Pat,
I think
you are very good as the devil's advocate, and highly appreciate you
provocations and stimulations. To better your critical skills, let me share
some observations:
1. Avoid
quibbling-niggling, pettifogging over small things;
2. View
ideas in the whole context;
3. Review
your understanding of nonsense.
To
understand the last
observation, you need a liberal intelligence. Everything in the
world has some sense and meaning, including nonsense, http://en.wikipedia.org/wiki/Nonsense. In
literature, there is a whole booming style, literary nonsense http://en.wikipedia.org/wiki/Literary_nonsense, using
all sorts of techniques and devices to create nonsensical effects, like L.
Carroll.
There is
nonsense (stupid, bad) and nonsense (intelligent, good). The samples of the
latter are when the parts make sense, while the whole is senseless, or vice
versa. The case of the former, when you know nothing about some domain of
knowledge, say, real ontology, then all its things will sound nonsensical; they
are not intelligible and understandable since transcend somebody's narrow mind,
his cognition, beliefs and perception.
If some
big ideas, as reality and its aspect, relation, beyond you kin and
understanding, this will make nonsense for you, for your particular mind,
however well-seasoned. I state as below: [relations are classified with
respects of their nature, mode of existence, the numbers of the relatives as
well as formal properties as transitivity, symmetry, reflexivity.] If
you are missing the clear meaning, then it is nonsense for you mind, nothing can
be done here.
Now, I
state [a relation can exist apart from the terms it relates], for it is
[the principle of order making the whole physical universe go:
space-time, forces, matter-energy relationships, fundamental interactions,
physical laws, all are natural kinds of relationships.] Again, you
can't get the meaning of it, another nonsense for your specialized
mind. For it may still believes the relation is an entity without a
reality, that the relation exists when the terms it connects
exist.
Another
source of nonsense to be mentioned is #2, when one is missing to see ideas,
concepts, statements in the whole context. This is a lore: "Many relations
relate things of different kinds." Answering to the discreet questions of
Ravi S, i specified:
[As such,
everything is connected with anything. For the sake of analysis, it is commonly
identified two types of relationships: simple, pure or
homogeneous, and complex, heterogeneous.
The first
type is composed of the same kinds of things as the relatives:
1. substances
related with substances, individuals with individuals, objects with objects, as
space relations;
2. states
with states; qualities (quantities) with qualities (quantities);
3. changes
with changes, processes with processes, actions with actions, events with
events, as causality and time relations;
4.
relationships with relationships, as analogy and proportion.
The second
type deals with different levels of relatives:
1.
whole/part, with many different sorts;
2.
universal/particular, as generalization or instantiation;
3.
class/member, as membership or subsumption.]
Azamat Abdoullaev
PS: I noticed
that your personal relationship with "relation" is rather casual,
http://www.w3.org/TR/2006/NOTE-swbp-n-aryRelations-20060412/, showing
shallow understanding of its exclusive status. Here i hold with Gian Zarri,
"very poor content", http://markmail.org/message/tk6ftny72wpfzgvg. It is always better to ask questions, if you
don't know something well, thus heading off badly nonsensical judgments.
----- Original Message -----
Sent: Friday, February 13, 2009 8:28
AM
Subject: Re: [ontolog-forum]
Relationship: n-ary vs binary
On Feb 11, 2009, at 10:55 AM, Azamat wrote:
Relation is a canonic
class of any ontology. It is characterized by substantial properties and
formal attributes. Of the material properties, there are their reality,
nature and type and direction of dependency. Of the second, there are
transitivity, symmetry, reflexivity, and n-ary, or cardinality, terms, or
tuples, of domains, elements, components, or
arguments).
None of the above makes
sense.
The typical
mathematical reading of relation is an extensive set of ordered
elements (as ordered pairs, Kuratowski, Wiener, Skolem; well-ordering
axiom).
i. [A relation R over the sets X1, …, Xk is a subset of their Cartesian
product, written R ⊆ X1 × … × Xk.].
ii. [A relation R over the sets X1, …, Xk is a (k+1)-tuple R = (X1, …, Xk, G(L)), where G(L) is a subset of
the Cartesian product X1 × … × Xk. G(L) is called
thegraph of L.]
So, one can say "an
n-ary relation is an ordered class of
n-tuples Exactly.
This is the standard mathematical "extensional" notion of relation, and is
used in logical ("Tarskian") semantics. However, it is in many ways more
natural to distinguish the relation itself from its extension (set of tuples),
as apparently different relations can have the same extension 'by accident'.
Of course, those who adopt an extensionalist discipline as a matter of
principle would disagree with this.
or it is an ordered
class of (n+1) tuple". Three things are of importance
here:
1. the components of
relations are of the same kind and sorts, objects, persons, qualities,
quantities, times;
Nonsense. Many relations relate
things of different kinds. In fact, these are the most important relations in
most ontologies.
2. ordering of
relations, their direction, a triadic 'giving', tetradic
'paying' or triadic
'betweenness';
What ordering are you referring to? The tuples are ordered by
definition (that is what 'tuple' means). Other than that - essentially the
ordering of the relational arguments - relations have no intrinsic
order.
3. the key sense of
relationship is represented by the graph, indicating its nature and kind: if
it's causal relation, temporal relation, spatial relation, semantic
relation, logical relation,
etc.
Wrong. This is not represented by the graph. In general, there
is no way to tell, given the graph of relation (which just means, given the
extension of the relation) what "kind" of relation it is. For example, any
causal relation can also be interpreted as a (weaker) temporal relation, since
there is a temporal relation with exactly the same graph (because causes never
follow their consequences.)
Think of the complex
case of social networks, where social relationships described in terms of
nodes (agents) and ties (relationships), of different sorts and kinds,
like as emotional, friendly, economical, political, or commercial links
and
connections.
Indeed, that is a rich collection of examples: but it is
misleading to think that all relations are similar to social relationships
between people.
Any general ontology
missing the class of relation as the fundamental category of reality is
internally defective.
Well, the point can be argued. Certainly, one must use
relations when describing reality. But a nominalist might balk at admitting
that these relations exist in the same sense that physical things
exist.
Pat H
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