Hi Pat, (01)
Isn't conducting the discussion at the level of formalisation the wrong
level.
To take an example. (02)
One could decide to use predication as the means to formalise the
instance/member relation as you suggest below. E.g. B(a) means a is an
instance of B.
One could also decide to have a binary relation predicate Mem(x, y) to
formalise it. E.g. Mem(b, a) means a is an instance of b.
One could even have a tertiary relation predicate for binary relations BRel
(x, y, z) and a constant m for the instance/member relation. So we would say
a is an instance of b as BRel (m, a, b). (03)
All of these presumably have the same intended interpretation. Hence, one
can devise a translation between these. The question is what these are an
interpretation of. This is the question I am interested in - and do not see
how it can be avoided.
I seem to recall someone saying that you need to understand what you are
trying to formalise before you formalise it. And that if you do not
understand it, then your chances of formalising it correctly are slim. Isn't
that the issue here?
Anyway, these are old arguments, which I'm sure you have had many times
before. (04)
On a different point. I am unclear about your argument regarding numbers.
You say below.
> >>>> That surely will not work. The natural number five is an
> >>>> individual, but
> >>> does not
> >>>> exist in space and time, even imaginary space and time.
Elsewhere, you say (I think) that you mean individual in the sense of not
having members. (05)
I assume this is your personal position.
As I know you know the first (?) real logical formulation of number by Frege
is as the extension of a concept
http://plato.stanford.edu/entries/frege/#NatNum . As I noted in my comment
to Matthew, there are neo-Fregean versions as well as structuralist views
such as Shapiro's. There are also views that take numbers as abstract
particulars. So, it looks as though there are views that regard numbers as
having members as well as those that do not.
I think Matthew took you to be saying that it is impossible to hold the view
that numbers can have members. (06)
Chris
> -----Original Message-----
> From: Pat Hayes [mailto:phayes@xxxxxxx]
> Sent: 20 December 2012 07:34
> To: Chris Partridge
> Cc: [ontolog-forum]
> Subject: Re: [ontolog-forum] Fwd: Ontologies and individuals
>
>
> On Dec 19, 2012, at 12:56 AM, Chris Partridge wrote:
>
> > Hi Pat,
>
> Hi Chris
>
> >
> > I know you have an irrational aversion to these topics.
>
> I have an impatience with philosophical debate being conducted without the
> rigor of actual philosophical discussion (which could be done by
publishing in
> a professional journal) and with a never-ending re-hashing of old, and to
my
> mind utterly pointless, issues.
>
> >> From an IT system building perspective, one needs some kind of
> >> structure to
> > organise the information in the system (an architecture)
>
> I entirely agree. I do not, however, think that having interminable
debates,
> citing Aristotle, on what constitutes an "individual", is a useful
contribution to
> any kind of architecture. If you want to discuss architecture, then at
least
> have the rigor to conduct these discussions using formal terms, ie let us
trade
> actual axioms rather than multiple paragraphs of half-digested
philosophical
> mush. I suggest that we can all use the CLIF dialect of ISO Common Logic,
> which is expressive, first order and easy to type.
>
> If we take predication to be our model of the "instance" or "member"
> relation, so that (A B) is the way to say that B is an instance/member of
A,
> then the axiom defining "individual" as having-no-instances would be
>
> (forall (x)(iff (IsIndividual x)(not (exists (y)(x y))) ))
>
> or possibly (but no longer first order)
>
> (forall (x)(iff (IsIndividual x)(not (exists (...y)(x ...y))) ))
>
> Is that what you want in your architecture? If so, I would be interested
to
> know what purpose you think it serves there.
>
> If CLIF is not to your taste, then let me ask an architectural question.
Take any
> formal axiom - you may supply it to suit your purposes - in which a name
> denoting (what you regard as an) "individual" occurs, and tell me what
formal
> entailments this sentence has which would be changed if that name were
> allowed to denote (what you regard as a) non-individual, and why. Or if
you
> prefer, swap the roles around and answer the corresponding question. Put
> another way: convince us that this debate has any actual *architectural*
> importance, by showing us one example of where it would matter.
>
>
> > - so the Pat
> > 'approach' of not having one is hardly practical, unless all you are
> > designing is a spreadsheet.
> > My and, I'm guessing, Matthew's experience is that these kinds of
> > structures
>
> What "structures" are you talking about here? AFAIKS, nobody in this
thread
> has mentioned "structures" previously.
>
> > are a useful practical device when dealing with large systems.
> > As you well know, they have also been studied for quite some time, and
> > rest on arguments more than intuitions.
>
> I don't in fact know what you are talking about here.
>
> > If you want to make some suggestion about the use of the term
> > 'individual', I wish you well in defending it, but I won't be holding my
breath.
>
> I already did. I suggest that the term be defined following Quine, to mean
> anything that can be the denotation of a bound variable. In CLIF, that
means
> anything in the universe of discourse, which is anything that can be
denoted
> by any name.
>
> > If you are suggesting that the terms we are using "cannot be described
> > or named " maybe you should re-read the literature.
>
> I was making an allusion to the final sentence of the Tractatus, which I
> thought might appeal to another philosopher. But never mind.
>
> Pat
>
> >
> > Chris
> >
> >> -----Original Message-----
> >> From: Pat Hayes [mailto:phayes@xxxxxxx]
> >> Sent: 19 December 2012 03:37
> >> To: [ontolog-forum] ; Chris Partridge
> >> Subject: Re: [ontolog-forum] Fwd: Ontologies and individuals
> >>
> >>
> >> On Dec 18, 2012, at 2:51 PM, Chris Partridge wrote:
> >>
> >>> As I understand it, the issue can be seen as what series of
> >>> architectural choices one makes.
> >>>
> >>> There is a distinction going back to Aristotle between things that
> >>> can have members and things that cannot (phrase this in the way that
> >>> suits you - instances, predicables, etc.).
> >>> If you choose to make that distinction, then you may then want to
> >>> tighten up what kind of things cannot have members, and argue that
> >>> these must all be concrete (a kind of abstract object nominalism) -
> > another
> >> choice.
> >>> If you make this second choice, you can resolve Pat's point about
> >>> numbers (at least, natural numbers) with some neo-Fregean approach.
> >>> Or, maybe a structuralist approach such as Shapiro's.
> >>> If you have made these two choices then a mental shorthand for the
> >>> distinction might be that it rests upon a concrete-abstract
> >>> distinction - but (architecturally) this is a much weaker and
> >>> murkier distinction to base things on, so not such a solid foundation.
> >>
> >> My objection is to the very idea that these questions are in any
> >> sense "foundational". They are indeed obscure, hard to decide, and
> >> rest upon
> > very
> >> fragile intuitions. But they are not foundational in the sense that
> > anything
> >> important rests upon them or depends on getting them right. They are,
> >> in
> > fact,
> >> almost completely irrelevant to any matter of concern to practical
> > ontology
> >> design, and can (and should) be ignored, unless one has far too much
> >> time
> > to
> >> waste. It is not an architectural decision at all: more like a
> >> decision
> > about what
> >> color smoke to blow up the chimney.
> >>
> >> Here is one way to decide the matter: anything that can be described
> >> or referred to is, ipso facto, an individual. And of things that
> >> cannot be
> > described
> >> or named, we must be silent.
> >>
> >> Pat
> >>
> >>
> >>> So, to make sense of this I think it helps to expose the
> >>> architectural choices one had made - and as the discussion shows (a)
> >>> we often do not do this and (b) there are a myriad of choices to
choose
> from.
> >>>
> >>> Chris
> >>>
> >>>> -----Original Message-----
> >>>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-
> forum-
> >>>> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> >>>> Sent: 18 December 2012 22:24
> >>>> To: [ontolog-forum] ; David Price
> >>>> Subject: Re: [ontolog-forum] Fwd: Ontologies and individuals
> >>>>
> >>>>
> >>>> On Dec 18, 2012, at 6:13 AM, David Price wrote:
> >>>>
> >>>>> On 18 Dec 2012, at 13:28, Alexander Titov wrote:
> >>>>>
> >>>>>> Dear Matthew,
> >>>>>>
> >>>>>> I would like to ask a few questions to understand you better:
> >>>>>>
> >>>>>>> MW: Someone mentioned that an individual is something that does
> >>>>>>> not
> >>>> have members (in the sense of a set having members) and that is
> >>>> close to
> >>> what
> >>>> I would mean, but that would make the null set an individual, so it
> >>>> is not
> >>> quite
> >>>> adequate. My definition of individual is something that exists in
> >>>> space
> >>> and
> >>>> time. I am not a set (or class or type or kind or sort etc) nor is
> >>>> my car
> >>> or this
> >>>> email. Nor is Sherlock Holmes to give a more difficult example. All
> >>>> these
> >>> things
> >>>> can be placed in space and time (even if it is imaginary space and
> > time) .
> >>> On the
> >>>> other hand, sets/classes/types are generally considered to exist
> >>>> outside
> >>> space
> >>>> and time.
> >>>>>>
> >>>>>> I understand that a 'main dichotomy' between an individual and a
> >>>> set/class/type is - existence in space and time (rather than having
> >>>> or not
> >>> having
> >>>> members).
> >>>>
> >>>> That surely will not work. The natural number five is an
> >>>> individual, but
> >>> does not
> >>>> exist in space and time, even imaginary space and time. Does Moby
> >>>> Dick,
> >>> the
> >>>> work, exist in space and time? (Where?) Some people think that sets
> >>>> exist
> >>> in
> >>>> time. There is hardly any position on these debates that has not
> >>>> been held
> >>> and
> >>>> defended by someone.
> >>>>
> >>>> Pat
> >>>>
> >>>>
> >>>>>
> >>>>> This depends on the metaphysics and language you've adopted. As
> >>>>> Pat
> >>> said,
> >>>> Individual means 'member of set' in logic and has nothing to do
> >>>> with space
> >>> and
> >>>> time. Matthew's comments are couched in 4-dimensionalism so
> >>>> Individual is "Thing that exists in some possible world" and so is
> >>>> entirely about space
> >>> and
> >>>> time. In 4-D, a Class can be a member of a Class, yet Classes are
> >>>> not
> >>> Individuals.
> >>>>>
> >>>>> So, without couching discussions into the approach/background that
> >>>>> is
> >>> the
> >>>> context, even Individual is not a clearly defined term.
> >>>>>
> >>>>>>
> >>>>>>> MW: On the other hand, sets/classes/types are generally
> >>>>>>> considered to
> >>>> exist outside space and time.
> >>>>>>
> >>>>>> Can we consider opposite - sets/classes/types do exist within
> >>>>>> space and
> >>>> time as well? For example, as a collection/set of space and time
> >>> extensions of
> >>>> all their members?
> >>>>>>
> >>>>>> What will happen if the criteria is joined: 'does not have members'
> >>>>>> and 'exists in space and time'? Not sure if it is better... We
> >>>>>> have now another (at least three) cases to think about.
> >>>>>
> >>>>> As Classes are things of which Individuals are members based on
> >>>>> some
> >>>> criteria so, by definition, Classes in 4D are not in space time.
> >>>> Classes
> >>> are
> >>>> identified by their extension, but that does not put them into
> >>>> space/time either.
> >>>>>
> >>>>> Cheers,
> >>>>> David
> >>>>>
> >>>>>
> >>>>
> >>
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