Re: Objects and Relations
Date: Fri, 16 Feb 2007 04:40:33 GMT
Message-ID: <5BaBh.1820$4c6.1481_at_news-server.bigpond.net.au>
David BL wrote:
[...]
PMFJI, but I think there is an essentially definitional misunderstanding
here. Although, you know, I'm only new at this, so take it with a grain
of salt. I'm really interrupting to see if I'm getting a better
understanding of all this, and I do so with some trepidation.
The word that I think is being used extremely loosely is 'entity'.
In your post you use it to describe, variously,
and a term that can be used to describe anything is basically useless.
*BTW, I'm using theory here in the sense of a logical theory, i.e. a set
of constants, functions, domains, etc. In this post, I'll not use theory
in any other sense.
I'm pretty sure that Jim is using 'entity' to describe 'things that we
might agree exist in the real world', or at least, things outside the
relational theory at hand. An in particular, I think that things that
exist within the theory are not entities, by definition.
Although Jim should feel free to correct me if I'm putting words into his mouth.
>
> The word "exists" appears a lot in mathematics. For example consider
>
> P = there exists nonzero integers x,y,z such that x^2 + y^2 = z^2
>
Loosely, I think that P should be understood as a sentence in a formal system; one that has a fixed interpretation. In particular, the interpretation of terms like 'integers', '^', '+' etc, are all fixed within that formal system. So, 'integers' within the theory would contain constants like '0', '1' and '2' (which are also within the theory) that are intended to represent zero, one, two (which are more nebulous things (possibly entities) that exist outside the theory).
For the theory to be considered good, we'd like those constants to have provable properties which accord with observable phenomena, like 'I have one apple, and give you one apple, how many apples do I have?'. My observation says I have zero apples, and my theory says I have '0' apples. Phew, my interpretation maps from '0' to zero, so my theory is good.
However, it is important to note that there is no interpretation defined within a relational theory. So, any interpretation (for example from the string "12345" within the theory to my particular tax file number) necessarily happens outside the relational model. In that sense, entities play no role within a relational theory. And even more particularly, there is no requirement that things within the theory are interpreted at all. That is, you can have a relational theory which does not require you to believe in entities at all.
I think the cornerstone of this misunderstanding is that you have been using the term entities to describe both things outside and things inside a relational theory. I'm pretty sure that's not the standard convention, at least within comp.databases.theory.
> Generally speaking mathematicians don't waste time arging about
> whether the integers exist. Instead they assume it,
I normally wouldn't quibble with this terminology, but to prove a sentence like 'P' above, mathematicians only assume integers exist in as much as they are defined within the formal system in which the proof of P is going to be carried out. They don't really care if one and two exist, only '1' and '2'.
> and ask more
> refined questions about existence like the one above. In this case P
> is true.
>
> Now if one believes that the integers don't exist at all then clearly
> P will be false.
If integers don't exist within the formal system above, P is not even well formed. If integers don't exist outside the formal system above, then it has not bearing on P's truth or falsehood within the system.
> Is such a philosophical position tenable for a
> mathematican? No! This makes me think mathematicians have a Platonic
> view whether they admit it or not.
I don't think it's relevant.
[... Rest snipped ... ]
As I said above, I'm pretty new at the relational model stuff. I'd be interested in feedback.
Cheers,
Joe
Received on Fri Feb 16 2007 - 05:40:33 CET