Re: So what's null then if it's not nothing?
Date: 10 Dec 2005 13:20:17 -0800
Message-ID: <1134249615.348640.135980_at_g44g2000cwa.googlegroups.com>
JOG wrote:
> vc wrote:
>
> > JOG wrote:
> > > vc wrote:
> > > > JOG wrote:
> > > > > vc wrote:
> > > > > > JOG wrote:
> > > > > > > vc wrote:
> > > > > > > > Jon Heggland wrote:
> > > > > > > > > In article <1134052742.347560.142840_at_o13g2000cwo.googlegroups.com>,
> > > > > > > > > boston103_at_hotmail.com says...
> > > > > > > > > >
> > > > > > > > > > > I don't think a "regular" unknown/missing SQL NULL for a 2VL boolean
> > > > > > > > > > > domain should be regarded a truth value. That would be inconsistent with
> > > > > > > > > > > how NULL works in other domains.
> > > > > > > > > >
> > > > > > > > > > Then the logic ceases to be such if its truth values set include a
> > > > > > > > > > value for which the equality predicate evaluates to anything other than
> > > > > > > > > > TRUE or FALSE as I said elsewere.
> > > > > > > > >
> > > > > > > > > It does *not* include such a value. NULL is not a truth value any more
> > > > > > > > > than it is a number or a string.
> > > > > > > >
> > > > > > > > I am missing something. If you store/use NULL as a logical value, haw
> > > > > > > > can it *not* belong to the logical vaue domain with its logical
> > > > > > > > operations? Sorry, but that does not make sense.
> > > > > > > [snip]
> > > > > > >
> > > > > > > But Null can never _be_ a logical value: it is by definition an
> > > > > > > indicator of the very absence of a logical value. In addition, as a
> > > > > > > logical value how could it possibly exist?
> > > > > >
> > > > > > I am not sure what point you are trying to make. Are you suggesting
> > > > > > that nulls be allowed in , say, Boolean columns ? Or just the opposite
> > > > > > ?
> > > > >
> > > > > That you cannot mathematically incorporate the null concept into a
> > > > > logical system in the way that has been proposed (i.e. 3VL, which
> > > > > obviously can be effective with more valid domains).
> > > >
> > > > I do not understand what exactly you are trying to say. Is it that
> > > > you cannot have a logic with more than two truth values ? That's
> > > > clearly wrong. What exactly does "3VL, which obviously can be
> > > > effective with more valid domains" mean ?
> > >
> > > Well, you answer your question when you quote me. Of course you can
> > > have 3VL. It just makes no sense with this domain. If I have {T, F, X},
> > > well fine, but if one then defines X as representing a lack of
> > > knowledge concerning T or F, the domain no longer makes sense.
> >
> > You are wrong: What X 'represents' does not matter. What matters are
> > the truth tables defining how logical connectives work.
> >
> > > X is
> > > describing the state of the other values - it is part of a
> > > meta-theorem, and has no place sitting next to T and F.
> >
> > This does not make any sense.
> >
> > >(One might want
> > > to analogise with quantifiers in second and third order logic).
> >
> > What has the second-order logic to do with the 3 VL propositional logic
> > ? Do you have any idea what second-order logic is ?
> >
> >
> > >
> > > >
> > > > > In a boolean
> > > > > column for example you could not place true, false and Null in a
> > > > > mathematically consistent system.
> > > >
> > > > You cannot because the Bollean domain does not include anything but
> > > > {true, false}.
> > >
> > > no, you are correct. Calling it a Boolean column is silly. A column
> > > with a domain {True, False and Null} is what was meant, as discussed
> > > above.
> >
> > As long as NULL is used in the truth tables, threre is no problem. A
> > problem will arise when one would claim that NULL=NULL evaluates to
> > anything but TRUE when it functions as a truth value.
> >
> > >
> > > >
> > > > >(i.e. it necessarily requires human's
> > > > > to interpret the inconsistency in the practical world)
> > > >
> > > > This, I do not understand. Interpretation of truth values is
> > > > irrelevant for the logical system to be possible.
> > >
> > > No you can't just stick any old values into a logical system. 3VL will
> > > obviously always work if you are thinking in terms of the symbols (that
> > > is how it is defined after all), but we are not dealing with things
> > > from a "formalist" standpoint here (bottom up).
> >
> > Why not ? That's how modern propositional logic is treated: just a
> > bunch of symbols with a bunch of rules.
> >
> > >We already have the
> > > meaning of null established and are attempting to work down (a
> > > "realist" or "platonist" standpoint), and as such we cannot just squash
> > > its characteristics into a symbol and expect everything to work, just
> > > because we've written down a truth table.
> >
> > That's how it's done in modern propositional logic. If you want to
> > invent your own math, be my guest.
> >
> > >
> > > >
> > > >
> > > > >
> > > > > >
> > > > > > > In a world where the equality relation over a logical domain is not reflexive?!? This whole
> > > > > > > argument makes no sense to me.
> > > > > >
> > > > > > Whose argument are you objecting to ?
> > > > >
> > > > > The argument that would incorportate Null != Null into the logical
> > > > > arrangement - this would mean that the equality relation in the domain
> > > > > would be non-reflexive, a nonsense in a logic system. This should be
> > > > > the stopping point for that train of thought imo.
> > > >
> > > > But, that's what I've been objectiong to myself in my lengthy dialog
> > > > with Jon, right ?
> > >
> > > Sure! It looks like we are just agreeing loudly. Perhaps it looked like
> > > I was arguing against you, but this was not the intention. Rather I was
> > > just making statements, sparked off by your comments
> >
> > OK.
> > .
> > >
> > > >
> > > > >
> > > > > > >. If you want to use nulls, well
> > > > > > > mathematically your looking at a meta-language, and you simply can not
> > > > > > > condense it all down into a single conceptual level (Or hofstadter
> > > > > > > might point out that you have to pass it up to the next djinn!).
> > > > > >
> > > > > > What's that supposed to mean ?
> > > > >
> > > > > That mathematical levels are being confused in this discussion (a very
> > > > > easy thing to do). Null talks about the underlying algebra - it is not
> > > > > part of it.
> > > >
> > > > That does not make any sense. Could you please elaborate on 'null
> > > > talking about underlying algebra' ?
> > > >
> > > > >As such it is the next mathematical layer, part of a meta
> > > > > language _about_ that level beneath it.
> > > >
> > > > See above.
> > >
> > > Well I've maybe explained this above. Null means we do not have a value
> > > for boolean X say, whereas True and False are actually instances of
> > > those values, that Null describes are missing.
> >
> > That's not so. One can employ any string of characters representing
> > truth values including NULL. The string 'NULL' meaning is in your
> > head, not in in a logic system you want to use.
> >
> > >Null is acting at a
> > > different level, as it describes an underlying theorem rather than
> > > being part of one.
> >
> > The above still does not make sense.
> >
> > > Now I understand my descriptions probably make this
> > > clear as mud, but this sort of consideration of theorems and
> > > meta-theorems and meta-meta-theorems is pretty much all modern
> > > mathematics is about (consider Godel's work).
> >
> >
> > Goedel's theorem has got zip to do with the stuff we are discussing
> > (what specific theorem by the way are you referring to?).
> >
> > >I do not teach this stuff
> > > (as you can probably tell) so all I can do is point you in the
> > > direction of the references I made before.
> > >
> > > All best, Jim.
>
> Ok, no problems. I won't try going through the individual points tit
> for tat.
Why not ?
> You can't seem to connect with analogy (you think I'm
> referring to using Godel's theorem in this context, where I am
> obviously not, but rather his realisation of seperate levels, any of
> which can be complete or consistent but never both.
>Its just an analogy
> to look at a mathematical system at different levels.), so I'll give up
> there. As such you also can't separate what a Null is from the other
> values in a domain you wish to squash with it (Codd also did not, Date
> et al. did but, as someone pointed out previously, attempted to express
> this intuitively as opposed to mathematically).
I am not sure at all what you are trying to say, sorry.
>
> However, while we differ there, we agree Null!=Null cannot be an
> acceptable state of affairs in a logical system, so (if I've followed
> your line correctly) you propose Null=Null
>be incorporated and assume
> that symbols in an abstract logical system can happily represent any
> old item in the real world, nevermind the intension of the domain set
> they come from, and yet still give the user intuitive results
I never said anything about using NULL as a truth value being intuitive
or otherwise.
.
>. I'm
> clearly not convincing you, so I guess all I can do is wish you good
> luck with that, and hope you continue to read the literature.
What specific lacunae do you suggest I should fill out by reading "the
literature" ? In other words, what mistakes did I make whist
discussing the subject. Please be specific, without dark hints at
Goedel's theorems and such, as I honestly might be missing something.
>
> _still_ all best vc, Jim ;)
Received on Sat Dec 10 2005 - 22:20:17 CET