Dear John, (01)
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). (02)
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. (03)
> 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'. (04)
MW: Accepted. (05)
> 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. (06)
MW: I don't have a problem with there being intensional definitions. The
question is what do they define? (07)
>
> 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." (08)
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." (09)
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." (010)
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. (011)
MW: Well I'm not an expert at lambda calculus, so could you explain how
this works for equiangular and equilateral triangles please? (012)
>
> 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. (013)
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. (014)
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). (015)
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. (016)
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. (017)
MW: I keep trying to say, I am talking about IDENTITY by extension, not
DEFINITION by extension!!! There is a difference. (018)
> 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. (019)
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. (020)
> 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. (021)
MW: No. It is the root of your misunderstanding. (022)
MW: But let me try to find something where we might disagree really. (023)
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. (024)
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. (025)
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. (026)
All of which has nothing to do with extensional definitions, and
everything to do with extensional identity. (027)
Regards (028)
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/ (029)
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