Dear Gunther, (01)
> Is there a way to get that back to the actual UoM
> discussion? Could you phrase the disputed issue
> in 2 succinct contrasting statements that are about
> our subject matter at hand?
>
> As for the sheep example Mathew give below, I am
> confused. I may be just a doctor and software engineer,
> not a chemical engineer that I would know much about
> the fine points of your dispute, but to me it seems
> that you would not make 2 definitions for sets of
> sheep (two-eyed and four-legged) if you were not
> interested in a difference here. And if you are interested
> in a difference, then the two sets are not the same
> even though their extension may be. (02)
MW: Apparently you are not a mathematician either. (03)
If you examine set theory you will find that two sets are the same if
they have the same extension. (04)
> But presumably
> you didn't know that before you defined your two sets
> and then determined their extensions (yes I like to
> drag epistemology into ontology). (05)
MW: Since all the sheep in the field had 2 eyes and 4 legs, it was
always going to turn out that when you looked at them you would find
this out. We were not considering what might have been, only what is. (06)
> But still I don't
> know quite what's the point? (07)
MW: I don't know. I am not the one that brought this stuff up. I am just
the one that is having their position misrepresented. I merely reserve
the right to correct those that do this. (08)
Regards (09)
Matthew West
Information Junction
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>
> regards,
> -Gunther
>
> Matthew West wrote:
> > Dear John,
> >
> > We are way off topic here. None of this is remotely relevant to
> maximum
> > allowable working temperatures or any idea of direct or indirect
> > properties. I have only been bringing engineering practice to the
> table
> > here and leaving any ontological bias elsewhere (for those that
> do not
> > know I have a BSc and PhD in Chemical Engineering, and 8 years
> practice
> > as a Chemical Engineer working on a refinery doing every kind of
> job
> > that a Chemical Engineer might do from plant design to plant
> operations,
> > safety and environment, process control, I even looked at the
> refinery
> > sewage system).
> >
> > I am also somewhat disappointed about the way you keep putting
> words in
> > my mouth that were never there. I do not talk about extensional
> > definitions, but extensionalism as an identity basis. There is a
> > difference, which you seem to keep missing.
> >
> >> MW> You are conflating two usages of intensional, so it is not I
> >> > who is suffering from a philosophers disease.
> >>
> >> First of all, I apologize for using the word 'disease'.
> >
> > MW: Accepted.
> >
> >> But
> >> the notion of intensional definition is so fundamental to logic,
> >> knowledge representation, ontology, and other areas that it will
> >> inevitably be used in multiple ways.
> >
> > MW: I don't have a problem with there being intensional
> definitions. The
> > question is what do they define?
> >
> >> For a precise definition of the distinction between intensional
> >> and extensional definitions, I have so often cited a short
> >> discussion by Alonzo Church that I put it on my web site:
> >>
> >> http://www.jfsowa.com/logic/alonzo.htm
> >>
> >> Following are the relevant quotations from that article:
> >>
> >> 1. "A function is a rule of correspondence by which when
> anything
> >> is given (as argument) another thing (the value of the
> >> function
> >> for that argument) may be obtained. That is, a function is
> an
> >> operation which may be applied on one thing (the argument)
> to
> >> yield another thing (the value of the function)."
> >>
> >> 2. "The foregoing discussion leaves it undetermined under what
> >> circumstances two functions shall be considered the same.
> >>
> >> The most immediate and, from some points of view, the best
> way
> >> to settle this question is to specify that two functions f
> and
> >> g
> >> are the same if they have the same range of arguments and,
> for
> >> every element a that belongs to this range, (f a) is the
> same
> >> as
> >> (g a). When this is done we shall say that we are dealing
> with
> >> functions in extension."
> >>
> >> 3. "It is possible, however, to allow two functions to be
> >> different
> >> on the ground that the rule of correspondence is different
> in
> >> meaning in the two cases although always yielding the same
> >> result
> >> when applied to any particular argument. When this is done
> we
> >> shall say that we are dealing with functions in intension."
> >
> > MW: Well on the one hand I can quite agree that you can decide
> that two
> > functions are different, even if they are extensionally the same.
> I
> > choose not to, but I do not require that others make the same
> choice. On
> > the other hand, the suggestion here is that the meaning is
> different,
> > and here I think there is more of a problem. Meaning as I
> understand it
> > is what links our terms to reality, and if two terms or
> definitions
> > point to the same thing, I am struggling as to how the meaning
> can be
> > different. Could you explain that specific point please?
> >> 4. "The notion of difference in meaning between two rules of
> >> correspondence is a vague one, but, in terms of some system
> >> of notation, it can be made exact In various ways."
> >
> > MW: Could you be explicit about which ways please?
> >> 5. "We shall not attempt to decide what is the true notion of
> >> difference in meaning but shall speak of functions in
> >> intension
> >> in any case where a more severe criterion of identity is
> >> adopted
> >> than for functions in extension. There is thus not one
> notion
> >> of function in intension, but many notions; involving
> various
> >> degrees of intensionality."
> >
> > MW: I would probably understand this if you could answer my
> questions
> > above.
> >> 6. Then Church goes on to define the lambda calculus and its
> >> method
> >> of "conversion" as his criterion for equality by intension:
> >> two defining rules have the same "meaning" by if either one
> >> can be converted to the other by method of the lambda
> >> calculus.
> >
> > MW: Well I'm not an expert at lambda calculus, so could you
> explain how
> > this works for equiangular and equilateral triangles please?
> >
> >> This definition is more precise than most, but it follows the
> same
> >> approach as most: an intensional definition is specified by
> some
> >> rule (declarative or procedural) and the application of that
> rule
> >> determines the set of instances, the extension. For small
> finite
> >> sets, it's possible to generate the complete extension. But for
> >> large sets, such as the set of all people, cows, or bacteria on
> the
> >> planet earth, a definition by extension is impossible in
> practice.
> >
> > MW: I think this is one of the confusions. I am concerned about
> > identity, not definition. So I am happy that two sets are the
> same if
> > you can show that the membership is necessarily the same (if one
> rule
> > that defines the membership can be converted to another as you
> state
> > above would probably do the trick for me). It is not simply a
> matter of
> > always listing all the elements, and then trying to work out if
> it is an
> > interesting list.
> >
> > MW: On the other hand if you come across two sets with
> intensional
> > definitions and they have the same membership, then I will deem
> that is
> > a proof that the two definitions are equivalent. I think there is
> a
> > problem if you do not, since if you have two terms that point to
> the
> > same thing, then you have to explain how the meaning is
> different,
> > which since this is linked to what things point to is I believe
> > problematic.
> >> For infinite sets, sets in the future, or sets in possible
> worlds,
> >> no definition by extension is possible even in theory (except
> >> perhaps
> >> by an appeal to God, but God doesn't usually answer such
> >> questions).
> >
> > MW: If I held the view you claim I do this would be true. But I
> don't,
> > so it isn't.
> >> MW> If you are claiming that maximum allowable working
> temperature
> >> is
> >> > a subtype of temperature, it seems perfectly reasonable to
> me.
> >> It
> >> > is not different from asking "How do I know which pieces of
> >> equipment
> >> > are pumps?" Is that a meaningless question?
> >>
> >> It is very different. You can determine whether an object is a
> >> pump
> >> by examining it and determining whether its parts and the way
> they
> >> move would be capable of pumping some liquid.
> >>
> >> But there are some types for which the instances cannot be
> >> determined
> >> by looking at them. In my 1984 book, I called them "role
> types".
> >> Examples include father, wife, sister, employee, author,
> student...
> >>
> >> For each of those types, there exists some relation to something
> >> external to the individual in question. No examination of the
> >> individual can determine whether or not it is an instance of
> >> that type. The only way to determine the role is by some
> >> external evidence, such as a DNA test of another individual,
> >> a marriage license, a birth certificate, etc.
> >>
> >> The maximum temperature is similar: it's a role type that can
> >> only be determined by something external. As Pat said, look
> >> at the specifications.
> >
> > MW: You make my point for me. Presumably you do not think that
> role
> > types are the same as the base types. That is all I am trying to
> say (by
> > analogy at least).
> >> JFS>> To preserve a semblance of consistency, Matthew was forced
> to
> >> >> adopt not just a four-dimensional ontology that treats
> >> extensions
> >> >> in an unobservable future as if they were just as concrete
> as
> >> >> anything observable in the present, but also sets in an
> >> infinity
> >> >> of purely imaginary possible worlds.
> >>
> >> MW> You try to make it sound as if this is something I just
> thought
> >> up,
> >> > whereas it is a quite standard approach....
> >>
> >> Many people, including me, are quite happy with a 4-D ontology.
> >> But
> >> combining a 4-D ontology with purely extensional definitions is
> >> most
> >> definitely *not* standard.
> >
> > MW: I keep trying to say, I am talking about IDENTITY by
> extension, not
> > DEFINITION by extension!!! There is a difference.
> >
> >> I am even happy to talk about sets of
> >> extensions in a 4-D universe. But like most logicians from
> >> Aristotle
> >> to Church and beyond, I would use the intensional definition as
> >> *primary* and the extension as something that is determined by
> the
> >> intension.
> >
> > MW: I am quite happy that an extension might be determined by an
> > intension, but when two definitions give the same extension, I
> will say
> > that they define the same thing. See my statements about meaning
> above.
> >
> >> But even those the extension might be definable as a
> >> theoretical construct, the intension is what we actually use to
> >> determine equality for anything but small finite sets that we
> >> can actually observe.
> >>
> >> MW> ... there is no problem in my constructing plans
> intentionally.
> >> > That does not however mean that their identity is defined
> >> > intentionally rather than extensionally.
> >>
> >> Please read the quotations by Church above. (And note that
> we're
> >> talking about intensions with an S, not intentions with a T.)
> >>
> >> Fundamental principle: Intensional definitions are prior.
> Except
> >> for small finite sets immediately observable, extensions are
> >> *always* determined by the intensions.
> >>
> >> MW> They are intentionally constructed, but their identity
> >> > is extensional.
> >>
> >> That is truly a meaningless quibble. Please read Church.
> >
> > MW: No. It is the root of your misunderstanding.
> >
> > MW: But let me try to find something where we might disagree
> really.
> >
> > Take the sheep in a field, and I am interested in two sets, one
> the set
> > of sheep with 2 eyes, the other the set of sheep with 4 legs. As
> it
> > happens all the sheep have two eyes and four legs, so the sets
> are the
> > same, and I would say that the two definitions have the same
> meaning
> > because they point to the same set.
> >
> > Now I would not be surprised if an intensionalist objected that
> yes
> > these definitions accidentally pointed to the same set, but that
> it is
> > not necessarily the case that sheep have two eyes and four legs.
> It is
> > possible that there are one eyed sheep and 3 legged sheep (at
> least).
> > Therefore these definitions pick out different classes.
> >
> > I would retort that you are changing the rules, you are now
> quantifying
> > over possible worlds where the sheep in that field do not all
> have 4
> > legs and 2 eyes, and if you wish to do that, then indeed they are
> > different, but these are different sets than the ones I was
> interested
> > in because they include those from possible worlds. Whereas above
> we are
> > restricted to the actual sheep in the actual field in this world.
> >
> > All of which has nothing to do with extensional definitions, and
> > everything to do with extensional identity.
> >
> > Regards
> >
> > Matthew West
> > Information Junction
> > Tel: +44 560 302 3685
> > Mobile: +44 750 3385279
> > matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
> > http://www.informationjunction.co.uk/
> > http://www.matthew-west.org.uk/
> >
> > This email originates from Information Junction Ltd. Registered
> in
> > England and Wales No. 6632177.
> > Registered office: 2 Brookside, Meadow Way, Letchworth Garden
> City,
> > Hertfordshire, SG6 3JE.
> >
> >
> >
> >
> >
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>
> --
> Gunther Schadow, M.D., Ph.D.
> gschadow@xxxxxxxxxxxxxxx
> Associate Professor Indiana University School of
> Informatics
> Regenstrief Institute, Inc. Indiana University School of
> Medicine
> tel:1(317)423-5521
> http://aurora.regenstrief.org
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