Re: identifying entities across database updates (was: Is a function a relation?)

"none (Reinier Post)" <rp_at_raampje.> wrote in message news:4a4d30b3$0$8961$703f8584_at_news.kpn.nl...
> Brian Selzer wrote:
>
>>I accept as an axiom that there are objects that can have a location in
>>time
>>or space. To formalize this, let C! be a 1-place relation that ranges
>>over
>>the objects in the Universe and expresses the property of having a
>>location
>>in time and space--that is, being concrete.
>
> Wait. Assuming that objects exist doesn't imply that we can uniquely
> identify them.

I'll buy that, but not for the reason you're suggesting. It is the assumption that there is a Universe that implies that the objects contained therein can be distinguished from one another.

> You and I, or even I and I, may very well disagree on
> how to partition the universe into objects, depending on the purpose of
> our description.

But you cannot deny that there can be objects that can be located in time or space, because there is overwhelming empiracle evidence to support it. Just look out the window.

>How many objects is a chair? How many objects is
> the character A? Can it be green? Is the chemical element C an object?
> Is course 430, Database Design and Administration at Moron University,
> an object?

Unlike you, I am not referring to an arbitrary partitioning. Interpretation is an instantaneous process--it occurs at a location in time. For abstract objects that cannot have a location in time, the instant of interpretation has no bearing on the outcome because abstract objects neither come into existence nor cease to exist, but for ordinary objects that can, the instant of interpretation may occur earlier than, at, or later than that location, and the outcome is different at each of those instants, for one occurs before the object came into existence, one occurs during its existence, and one occurs after it ceases to exist.

> The reconciliation of different, overlapping database
> schemas, even within the same organization, is an important practical
> problem.

So what? How does that bear on whether there can be things that can have a location in time or space?

> So your relation is rather big. It certainly isn't a normal
> database relation.

C! is a 1-place relation term in a formal language. It is not a database relation, and I never said that it was. It could certainly belong to the predicates of database relations, though.

> In order to apply the relational model, we don't have to assume the
> existence of objects at all. It's an extra step you choose to make.
> Aren't you just complicating matters for ytourself, and for the
> rest of us?

You are so totally wrong: if we don't assume the existence of objects, then there is no need for the basic assumptions of the relational model: the unique name assumption, the closed world assumption, and the domain closure assumption.

>>Given C!, the properties of
>>being ordinary, O!, and being abstract, A!, can be defined. Only those
>>objects that can have a location in time or space are ordinary, and those
>>are exactly the objects that possibly exemplify C!; every other object is
>>abstract and as such cannot have a location in time or space, and the
>>abstract objects are exactly the objects that don't possibly exemplify C!.
>>
>>The integer 5 is an abstract object. Abstract objects do not actually
>>exist: they just are.
>
> But can we identify them uniquely? Are the character 'A', the
> ASCII character 'A', the English character 'A', and the Arial character
> 'A' the same object, or are they not; if not, how many different objects
> are they? Why call these things objects at all? Isn't it better to
> call them something else? 'Values' comes to mind.

For me, 'symbols' comes to mind because 'values' are objects fixed at the instant of interpretation. Some values are fixed to symbols; some values are fixed to complex language terms, such as descriptions or function applications.

>Under the Domain Closure Assumption, the only objects
>>that actually exist are those that exemplify C! and are represented in the
>>database, but that doesn't mean that abstract objects can't be discussed:
>>it
>>just means that the quantifier forall ranges over every object that can
>>possibly be, which includes all objects that cannot have a location in
>>time
>>and space, all objects that can, but don't, and all objects that actually
>>do.
>
> I think that's a bit much to ask. You can't quantify over them
> unless you know how to find them and to tell them apart.

Actually, you've got it backwards: you can't find them or tell them apart unless you can quantify over them. Properties are expressed in logic as 1-place relations that range over the objects in the Universe. Objects that have a property exemplify its 1-place relation; objects that don't don't. You can distinguish between objects only if one exemplifies the 1-place relation for a property that the other doesn't, and you can only find objects if you can distinguish between them.

>>It is a consequence of assuming a fixed domain of quantification for
>>actual existence to be expressed as a predicate--call it E!. Obviously,
>>E!
>>implies C!.
>
> Existence is a property of predicates or properties, not of
> objects or values.

Neither properties nor predicates can have a location in time or space; therefore, you're wrong: existence is not a property of predicates or properties. It is nonsensical to state that red exists, but one can sensibly state that something that does exist is red. "The balloon is red."

> It is nonsensical to state that 3 exists.

I think I pointed that out. Abstract objects do not actually exist: they just are.

> But I'm not sure that you need O! or E! anyway.
>
>>In contrast to the assignment of the integer 5, which as an abstract
>>object
>>does not exemplify C!, for the assignment to PQ to succeed, due to the
>>Domain Closure Assumption the objects that each tuple in the relation maps
>>to must exist--that is, they must exemplify E! which implies that they
>>must
>>exemplify C!. In that sense, the assignment of the relation asserts the
>>existence of the objects that its tuples map to, so it's not that much of
>>a
>>stretch to say that the relation just sprang into existence. Of course,
>>all of this assumes that the user making the assertion is not lying or
>>mistaken.
>
> And this is your weak point. You want to express identity beyond
> identifiability by attributes,

This is not true. I didn't say this, nor did I imply it. I wouldn't even think of it because identity is a relation, and has a strict formal definition both for ordinary objects and for abstract objects. You are conflating the concept of identity with the concept of identification. They are completely unrelated. This is the crux of the issue: you are operating under the false notion that what identifies something at one time identifies the same thing at all times. While that is true of abstract objects since abstract objects cannot have a location in time, it is clearly not true for ordinary objects, as I have pointed out on numerous occasions.

I guess this is partly my fault: I should have stuck with the word 'thing' rather than 'object' due to all of the OO baggage that 'object' carries with it, but for the record: you brought up OO. I didn't!

<snipped fallacious argument based upon the misrepresentation of my position> Received on Fri Jul 03 2009 - 16:59:30 CEST