Dear Matthew, (01)
MW> You are conflating two usages of intensional, so it is not I
> who is suffering from a philosophers disease. (02)
First of all, I apologize for using the word 'disease'. 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. (03)
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: (04)
http://www.jfsowa.com/logic/alonzo.htm (05)
Following are the relevant quotations from that article: (06)
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)." (07)
2. "The foregoing discussion leaves it undetermined under what
circumstances two functions shall be considered the same. (08)
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." (09)
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." (010)
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." (011)
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." (012)
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. (013)
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. (014)
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 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? (016)
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. (017)
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... (018)
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. (019)
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. (020)
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. (021)
MW> You try to make it sound as if this is something I just thought up,
> whereas it is a quite standard approach.... (022)
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. 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. 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. (023)
MW> ... there is no problem in my constructing plans intentionally.
> That does not however mean that their identity is defined
> intentionally rather than extensionally. (024)
Please read the quotations by Church above. (And note that we're
talking about intensions with an S, not intentions with a T.) (025)
Fundamental principle: Intensional definitions are prior. Except
for small finite sets immediately observable, extensions are
*always* determined by the intensions. (026)
MW> They are intentionally constructed, but their identity
> is extensional. (027)
That is truly a meaningless quibble. Please read Church. (028)
John (029)
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