Re: identity (was: names as predicates)

[cowan (John Cowan)]

la glis. cusku di'e:
>>> (My skepticism about the dichotomy of names and predicates
>>> is related to my distrust of equality as a primitive notion
>>> in predicate logic.  I suspect that the abstract notion of
>>> equality misleads us concerning the nature of perception;
>>> in this view, equality is properly applied--if at all--only
>>> to abstractions and not to physical objects.)

la djan. cau'n goi mi cusku di'e:
>> I don't understand this.  (BTW, by "equality" I assume you mean "identity";
>> what is expressed by the Lojban word "du" or the Old Loglan equivalent "bi".)
>> Why shouldn't identity be applied to physical objects?  It is simply that
>> relationship which holds only between a thing and itself: the smallest
>> reflexive relation, in Kripke's definition.

la .erek. reimnd. cusku di'e:
> The previous poster was correct (damn, I wish more people on this list new
> some General Semantics).  Identity cannot even obtain between two observations
> of an object made at different times, because every `object' changes
> constantly (in GS terms, "There are no things, only processes.").

So what?  A process can be self-identical too.  "lo pu'u me mi" (the process
of me) is as good a sumti as "mi".

> You may if you wish assert identity between two observations of an object at
> the *same* time, but even this is shaky;  two different observations will yield
> two different sets of data, and the a-prioristic assumption of "identity"
> sweeps the issue of how you justify connecting one set to the other under the
> rug.

This seems to express a different kind of identity from what is meant by
"du"; if the observations are TWO observations, then it certainly would be
incorrect to assert that "du" holds between them.  However, "du" holds
between an observation and the SAME observation.  Perhaps "you cannot
step twice in the same river":  but if you step once, then "du" holds between
that "nu stapa" (event of stepping) and itself.

> A sane language should only allow "identity" to be asserted between abstractions
> in a formal system (what philosophers call "formal identity").  The strongest
> assertion a sane language should allow you to express about other things
> is "x is indistinguishable from y for purpose z"

That is indeed the proposed place structure for "mintu":

	x1 is the same/identical thing as x2 by standard x3

"Standard" is a generalization of "purpose".

There is also "dunli", which is being broader and allows
for other kinds of equality besides identity:

	x1 is equal to x2 in/on property/dimension/quantity/quality x3

and which (I think) should have "by standard x4".  Example:

	ro prenu cu dunli ro prenu le flalu le ka merko
	All persons are-equal-to all-persons in-property the law
		by-standard American-ness.

> [C]onsider carefully
> what it means to say that something is "not red" or "cold" (the problem is
> easier to see in negated statements).

Note that this is scalar negation, which in Lojban is explicitly treated
as non-logical negation.

> In fact, you cannot apply logic to "reality" at all.  You can only apply it to
> abstractions captured from reality.  Thankfully, it happens that the
> capturing process often preserves enough of what's important that your logic
> manipulations can be used to predict the future of "reality" -- but there is
> *no a-priori guarantee* that this need be the case.  There is no identity
> anywhere; there's just "close enough for predictive work".

I suppose it depends what you call an "abstraction".  To me, numbers and
sets are as "concrete" as rocks and trees.  I think the language backs me
up here -- in Lojban, an abstraction is what is expressed with an abstractor,
or what is described by a selbri calling for an abstractor in the place
structure.

> I'd forgotten that lojban supported a "material identity" assertion.  This is
> a serious flaw.  Is there any chance we can fix it, say by adding to the place
> structure of "du"?

Fine, don't use "du" except between objects you call abstract.  Use
one of the above gismu instead.

--
cowan@snark.thyrsus.com		...!uunet!cbmvax!snark!cowan
		e'osai ko sarji la lojban