On Oct 28, 2015, at 1:17 AM, Thomas Johnston <tmj44p@xxxxxxx> wrote: (01)
> <<<
> Sets don't have universes of discourse: that notion arises in giving a
>semantics to a language (hence "discourse"). Do you mean, they are all subsets
>of a (large) set of possible values, like the domain and range of a function?
>
> No, I mean to say what I said. If a set consists of all people who have blue
>eyes, then the universe of discourse is all people, and the set membership
>criterion is "blue eyes". (02)
But that is the same set as the set of all blueeyed things that are people. So
on what basis can you say that the *set* (not your way of describing it, but
the set itself) has a universe of discourse distinct from its membership
criterion? This set is {x: Person(x) & Blueeyed(x)}, and that '&' in there is
symmetric. (03)
> If the set consists of all of my customers, then the universe of discourse
>might be all adults, and the set membership criterion might be having applied
>for customer status and having a credit score of 750 or above.
>
> Translating those statements into a terminology that only mathematicians are
>comfortable using would not correct any mistakes in what I said, or indeed
>eliminate any ambiguities. (Please correct me if I'm wrong.)
>
> And with what assumptions do you correct me for using the terminology I did
>use? (04)
Well, that term "universe of discourse" is widely, and as far as I know only,
used in the context of logical or linguistic semantics, where it typically
refers to the set over which the universal quantifier ranges. For example, the
(not particularly formal) Free Dictionary defines it as "A class containing all
the entities referred to in a discourse or argument". I have never previously
come across it being used to refer to some property of a set. (05)
> Is it that technical terms are each defined in a specific context, and that
>any use of them outside that context is inappropriate, or perhaps even wrong?
>If so, how do you draw boundaries that delineate those contexts, separating
>them from, for example, wider contexts which incorporate them? (06)
Of course you are free to use terminology in any way you prefer, but if you use
it in nonstandard ways without explanation, you are liable to be
misunderstood. (07)
> > , and (b) the same "predicate" (as Stoll puts it), or "set membership
>criterion" as I would prefer to put it.
>
> Well now, that can't be correct, because if they had the same membership
>criterion then they would be the same set. You must be referring to something
>else, and it would be very helpful to know what it is. Can you give an
>example?
>
> I agree that they would. (08)
So your position is that all the sets in a "timevarying set" are the same set?
So timevarying sets do not in fact vary? That seems rather implausible (?) (09)
> Take a table with a set of 10 rows at time t. Delete one of those rows. The
>table now instantiates a different set of rows, at time t+n. Add back the
>deleted row. The table now instantiates the same set of rows it instantiated
>at time t+n. The same set has occurred twice, in a temporal sequence of sets. (010)
I fail to see how this has any bearing on the point being discussed, which had
to do with sets and membership criteria. (011)
> I will make a guess, but forgive me if I get this wrong. There are
>individuals whose properties may vary with time. Let us write this using the
>convention that P(x, t) means that x has property P at time t. The (a?)
>"varying set" associated with P is the (a?) function S from times to sets such
>that for all t, S(t) is (a subset of?) {x: P(x, t)} . Is that more or less
>right?
> >>>
>
> Your description is at a higher level of abstraction than mine is; for that
>reason, I consider it a less appropriate way of saying what I said than the
>exact language I used to say it. (012)
But your way of saying it seems (?) to have an unintuitive consequence (which
is not implied by the more precise way of saying it.) (013)
> I was talking about tables and their sets of rows, and I think that what I
>said was both clear, correct, and wellsuited for the context of the
>discussion. (014)
I guess I never find verbal descriptions of formal constructs (such as tables
and sets and so on) as precise as simple mathematical descriptions. As we have
been talking about sets and times and properties, is it really impossibly
"abstract" to use conventional set notation? (015)
And, disregarding aesthetics, was my description wrong? (016)
> > (v) The temporallyordered sequence of those states, then, constitutes the
>lifehistory of that table. (This temporallyordered sequence is not itself a
>set, because the same set may occur in the sequence at multiple noncontiguous
>periods of time.)
>
> Does each state have an associated time (perhaps a timeinterval)? If so, it
>would be both more natural and more useful to model this mathematically as a
>function from times to sets (=states). And, just as an aside, are you sure
>that a state of a table really is something as simple as a set?
>
> Are you sure that no sense can be made of referring to the state of a table
>that way? (017)
I would have thought that tables were more highly structured than sets. For
(just one) example, can a table have duplicates? But I may be wrong; I do not
claim to be an authority on tables. (018)
> re your aside, it would take someone pretty simple to think that a table
>really is something as simple as a set. (019)
?? But my reason for the aside was that YOU had just said that the state of a
table was a set (and so the table itself was a "timevarying set".) I am now
completely confused. Did I misunderstand you? (020)
> My own simple definition of a table is, roughly, that it is a type whose
>tokens are rows (021)
Sorry, but I cannot make sense of this, either. The table is a type of the
rows? Really? It follows then that the rows are instances of the table, which
with the best will in the world I cannot make into a coherent idea. (022)
> ; that under a linguistic interpretation, those rows are declarative
>sentences (023)
Sentence tokens, I presume from the above? (024)
> within a Gricean context; that all orthographically identical rows are
>sentence tokens of the same statement; (025)
OK, but as you have already asserted that they are tokens *of the table*, how
can they also be tokens of statements? (Or should I infer that the table *is*
the statement?) (026)
> that under a logical interpretation, it corresponds to an
>existentiallyquantified statement schema, and its rows to instantiations of
>that schema; that under an ontological interpretation, it is an Aristotelian
>secondary substance and its rows are Aristotelian primary substances. I have
>also given a relational + type/token + linguistic + logical + ontological
>interpretations of columns of relational tables (in Chapter 5 of my second
>book).
>
> I'll look forward to any corrections you may have, but at that point, I'm
>going to stop communicating with you. (027)
As you wish. (028)
> There has been only one other author in my life with whom communication has
>been, for me, this tense. For my part, the tension I feel with you and this
>other author is based on the anticipation that whatever I write will be
>interpreted so as to make me look as foolish as possible. (029)
I assure you that my only aim has been to understand what you are intending to
say, which has required at times pointing out what to me seem like errors of
usage, which you have been at pains to correct. I have no agenda to make anyone
look like anything. (I will admit that the issue of 'timevarying sets' which
first brought me into this dialog is a sore point with me, as this confused
idea seems to have a wide currency and, as author and 'explainer' of the RDF
semantics, I have had to have this debate many times previously.) (030)
> I always write on the basis of assuming that the other party is intelligent,
>and that if I don't fully understand him, that perhaps a little effort on my
>part will enable me to make him out to be something other than completely
>uninformed. With you and the other party I alluded to, this conversational
>stance of mine puts me at a real disadvantage.
>
> Everyone expresses themselves in their own idiolect (a tautology, of course).
>Here in this forum, our idiolects hopefully coalesce on a dialect whose
>subject matter is databases, logic, semantics, ontology, and related concepts.
>If the idiolect I use seems as unintelligible, or perhaps just simply wrong,
>to others in this forum as it apparently does to you, then my only
>selfrespecting course is to withdraw from this forum. (031)
Please do not withdraw from the forum because of me. If you prefer, I will
simply filter messages from you so that am not stimulated by any comments in
them to risk engaging you in conversation. (032)
Best wishes (033)
Pat Hayes (034)
>
> But I don't like conversing with people who make me look stupid because, for
>the most part, I don't think I am stupid.
>
> Regards, and regrets,
>
> Tom Johnston
>
> On Tuesday, October 27, 2015 6:21 PM, Pat Hayes <phayes@xxxxxxx> wrote:
>
>
>
> On Oct 27, 2015, at 4:06 PM, Thomas Johnston <tmj44p@xxxxxxx> wrote:
>
> > Response to Pat's Comment
> >
> >
> > Are there timevarying sets, in the sense of sets whose membership varies
>over time? Of course not. And so, although I never said that the term
>"timevarying set" referred to the notion of a set whose membership varied
>over time, it is certainly easy to read the term that way. So I spoke
>carelessly, and I apologize for that.
> >
> > I seem to recall adopting the term "timevarying set" from Chris Date. That
>doesn't legitimate the term, but it may explain why it came to mind as I wrote
>my comment. And the fact that an important author in the field of relational
>databases also uses the term suggests that there is something that he, like I,
>think that the term might usefully be referring to.
> >
> > In my case, as indicated in my reply to John Sowa in this same thread, I
>think the term is a reasonable one to be used to refer to a specific temporal
>sequence of sets. The idea is that each transformation of (update to) a
>relational table puts that table in a new state; and it is each of those
>states that is a set, and the temporal sequence of those sets that I used the
>term "timevarying set" to refer to.
> >
> > I expressed this idea much more clearly in my reply to John Sowa in this
>thread, written at close to the same time as my reply to Pat. Here's a summary
>statement of what I said:
> >
> > (i) A table in a relational database is a timevarying object.
> >
> > (ii) A transformation to the contents of a table (i.e. an insert, update or
>delete) replaces the current state of the table with a different state.
> >
> > (iii) Each of those states is a set – specifically a subset of the
>Cartesian Product of the ordered set of sets which makes up the columns of the
>table.
> >
> > (iv) At any point in time in the lifehistory of a table, it is in one and
>only one state; it physically realizes one and only one set.
> >
> > (v) The temporallyordered sequence of those states, then, constitutes the
>lifehistory of that table. (This temporallyordered sequence is not itself a
>set, because the same set may occur in the sequence at multiple noncontiguous
>periods of time.)
>
> Does each state have an associated time (perhaps a timeinterval)? If so, it
>would be both more natural and more useful to model this mathematically as a
>function from times to sets (=states). And, just as an aside, are you sure
>that a state of a table really is something as simple as a set?
>
> > (vi) I used the name "timevarying set" to refer to that temporal sequence
>of sets.
>
> It would be much simpler if you didn't, though :)
>
> > (vii) What relates the sets in each of these "timevarying sets"? If we use
>the Principle of Extension, I don't see a straightforward answer to the
>question. But if we use the Principle of Abstraction, the answer is that the
>sets in a "timevarying set" are related by having (a) the same universe of
>discourse
>
> Sets don't have universes of discourse: that notion arises in giving a
>semantics to a language (hence "discourse"). Do you mean, they are all subsets
>of a (large) set of possible values, like the domain and range of a function?
>
> > , and (b) the same "predicate" (as Stoll puts it), or "set membership
>criterion" as I would prefer to put it.
>
> Well now, that can't be correct, because if they had the same membership
>criterion then they would be the same set. You must be referring to something
>else, and it would be very helpful to know what it is. Can you give an
>example?
>
> I will make a guess, but forgive me if I get this wrong. There are
>individuals whose properties may vary with time. Let us write this using the
>convention that P(x, t) means that x has property P at time t. The (a?)
>"varying set" associated with P is the (a?) function S from times to sets such
>that for all t, S(t) is (a subset of?) {x: P(x, t)} . Is that more or less
>right?
>
> > As an aside I also note (since this topic is one I have worked on for a
>long time), that the standard (ISO 9075:2011 and/or TSQL2) theories of
>bitemporal data include the notion that there are two "timevarying sets" (in
>this sense) corresponding to each table, one tracking the temporallyordered
>change of state of the objects represented by rows in each table, and the
>other tracking the temporallyordered change of state of each table itself.
>
> That sounds like the distinction between vlaid and transaction time(?). To
>properly model this requires having a more nuanced model of time.
>
>
> Pat
>
> > With this interpretation of the phrase "timevarying set", and with
>relational database tables being the original topic under discussion, my
>original point can be rephrased like this: a relational table is a
>"timevarying set" (i.e. a temporal sequence) of table states, each state
>being a specific collection of rows. By the Principle of Abstraction, what
>each of those states has in common is that they are defined on the same
>universe of discourse (a Cartesian Product of sets) and use the same set
>membership criterion.
> >
> > And I once again apologize for using a term which originally seemed
>innocuous enough, but which I now realize is more naturally understood the way
>Pat understood it – as an oxymoron. I will henceforth try to use some such
>term as "temporal sequence of table states (sets)".
>
> >
> >
>
> 
> IHMC (850)434 8903 home
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> phayes@xxxxxxx http://www.ihmc.us/users/phayes
>
>
>
>
>
>
>
> (035)

IHMC (850)434 8903 home
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 mobile (preferred)
phayes@xxxxxxx http://www.ihmc.us/users/phayes (036)
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