scientific talk,
perhaps.

temci tem tei time x1 is the
time-duration/interval/period/elapsed time from
time/event x2 to time/event x3

It comes in chunks.

On 11/30/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
> > On 11/30/05, John E Clifford
> > <clifford-j@sbcglobal.net> wrote:
> > > --- Jorge Llambías <jjllambias@gmail.com>
> > wrote:
> > >
> > > > On 11/29/05, John E Clifford
> > > > <clifford-j@sbcglobal.net> wrote:
> > > > > 2. Neither kinds nor stages of
> > individuals
> > > > seems
> > > > > to me to be like the real line in the
> > > > relevant
> > > > > ways.
> > > >
> > > > It depends on what you take to be *the*
> > > > relevant ways, I suppose.
> > > > In the only way I claimed them to be alike
> > is
> > > > in their satisfying
> > > > all of the listed thesis except for the one
> > > > about breaking down
> > > > completely into individuals.
> > >
> > > Cases?
> >
> > Cases of what?
>
> Things we might really use that satisfy all the
> theses not tied with foundation.

Dogs, unicorns, events of running, theories, lies, all kinds of things.

> > > Well, {ru'i} doesn't seem to have anything to
> > do
> > > with the continuum; it merely means "without
> > > significant interruption" "whenever there is
> > an
> > > occasion" even.
> >
> > So you take time to be *linguistically*
> > discrete? Interesting.
>
> Well, I didn't say so; I just made a comment
> about {ru'i}, which seems to me to say nothing
> about the nature of time.

Oh, I agree. It only says something about how time
is dealt with linguistically, not about its nature.

> But, so far as I can
> tell, Lojban at least (but I think English too)
> treats time as discrete in most situations --
> other than certain kinds of scientific talk,
> perhaps.

So when you ask how long something took, you expect
some number of indivisible chunks as an answer?

> temci tem tei time x1 is the
> time-duration/interval/period/elapsed time from
> time/event x2 to time/event x3
>
> It comes in chunks.

I always thought x1 of temci was a continuous interval
rather than a (very large?) number of (very small?) chunks.

If you mean that the x1 is one chunk, then the system of
time chunks seems to satisfy all the theses not tied with
foundation.

mu'o mi'e xorxes

Posted by pycyn on Thu 01 of Dec, 2005 16:55 GMT posts: 2388

> On 11/30/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge Llambías <jjllambias@gmail.com>
> wrote:
> > > On 11/30/05, John E Clifford
> > > <clifford-j@sbcglobal.net> wrote:
> > > > --- Jorge Llambías <jjllambias@gmail.com>
> > > wrote:
> > > >
> > > > > On 11/29/05, John E Clifford
> > > > > <clifford-j@sbcglobal.net> wrote:
> > > > > > 2. Neither kinds nor stages of
> > > individuals
> > > > > seems
> > > > > > to me to be like the real line in the
> > > > > relevant
> > > > > > ways.
> > > > >
> > > > > It depends on what you take to be *the*
> > > > > relevant ways, I suppose.
> > > > > In the only way I claimed them to be
> alike
> > > is
> > > > > in their satisfying
> > > > > all of the listed thesis except for the
> one
> > > > > about breaking down
> > > > > completely into individuals.
> > > >
> > > > Cases?
> > >
> > > Cases of what?
> >
> > Things we might really use that satisfy all
> the
> > theses not tied with foundation.
>
> Dogs, unicorns, events of running, theories,
> lies, all kinds of things.
>
I'm not sure whether you, the at least occasional
champion of contextual relevance, have here
brought in some totally irrelevant set of theses
or whether you have some (unnamed) relation and
operator for each of these sets that satisfies
all the theses for "in" and "+" on the Bunches
page, except those that rest on the foundation
thesis. I can't think what those relations and
operators might be: the obvious ones for dogs and
and lies - packs — and for unicorns — herds --
all seem to be founded, that is, get down
eventually to individual dogs or lies or
unicorns (lies may not be order-irrelevant, that
is may fail symmetry).

> > > > Well, {ru'i} doesn't seem to have
> anything to
> > > do
> > > > with the continuum; it merely means
> "without
> > > > significant interruption" "whenever there
> is
> > > an
> > > > occasion" even.
> > >
> > > So you take time to be *linguistically*
> > > discrete? Interesting.
> >
> > Well, I didn't say so; I just made a comment
> > about {ru'i}, which seems to me to say
> nothing
> > about the nature of time.
>
> Oh, I agree. It only says something about how
> time
> is dealt with linguistically, not about its
> nature.

Nothing even linguistically. And if it did, it
would say that time is not even dense, let alone
analogous to the real line, since ti says that
there is nothing between two occurrences of the
event called continuous. As for other linguistic
evidence, we note that we have concepts like
"next," {lamji} which clearly apply to time and
suggest a well-ordering, not even a dense one
again.

> > But, so far as I can
> > tell, Lojban at least (but I think English
> too)
> > treats time as discrete in most situations --
> > other than certain kinds of scientific talk,
> > perhaps.
>
> So when you ask how long something took, you
> expect
> some number of indivisible chunks as an answer?

Yup — and that is what I get: a day, a second,
3.5 nanoseconds, and so on. Always with a unit
(by definition in Lojban's case) and always with
a discrete total. I suppose it is conceivable
that someone say "root 2 seconds" but I would
take that to be some sort of scientific talk,
since I don't see how he would have measured it.

> > temci tem tei time
> x1 is the
> > time-duration/interval/period/elapsed time
> from
> > time/event x2 to time/event x3
> >
> > It comes in chunks.
>
> I always thought x1 of temci was a continuous
> interval
> rather than a (very large?) number of (very
> small?) chunks.

That is about what it is scientifically, perhaps,
but not linguistically, where the answer is
always in terms of (variously sized) chunks.

> If you mean that the x1 is one chunk, then the
> system of
> time chunks seems to satisfy all the theses not
> tied with
> foundation.

Well, the system of sizes of time chunks is
probably dense (not a continuum. since the lower
bound is outside the system, not being an
interval). But on any given occasion the answer
is linguistically in terms of some unit.
Scientifically, this may be an approximation, but
we were after the linguistic facts here, not the
scientific.

I am not quite sure how we got off on this
intersting but so far rather useless discussion
(nor do I care). So, back to the point: any
additional theses that seemed to be required for
bunches? Any surprising consequences of these
theses — particularly ones that show the set
inconsistent? Independence proofs for anything
other than the foundation thesis?

On 12/1/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
> > On 11/30/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> > > Things we might really use that satisfy all the
> > > theses not tied with foundation.
> >
> > Dogs, unicorns, events of running, theories,
> > lies, all kinds of things.
> >
> I'm not sure whether you, the at least occasional
> champion of contextual relevance, have here
> brought in some totally irrelevant set of theses

No, just the ones you have listed.

> or whether you have some (unnamed) relation and
> operator for each of these sets that satisfies
> all the theses for "in" and "+" on the Bunches
> page, except those that rest on the foundation
> thesis.

No, not any unnamed relation, just the "subkind" relation
I named the first time I mentioned kinds.

> > > > > Well, {ru'i} doesn't seem to have anything to do
> > > > > with the continuum; it merely means "without
> > > > > significant interruption" "whenever there is an
> > > > > occasion" even.
>
> Nothing even linguistically. And if it did, it
> would say that time is not even dense, let alone
> analogous to the real line, since ti says that
> there is nothing between two occurrences of the
> event called continuous.

Why two occurrences? It says something about the one event
being continuous.

> As for other linguistic
> evidence, we note that we have concepts like
> "next," {lamji} which clearly apply to time and
> suggest a well-ordering, not even a dense one
> again.

I don't and never disputed that we often treat time discretely.
{<number> roi} is the clearest example in Lojban for that,
I think. The question at hand is whether or not we sometimes
treat it as if it were continuous (independently of its true
physical nature.)

> > So when you ask how long something took, you
> > expect
> > some number of indivisible chunks as an answer?
>
> Yup — and that is what I get: a day, a second,
> 3.5 nanoseconds, and so on.

You take 3.5 nanoseconds as counting half-nanoseconds?
Otherwise, if nanoseconds are treated as indefinitely divisible,
it sounds as a continuous measure.

And in Lojban it is even more clear, because a duration is
{lo navysnidu be li 3.5} and not {3.5 navysnidu}

> Always with a unit
> (by definition in Lojban's case) and always with
> a discrete total. I suppose it is conceivable
> that someone say "root 2 seconds" but I would
> take that to be some sort of scientific talk,
> since I don't see how he would have measured it.

You take the fact that we don't normally use irrational
numbers as measures as evidence that we consider
things to be discretely (and finitely) divisible? Very
interesting point of view, even if hard to understand.

> > I always thought x1 of temci was a continuous
> > interval
> > rather than a (very large?) number of (very
> > small?) chunks.
>
> That is about what it is scientifically, perhaps,
> but not linguistically, where the answer is
> always in terms of (variously sized) chunks.

No, I'm not talking about it scientifically, I mean in ordinary
contexts. I cannot normally conceive of durations as strings
of little time-chunks. It never occurred to me that others
would think of that as the natural point of view.

> > If you mean that the x1 is one chunk, then the
> > system of
> > time chunks seems to satisfy all the theses not
> > tied with
> > foundation.
>
> Well, the system of sizes of time chunks is
> probably dense (not a continuum. since the lower
> bound is outside the system, not being an
> interval). But on any given occasion the answer
> is linguistically in terms of some unit.
> Scientifically, this may be an approximation, but
> we were after the linguistic facts here, not the
> scientific.

There are many units that measure continuous quantities,
so I don't see how the answer being in terms of a unit
makes it a bunch measure. Especially if you allow fractional
measures!

> I am not quite sure how we got off on this
> intersting but so far rather useless discussion
> (nor do I care). So, back to the point: any
> additional theses that seemed to be required for
> bunches?

It would be nice to have the foundation theses expressed formally.
I'm not quite sure how that would go.

> Any surprising consequences of these
> theses — particularly ones that show the set
> inconsistent?

I can't see anything strange in them.

> Independence proofs for anything
> other than the foundation thesis?

None of the others seem especially noteworthy to me.
The "no empty bunches" is slightly ambiguous. What does
"empty" mean? I take it it does not mean that every bunch
has at least one bunch in it because that follows directly
from every bunch being in itself, so I suppose it means that
for every bunch there is at least one *individual* bunch in it.
I would say this thesis goes closely together with the
foundation one (and it is in fact stated in the same
parenthetical comment).

mu'o mi'e xorxes

Posted by pycyn on Fri 02 of Dec, 2005 05:25 GMT posts: 2388

> On 12/1/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge Llambías <jjllambias@gmail.com>
> wrote:
> > > On 11/30/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > > > Things we might really use that satisfy
> all the
> > > > theses not tied with foundation.
> > >
> > > Dogs, unicorns, events of running,
> theories,
> > > lies, all kinds of things.
> > >
> > I'm not sure whether you, the at least
> occasional
> > champion of contextual relevance, have here
> > brought in some totally irrelevant set of
> theses
>
> No, just the ones you have listed.
>
> > or whether you have some (unnamed) relation
> and
> > operator for each of these sets that
> satisfies
> > all the theses for "in" and "+" on the
> Bunches
> > page, except those that rest on the
> foundation
> > thesis.
>
> No, not any unnamed relation, just the
> "subkind" relation
> I named the first time I mentioned kinds.

But that is 1) not obviously unfounded and 2) not
not obviously connect with the various things you
mentioned. They are all kinds, I suppose, and
have various subkinds. But they are also just
the sorts of things where the subkind relation is
founded on individuals (I am not sure there are
subkinds that are not so founded, outside of
mathematics perhaps).

> > > > > > Well, {ru'i} doesn't seem to have
> anything to do
> > > > > > with the continuum; it merely means
> "without
> > > > > > significant interruption" "whenever
> there is an
> > > > > > occasion" even.
> >
> > Nothing even linguistically. And if it did,
> it
> > would say that time is not even dense, let
> alone
> > analogous to the real line, since ti says
> that
> > there is nothing between two occurrences of
> the
> > event called continuous.
>
> Why two occurrences? It says something about
> the one event
> being continuous.

Yes, but you want to make it say something about
the continuum and that takes looking at pairs of
things (between any two there is another, every
pair of sets contains at least one bound, and so
on).

> > As for other linguistic
> > evidence, we note that we have concepts like
> > "next," {lamji} which clearly apply to time
> and
> > suggest a well-ordering, not even a dense one
> > again.
>
> I don't and never disputed that we often treat
> time discretely.
> {<number> roi} is the clearest example in
> Lojban for that,
> I think. The question at hand is whether or not
> we sometimes
> treat it as if it were continuous
> (independently of its true
> physical nature.)

Well, that is not the apparent question you
raised at the beginning, but of course we do
treat it that way sometimes when we are doing
scientific things. But I doubt that there is a
use of {temci} or other temporal words outside of
specialized contexts that is clearly taking time
as continuous. We tend to measure time and that
gets us into units and definite fractions of
units. At best we take time as continuous when we
think about a thing called "time" rather than
what is happening.

> > > So when you ask how long something took,
> you
> > > expect
> > > some number of indivisible chunks as an
> answer?
> >
> > Yup — and that is what I get: a day, a
> second,
> > 3.5 nanoseconds, and so on.
>
> You take 3.5 nanoseconds as counting
> half-nanoseconds?
> Otherwise, if nanoseconds are treated as
> indefinitely divisible,
> it sounds as a continuous measure.

But they are not indefinitely divided. In any
given case, we stop with fixed fractions of
units. We could, of course, take a more precise
fraction of that unit, but that process cannot go
on indefinitely except in theory. That is, in
theory time is continuous in the mathematical
sense, but in ordinary language we treat it as
discrete, varying the units involved as is
convenient. And it was the latter issue that you
began by raising.

> And in Lojban it is even more clear, because a
> duration is
> {lo navysnidu be li 3.5} and not {3.5
> navysnidu}

Now, that is an interesting point (there was
bound to be one eventually). Lojban doesn't have
units, only measure functions which give raw
numbers. But would we ever say "its duration in
seconds is root 2" as we can say that its length
in inches is? If we can say it (outside of
examples), what does it mean?

> > Always with a unit
> > (by definition in Lojban's case) and always
> with
> > a discrete total. I suppose it is
> conceivable
> > that someone say "root 2 seconds" but I would
> > take that to be some sort of scientific talk,
> > since I don't see how he would have measured
> it.
>
> You take the fact that we don't normally use
> irrational
> numbers as measures as evidence that we
> consider
> things to be discretely (and finitely)
> divisible? Very
> interesting point of view, even if hard to
> understand.

We don't even take advantage of the putative
infinite divisibility of time intervals in the
way we do of space, for example. And, of course
(in both cases) scientific work, when striving
for accuracy, always gets down to units that are
not further divisible.

> > > I always thought x1 of temci was a
> continuous
> > > interval
> > > rather than a (very large?) number of (very
> > > small?) chunks.
> >
> > That is about what it is scientifically,
> perhaps,
> > but not linguistically, where the answer is
> > always in terms of (variously sized) chunks.
>
> No, I'm not talking about it scientifically, I
> mean in ordinary
> contexts. I cannot normally conceive of
> durations as strings
> of little time-chunks. It never occurred to me
> that others
> would think of that as the natural point of
> view.

I am just going — as I took you to be wanting --
on the linguistic evidence. How you conceive it
may well be influenced by all sorts of things,
but your speech always comes out in chunks, like
the dictionary says.
>
> > > If you mean that the x1 is one chunk, then
> the
> > > system of
> > > time chunks seems to satisfy all the theses
> not
> > > tied with
> > > foundation.
> >
> > Well, the system of sizes of time chunks is
> > probably dense (not a continuum. since the
> lower
> > bound is outside the system, not being an
> > interval). But on any given occasion the
> answer
> > is linguistically in terms of some unit.
> > Scientifically, this may be an approximation,
> but
> > we were after the linguistic facts here, not
> the
> > scientific.
>
> There are many units that measure continuous
> quantities,
> so I don't see how the answer being in terms of
> a unit
> makes it a bunch measure. Especially if you
> allow fractional
> measures!

The point is that you don't use all that
continuity stuff; you just use finitely divided
units (thus giving rise to smaller units: deci,
centi and so on). Now, there may be no
theoretical end to how much smaller the units
are, but we don't pursue that in language; we
take a convenient unit and stick with it (for a
sentence or so at least).

> > I am not quite sure how we got off on this
> > interesting but so far rather useless
> discussion
> > (nor do I care). So, back to the point: any
> > additional theses that seemed to be required
> for
> > bunches?
>
> It would be nice to have the foundation theses
> expressed formally.
> I'm not quite sure how that would go.

How much more formal do you want than that every
bunch breaks down without remainder (or loss)
into individuals? I even wrote it out in
quasi-formal language and will — when I get a
symbolism I am comfortable with — do it again in
that formalism. What is obscure here?

> > Any surprising consequences of these
> > theses — particularly ones that show the set
> > inconsistent?
>
> I can't see anything strange in them.
>
> > Independence proofs for anything
> > other than the foundation thesis?
>
> None of the others seem especially noteworthy
> to me.
> The "no empty bunches" is slightly ambiguous.
> What does
> "empty" mean? I take it it does not mean that
> every bunch
> has at least one bunch in it because that
> follows directly
> from every bunch being in itself, so I suppose
> it means that
> for every bunch there is at least one
> *individual* bunch in it.
> I would say this thesis goes closely together
> with the
> foundation one (and it is in fact stated in the
> same parenthetical comment).

Yes, that sounds about right. Didn't I say that.
It follows from foundation but could be listed
separately if I didn't before.

Posted by xod on Fri 02 of Dec, 2005 05:35 GMT posts: 143

Jorge Llambías wrote:

>On 12/1/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
>
>
>>--- Jorge Llambías <jjllambias@gmail.com> wrote:
>>
>>
>>
>>>I always thought x1 of temci was a continuous
>>>interval
>>>rather than a (very large?) number of (very
>>>small?) chunks.
>>>
>>>
>>That is about what it is scientifically, perhaps,
>>but not linguistically, where the answer is
>>always in terms of (variously sized) chunks.
>>
>>
>
>No, I'm not talking about it scientifically, I mean in ordinary
>contexts. I cannot normally conceive of durations as strings
>of little time-chunks. It never occurred to me that others
>would think of that as the natural point of view.
>
>

It's not. That we generally refer to non-zero intervals of time does not
mean that we treat it as discrete. Those interval endpoints can be
situated anywhere in the timeline, and that means we treat it as
continuous. Furthermore, people refer to instants and moments which have
no duration, like a point in space has no size. A pixel, however, does
have size. And there is no analogous time-pixel in English.

--
username=admin
password=21232f297a57a5a743894a0e4a801fc3

On 12/1/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge Llambías <jjllambias@gmail.com> wrote:
>
> > No, not any unnamed relation, just the
> > "subkind" relation
> > I named the first time I mentioned kinds.
>
> But that is 1) not obviously unfounded and 2) not
> not obviously connect with the various things you
> mentioned. They are all kinds, I suppose, and
> have various subkinds. But they are also just
> the sorts of things where the subkind relation is
> founded on individuals

It's becoming hard for me to tell what the argument is
about here. My claim is that kinds satisfy all the theses
listed except the foundation one, because for the most
part kinds always have proper subkinds.

The individual dog "Fido", for example, would not normally
be taken as a kind of dog. If someone asks "What kind of
dog do you have?", answering "Fido" would be odd.

Whether or not we use individuals in order to form our
conception of kinds is, it seems to me, a separate issue.
Even if it were true in all cases (which seems doubtful), it
does not follow that a system of kinds must include
the foundation thesis.

> But I doubt that there is a
> use of {temci} or other temporal words outside of
> specialized contexts that is clearly taking time
> as continuous. We tend to measure time and that
> gets us into units and definite fractions of
> units. At best we take time as continuous when we
> think about a thing called "time" rather than
> what is happening.

I can only report that I think of the flow of events as
something continuous. Even when watching a movie
for example, even _knowing_ that what I'm seeing is really
a discrete sequence of images, I can't help but seeing
it as something continuous.

> But would we ever say "its duration in
> seconds is root 2" as we can say that its length
> in inches is? If we can say it (outside of
> examples), what does it mean?

I don't think one would normally say that the length
of something in inches is root 2. I don't see much
difference in the way we measure lengths and
durations.

> We don't even take advantage of the putative
> infinite divisibility of time intervals in the
> way we do of space, for example.

I see no significant difference in the way we treat space
and time. In fact cross metaphores are very prevalent.

> > It would be nice to have the foundation theses
> > expressed formally.
> > I'm not quite sure how that would go.
>
> How much more formal do you want than that every
> bunch breaks down without remainder (or loss)
> into individuals? I even wrote it out in
> quasi-formal language and will — when I get a
> symbolism I am comfortable with — do it again in
> that formalism. What is obscure here?

It's not exactly obscure, I can intuitively understand
pretty well what it means. But I see nothing close to
a formalization (of that particular thesis) yet.

xod wrote:
> That we generally refer to non-zero intervals of time does not
> mean that we treat it as discrete. Those interval endpoints can be
> situated anywhere in the timeline, and that means we treat it as
> continuous.

I agree.

> Furthermore, people refer to instants and moments which have
> no duration, like a point in space has no size. A pixel, however, does
> have size. And there is no analogous time-pixel in English.

I think "moments" are sometimes thought of as having duration
("wait a moment" for example) and sometimes as points.
dictionary.com has:

1. A brief, indefinite interval of time.
2. A specific point in time, especially the present time: He is not
here at the moment.

mu'o mi'e xorxes

Jorge Llambías scripsit:

> I don't think one would normally say that the length
> of something in inches is root 2. I don't see much
> difference in the way we measure lengths and
> durations.

The trouble is that "length" is polymorphic; we speak of the measured
length of a physical object (which is a rational interval, like
"10 cm +/- 5%") as well as the calculated or stipulated length of a
mathematical object (which is a single real number). Duration is not
treated symmetrically: we do not talk of the duration of a mathematical
object, so all durations are measured values.

--
I marvel at the creature: so secret and John Cowan
so sly as he is, to come sporting in the pool jcowan@reutershealth.com
before our very window. Does he think that http://www.reutershealth.com
Men sleep without watch all night? --Faramir http://www.ccil.org/~cowan

On 12/2/05, John.Cowan <jcowan@reutershealth.com> wrote:
> The trouble is that "length" is polymorphic; we speak of the measured
> length of a physical object (which is a rational interval, like
> "10 cm +/- 5%") as well as the calculated or stipulated length of a
> mathematical object (which is a single real number). Duration is not
> treated symmetrically: we do not talk of the duration of a mathematical
> object, so all durations are measured values.

I agree that when we measure an object, whether in space or time,
we obtain as a result a rational number, with some explicit or implicit
error. But I don't think this means that we conceive of the object
as consisting of a discrete aggregate of unit objects in whatever
scale we are using. I'm pretty sure I don't anyway.

As for abstractions, it's true that Euclidean space is more
familiar than Minkowski spacetime, and time is not treated
symmetrically with space in important ways, but as far as
continuity goes, I don't really see a difference.

mu'o mi'e xorxes

Posted by pycyn on Fri 02 of Dec, 2005 17:30 GMT posts: 2388

> On 12/1/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge Llambías <jjllambias@gmail.com>
> wrote:
> >
> > > No, not any unnamed relation, just the
> > > "subkind" relation
> > > I named the first time I mentioned kinds.
> >
> > But that is 1) not obviously unfounded and 2)
> not
> > not obviously connect with the various things
> you
> > mentioned. They are all kinds, I suppose,
> and
> > have various subkinds. But they are also
> just
> > the sorts of things where the subkind
> relation is
> > founded on individuals
>
> It's becoming hard for me to tell what the
> argument is
> about here. My claim is that kinds satisfy all
> the theses
> listed except the foundation one, because for
> the most
> part kinds always have proper subkinds.
>
> The individual dog "Fido", for example, would
> not normally
> be taken as a kind of dog. If someone asks
> "What kind of
> dog do you have?", answering "Fido" would be
> odd.
>
> Whether or not we use individuals in order to
> form our
> conception of kinds is, it seems to me, a
> separate issue.
> Even if it were true in all cases (which seems
> doubtful), it
> does not follow that a system of kinds must
> include
> the foundation thesis.

Well, the way I would do kinds — as collocations
of properties, the foundation thesis is, I think,
derivable, since there comes a point when all the
properties are dealt with one way or the other
and those kinds cannot have subkinds other than
themselves. But you may do kinds differently and
that may well give different results. Or you may
exclude transcendental kinds, which takes an
anti-foundation axiom, I think. I said that some
people did not like individuals as infima species
and took you as saying you were not one of those;
I stand corrected.

In any case, this argument is otiose: the issue
was whether ther was a useful system that did not
have the foundation thesis but otherwise was like
bunches and we have that, thank you, in union of
real line segments (well, I am not sure about
useful, but it is surely good enough for the
purpose at hand: showing that tha thesis is
indepndent of the others).

> > But I doubt that there is a
> > use of {temci} or other temporal words
> outside of
> > specialized contexts that is clearly taking
> time
> > as continuous. We tend to measure time and
> that
> > gets us into units and definite fractions of
> > units. At best we take time as continuous
> when we
> > think about a thing called "time" rather than
> > what is happening.
>
> I can only report that I think of the flow of
> events as
> something continuous. Even when watching a
> movie
> for example, even _knowing_ that what I'm
> seeing is really
> a discrete sequence of images, I can't help but
> seeing
> it as something continuous.

But the issue is not how you think of the flow of
events (loading the issue) or what you say in
English or anything other than what is the
linguistic nature of time in Lojban. And the
answer seems to be that time is always in
measurable intervals each immediately preceded
and immediately followed by another interval.
These intervals may be measured to any desired
degree of precision, that is a measure function
in terms of some unit may take a rational number
with any desired sized denominator (not reals
because you cannot measure irrationals nor even
compute them in one dimension). So, the systems
for measuring times are dense, but what they
measure are discrete.
All of which is again largely irrelevant. I did
not claim that time was discrete or even that
Lojban treats time as discrete — that was
attributed to me by xorxes to cover his
misreading of a Lojban word. However, as you
see, the claim that Lojban treats time as
discrete can be carried quite a ways. Whether it
is far enough to give a definitive answe, I am
not sure. And, as I have said before, I don't
really care, since nothing seems to hang on the
answer at the moment.

> > But would we ever say "its duration in
> > seconds is root 2" as we can say that its
> length
> > in inches is? If we can say it (outside of
> > examples), what does it mean?
>
> I don't think one would normally say that the
> length
> of something in inches is root 2. I don't see
> much
> difference in the way we measure lengths and
> durations.

Well the length of a diagonal of a unit square is
root 2. That one comes up a lot.

> > We don't even take advantage of the putative
> > infinite divisibility of time intervals in
> the
> > way we do of space, for example.
>
> I see no significant difference in the way we
> treat space
> and time. In fact cross metaphores are very
> prevalent.

They are in English and that habit has been built
into Lojban, so I suppose that we havce to say
that Lojban treats them the same. But, of
course, Lojban taks space as coming in discrete
chunks, measured rationally (although in two or
more dimension you can compute irrationals so
they can come in as well).
>
> > > It would be nice to have the foundation
> theses
> > > expressed formally.
> > > I'm not quite sure how that would go.
> >
> > How much more formal do you want than that
> every
> > bunch breaks down without remainder (or loss)
> > into individuals? I even wrote it out in
> > quasi-formal language and will — when I get
> a
> > symbolism I am comfortable with — do it
> again in
> > that formalism. What is obscure here?
>
> It's not exactly obscure, I can intuitively
> understand
> pretty well what it means. But I see nothing
> close to
> a formalization (of that particular thesis)
> yet.

As you are fond of saying in similar situations,
what exactly do you want? I hope that, as I do,
you will give a fairly precise answer.

I gather that the point is that there is no
thesis that says directly "Every bunch breaks
down without remainder into individuals" although
(for finite bunches only, admittedly)the
foundation thesis (what I am calling ...) does
amount to that by induction. But even that
presupposes something to induce on and the
symbolism does not yet have that — the depth (or
cardinality) of a bunch. As noted, we could go
over to the corresponding sets and work it out
there but it would be nicer not to have to use
that apparatus. I have a few variant systems
which look promising for getting this point
across (and, if worse comes to worst, I can
always check out the various systems that batches
represent to see how they do it.)

> xod wrote:
> > That we generally refer to non-zero intervals
> of time does not
> > mean that we treat it as discrete. Those
> interval endpoints can be
> > situated anywhere in the timeline, and that
> means we treat it as
> > continuous.
>
> I agree.
No, by defintion thend points are always
immediately adjacent to another event — the
previous and the next. There is no timeline on
which they are laid out; the timeline is in
Lojban (if it can be done at all) an abstraction
from sequences of intervals — the rest is not in
the language but in what is said in the language.

> > Furthermore, people refer to instants and
> moments which have
> > no duration, like a point in space has no
> size. A pixel, however, does
> > have size. And there is no analogous
> time-pixel in English.
>
> I think "moments" are sometimes thought of as
> having duration
> ("wait a moment" for example) and sometimes as
> points.
> dictionary.com has:
>
> 1. A brief, indefinite interval of time.
> 2. A specific point in time, especially the
> present time: He is not
> here at the moment.

In any case, that ia bout English, not Lojban.
There are no time points in Lojban, only
intervals of time.

Posted by pycyn on Fri 02 of Dec, 2005 18:57 GMT posts: 2388

wrote:

> --- Jorge Llambías <jjllambias@gmail.com>
> wrote:

> >
> > > > It would be nice to have the foundation
> > theses
> > > > expressed formally.
> > > > I'm not quite sure how that would go.
> > >
> > > How much more formal do you want than that
> > every
> > > bunch breaks down without remainder (or
> loss)
> > > into individuals? I even wrote it out in
> > > quasi-formal language and will — when I
> get
> > a
> > > symbolism I am comfortable with — do it
> > again in
> > > that formalism. What is obscure here?
> >
> > It's not exactly obscure, I can intuitively
> > understand
> > pretty well what it means. But I see nothing
>

> close to
> a formalization (of that particular thesis)
> yet.

<<As you are fond of saying in similar
situations,
what exactly do you want? I hope that, as I do,
you will give a fairly precise answer.

I gather that the point is that there is no
thesis that says directly "Every bunch breaks
down without remainder into individuals" although
(for finite bunches only, admittedly)the
foundation thesis (what I am calling ...) does
amount to that by induction. But even that
presupposes something to induce on and the
symbolism does not yet have that — the depth (or
cardinality) of a bunch. As noted, we could go
over to the corresponding sets and work it out
there but it would be nicer not to have to use
that apparatus. I have a few variant systems
which look promising for getting this point
across (and, if worse comes to worst, I can
always check out the various systems that batches
represent to see how they do it.)>>

And there is at a very simple level
Ax:x in a x in b => a in b
whence
Ax: x in ax in b & Ay: y in b y in a => a = b

This still may not be totally explicit, but it
does say that all that counts are individuals (if
there are other things they are wholly determined
by the indivuals and we have no other things
offered so far. I suppose we could have an array
of functions, one for each number such that, for
a bunch with n individual members, fn of those
members is also a member (and indeed, to really
work, fi for each i membered subunch). The
functions don't need ever make a difference but
they would mean that technically bunches don't
decompose into individuals without remainder -
not even the bunches called individuals,
apparently. It may be, of course, that what I
called foundations prevents that, since if we
take one individual out (even with its f1) what
remains would not be a bunch in these terms since
it would contain fns for subunches which are no
longer in it. Is that enough?

On 12/2/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> Well, the way I would do kinds — as collocations
> of properties, the foundation thesis is, I think,
> derivable, since there comes a point when all the
> properties are dealt with one way or the other

Do you presuppose that only a finite number of properties
are available? Otherwise, why would there come a point
when all the properties are dealt with?

> But the issue is not how you think of the flow of
> events (loading the issue) or what you say in
> English or anything other than what is the
> linguistic nature of time in Lojban.

Originally the issue was whether or not stages of
individuals constituted an example of a system
without the foundation thesis.

Even reducing the issue to the linguistic nature of time
in Lojban, I am not at all convinced that Lojban treats
time differently than other languages. In my view,
Lojban does not impose a particular conception
of discrete or continuous time on its speakers. Both
views would seem to be available and represented.

> However, as you
> see, the claim that Lojban treats time as
> discrete can be carried quite a ways. Whether it
> is far enough to give a definitive answe, I am
> not sure. And, as I have said before, I don't
> really care, since nothing seems to hang on the
> answer at the moment.

Nothing seems to hang on the answer, true. (Except,
perhaps, the issue of whether stages of individuals
constitute an example of a system without the foundation
thesis, but we already have other examples anyway.)

> > But I see nothing close to
> > a formalization (of that particular thesis) yet.
>
> As you are fond of saying in similar situations,
> what exactly do you want? I hope that, as I do,
> you will give a fairly precise answer.

I don't require anything, really. All I said was that it would
be nice to see that thesis expressed in formal terms, like
all the others in the page, in terms of "in" and "+" and not
in terms of undefined (though intuitively clear) things like
"breaks down completely". But I certainly won't be accusing
you of not making sense if such a formal statement turns
out to be difficult or for whatever reason inconvenient.

> > xod wrote:
> > > That we generally refer to non-zero intervals
> > of time does not
> > > mean that we treat it as discrete. Those
> > interval endpoints can be
> > > situated anywhere in the timeline, and that
> > means we treat it as
> > > continuous.
> >
> > I agree.
> No, by defintion thend points are always
> immediately adjacent to another event — the
> previous and the next. There is no timeline on
> which they are laid out; the timeline is in
> Lojban (if it can be done at all) an abstraction
> from sequences of intervals — the rest is not in
> the language but in what is said in the language.

Couldn't {ze'e} be pretty much a representation of the
timeline?

> > 1. A brief, indefinite interval of time.
> > 2. A specific point in time, especially the
> > present time: He is not here at the moment.
>
> In any case, that ia bout English, not Lojban.
> There are no time points in Lojban, only
> intervals of time.

What about {mokca}:

mokca moc point ; 'moment'
x1 is a point/instant/moment 0-dimensional shape/form
in/on/at time/place x2
x1 is dimensionless; (cf. jipno, jganu, linji, stuzi, tcika)

mu'o mi'e xorxes

On 12/2/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> And there is at a very simple level
> Ax:x in a x in b => a in b
> whence
> Ax: x in ax in b & Ay: y in b y in a => a = b
>
> This still may not be totally explicit, but it
> does say that all that counts are individuals (if
> there are other things they are wholly determined
> by the indivuals and we have no other things
> offered so far.

That, together with Ex x in a, would seem to do it,
as far as I can tell.

Now all that remains is sorting out the axioms from the
theorems.

mu'o mi'e xorxes

Posted by pycyn on Fri 02 of Dec, 2005 21:26 GMT posts: 2388

> On 12/2/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > Well, the way I would do kinds — as
> collocations
> > of properties, the foundation thesis is, I
> think,
> > derivable, since there comes a point when all
> the
> > properties are dealt with one way or the
> other
>
> Do you presuppose that only a finite number of
> properties
> are available? Otherwise, why would there come
> a point
> when all the properties are dealt with?
Not finite, but I do assume that all kinds are in
the system. So, "point" may be a bad choice of
words, since the point comes with the system
already.

> > But the issue is not how you think of the
> flow of
> > events (loading the issue) or what you say in
> > English or anything other than what is the
> > linguistic nature of time in Lojban.
>
> Originally the issue was whether or not stages
> of
> individuals constituted an example of a system
> without the foundation thesis.

True but that somehow led to this muck about time
in Lojban, whose formulation I think I have
correctly.

> Even reducing the issue to the linguistic
> nature of time
> in Lojban, I am not at all convinced that
> Lojban treats
> time differently than other languages. In my
> view,
> Lojban does not impose a particular conception
> of discrete or continuous time on its speakers.
> Both
> views would seem to be available and
> represented.
Then, the issue was ill-formed. That is, if
there is no one way that Lojban treats time,
there is no one way that Lojban views time. I am
not sure I agree with the first part of this, but
that doesn't really matter. We can, to be sure,
do allsorts of things with languages that don't
deal with things that way — process philosophy
in English, a static metaphysical language, for
example )Buddhism in Sanskrit is even worse)-- so
the fact that we can talk about time as a
continuum or as series doesn't tell us what it is
in the language.

> > However, as you
> > see, the claim that Lojban treats time as
> > discrete can be carried quite a ways.
> Whether it
> > is far enough to give a definitive answer, I
> am
> > not sure. And, as I have said before, I
> don't
> > really care, since nothing seems to hang on
> the
> > answer at the moment.
>
> Nothing seems to hang on the answer, true.
> (Except,
> perhaps, the issue of whether stages of
> individuals
> constitute an example of a system without the
> foundation
> thesis, but we already have other examples
> anyway.)
>
>
> > > But I see nothing close to
> > > a formalization (of that particular thesis)
> yet.
> >
> > As you are fond of saying in similar
> situations,
> > what exactly do you want? I hope that, as I
> do,
> > you will give a fairly precise answer.
>
> I don't require anything, really. All I said
> was that it would
> be nice to see that thesis expressed in formal
> terms, like
> all the others in the page, in terms of "in"
> and "+" and not
> in terms of undefined (though intuitively
> clear) things like
> "breaks down completely". But I certainly won't
> be accusing
> you of not making sense if such a formal
> statement turns
> out to be difficult or for whatever reason
> inconvenient.

But the foundation thesis is in terms of "+" and
"in." In what way is it defective? Any thing
other than that it applies only to finite cases?

> > > xod wrote:
> > > > That we generally refer to non-zero
> intervals
> > > of time does not
> > > > mean that we treat it as discrete. Those
> > > interval endpoints can be
> > > > situated anywhere in the timeline, and
> that
> > > means we treat it as
> > > > continuous.
> > >
> > > I agree.
> > No, by definition the end points are always
> > immediately adjacent to another event — the
> > previous and the next. There is no timeline
> on
> > which they are laid out; the timeline is in
> > Lojban (if it can be done at all) an
> abstraction
> > from sequences of intervals — the rest is
> not in
> > the language but in what is said in the
> language.
>
> Couldn't {ze'e} be pretty much a representation
> of the
> timeline?
Well, unqualified it would seem to apply to
events that take up all of time, but that doesn't
give a time *line,* just an all-inclusive
interval (a slight misnomer, obviously).

> > > 1. A brief, indefinite interval of time.
> > > 2. A specific point in time, especially the
> > > present time: He is not here at the moment.
> >
> > In any case, that is about English, not
> Lojban.
> > There are no time points in Lojban, only
> > intervals of time.
>
> What about {mokca}:
>
> mokca moc point ; 'moment'
> x1 is a point/instant/moment 0-dimensional
> shape/form
> in/on/at time/place x2
> x1 is dimensionless; (cf. jipno, jganu,
> linji, stuzi, tcika)

Well, that seems to be a spatial term extended by
analogy to time, once we get the idea that there
is an analogy to use. It does not jibe with
{temci}, which is the authoritative word aon
time, I suppose.

On 12/2/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> We can, to be sure,
> do allsorts of things with languages that don't
> deal with things that way — process philosophy
> in English, a static metaphysical language, for
> example )Buddhism in Sanskrit is even worse)-- so
> the fact that we can talk about time as a
> continuum or as series doesn't tell us what it is
> in the language.

That assumes that there is something that it is
in the language. I see no evidence for this underlying
picture of time that Lojban is supposed to support, but
maybe I haven't looked in the right places.

mokca
> Well, that seems to be a spatial term extended by
> analogy to time, once we get the idea that there
> is an analogy to use. It does not jibe with
> {temci}, which is the authoritative word aon
> time, I suppose.

I don't see any reason to suppose {temci} to be more
authoritative than {mokca}. Is it because it uses "time"
as its keyword?

In any case, I don't see that either {temci} or {mokca} would
favour a continuous or discrete view of time, since both are
compatible with both. In a continuous timeline, there is no
problem in having continuous intevals between intervals, or
in having points within the intervals. In a discrete view, there
is no problem in the constituents being points and the intervals
between two other intervals consisting of a finite number of
points. I wouldn't even hesitate a mokca in using mokca for
a quantum of time with some very brief finite duration despite
the double insistence in the definition for 0-dimension.

If the language had some underlying preference for one of the
views, I would look for it in the closed class of structure words,
not in the open class of brivla. It is trivial to introduce brivla
with meanings such as "x1 is a discrete quantum of time"
or "x1 is a continuous stretch of time", or whatever one prefers,
and the language is practically left untouched by having those
words.

Now, if we examine the tense words (I suppose that's the most
obvious place to look for a bias in the language with respect to
this) I can't find a single one of them that would favour one view
or the other.

ca, pu, ba only address the ordering of events, but both discrete
and continuous intervals can be ordered.

zi, za, zu, ze'i, ze'a, ze'u give lengths of intervals. I have an easier
time in thinking of lengths as continuous, but again they can be
thought of as a relatively small/large number of discrete constituents
too, so this is not decisive.

ru'i, di'i, ta'e say how an event covers an interval, but the interval
again can be thought of as a continuous stretch or as a chain of
little chunks. Similarly for <number> roi.

So, if there is an underlying view favoured by the language, where
or how is it expressed?

mu'o mi'e xorxes