John, (Pat,) (01)
WRT the first statement (unfortunately deleted) (02)
I'd like to thank Pat for his clear comments on intensional sets - this red
herring seems to come up every few weeks. (03)
Maybe we should frame his response (or an earlier response by ChrisM) and
just refer to it in future.
" the identity criteria *for
> sets* are indeed extremely simple and completely beyond controversy:
> identity of sets simply means having the same members. There is no
> such thing as an intensional set, or a non-extensional set, or a set
> which changes with time, etc.. "
+1 as you would say. (04)
JS>> Unfortunately, there was comparatively little work in analyzing the
> application of logic to the real world.
I assume by 'logic' here you mean 'sets' - as these are what you are
critiquing.
I suspect people like Lewis, Heller, Jubien and Sider would find your
comment odd (well, incorrect - well, logically false). (05)
WRT the second statement (unfortunately deleted) (06)
> 2a But two types are considered identical iff they have the same
> definitions (07)
I do not see much connection between your comments below and the concerns I
raised. (08)
You responded earlier - For definitions, "the same" could be replaced by
"provably equivalent"
but in some cases, the proof may be nontrivial. (09)
So (taking a classic case) using your proposed criteria, how does one prove
whether or not these two are identical:
- The author of Waverly
- The person named Walter Scott
Or
- The person named Cicero
- The person named Tully (010)
Does it depend upon the logic you use or the axioms in the system?
Do you need question begging axioms such as (Cicero = Tully) to show they
are identical. (011)
Would you be happy with a situation where these were NOT identical? Because
they were not "provably equivalent". (012)
Just to be clear, I am not arguing for one side or the other, I just think
we need to be clear. (013)
Regards,
Chris Partridge
Chief Ontologist (014)
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> -----Original Message-----
> From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx [mailto:uom-ontology-std-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> Sent: 07 October 2009 18:40
> To: John F. Sowa
> Cc: uom-ontology-std
> Subject: Re: [uom-ontology-std] What is mass?
>
>
> On Oct 7, 2009, at 8:12 AM, John F. Sowa wrote:
>
> > Chris,
> >
> > CP> I can see the problem for types - which one does not escape
> >> by saying "the same" could be replaced by "provably equivalent.
> >>
> >> However, I cannot see the problem for sets - and cannot see
> >> where you explain this in your response (maybe I missed it).
> >> Could you give us some idea what you mean.
> >
> > I have mentioned those issues in many different ways in many
> > emails over the years. I'll summarize the points briefly.
>
> John, just to clarify. Your point is that real-world identity criteria
> are complex and nontrivial to state, and even can be subject to
> rational disagreement; and that identity criteria for sets do not face
> up to these challenges. All this is true, but it does not address
> Chris' point, above, which is simply that the identity criteria *for
> sets* are indeed extremely simple and completely beyond controversy:
> identity of sets simply means having the same members. There is no
> such thing as an intensional set, or a non-extensional set, or a set
> which changes with time, etc.. The use of set language burns away all
> such complexities and doubts: indeed, that is what it was invented
> for. So it is misleading and strictly incorrect to use phrases like
> 'intensional set' when talking about a collection defined in some way
> that leaves some room for doubt or interpretation regarding exactly
> what it is a collection of, or what exactly its members are. Such
> collections may be important, but if their identity criteria are in
> any way blurry or dependent upon some contextually provided source of
> information, then they are simply *not sets*. So the problems you
> mention, below, are not problems with identity between sets.
>
> > One of the problems with 20th century logic is that the great
> > technical advances were made in the application of logic to the
> > foundations of mathematics. As a mathematician, I consider that
> > a perfectly fine use for logic.
> >
> > Unfortunately, there was comparatively little work in analyzing
> > the application of logic to the real world. Carnap, for example,
> > did make the attempt in his Logische Aufbau der Welt, but he
> > abstracted away all the messy details. The later chapters of his
> > book, which include all the interesting stuff, are pure hand waving.
> >
> > The reason why Peirce, Whitehead, and the later Wittgenstein are
> > my favorite logicians is that they faced the messy details head on.
> > Following is a quotation from Whitehead's last book _Modes of
> > Thought_, which I highly recommend:
>
> +1 on that. It is very hard to find a clearer thinker than ANW.
>
> > ANW> In logical reasoning, which proceeds by use of the variable,
> >> there are always two tacit presuppositions -- one is that the
> >> definite symbols of composition can retain the same meaning as the
> >> reasoning elaborates novel compositions. The other presupposition
> >> is that this self-identity of each variable can be preserved when the
> >> variable is replaced by some definite instance.... The baby in the
> >> cradle and the grown man in middle age are in some senses identical
> >> and in other senses diverse. Is the train of argument in its
> >> conclusions substantiated by the identity or vitiated by the
> >> diversity? (pp. 145-146)
> >
> > In mathematics, those sets and the variables that refer to them
> > are always perfectly well defined. But whenever you talk about
> > anything in the real world -- including people -- those things are
> > constantly in flux. You can never be certain that two different
> > references to what is supposed to be "the same thing" are really
> > "exactly the same" for whatever abstraction is being considered.
>
> Well, never is a bit strong. But this needs to be spelled out
> carefully, yes.
>
> Pat
>
> >
> > John
> >
> >
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