1. Ontology: from entities to operations
• Have we to change classical ontology in order to deal with the
novelties of the web?
• Barry Smith: no! just use : substances, accidents (relations),
continuants and occurrents, it is enough
• Problems: formulation can change intention, localisation and label
can make access more or less frequent, frequency of access can
change the hierarchy of links , or define new types of users,
introducing new “accidents” . What ontology for these changes?
• Post-fregean problem: if Hesperus and Phosphorus are related to
Venus, the network of Venus is enriched: the resource changes
(while remaining anchored in the node Venus). Venus is still there,
but in a different network (a planet, a goddess, an example for
philosophical problems of reference!)
• What ontological status have the introduction of nodes, the
labelisation, the exploitation of links?

2. hypothesis
• Networks make more sallient the possibility of changing the
meaning of an element by changing its relations
• Relations constitute the meaning
• Operations of constitution of the network change the impact of
the constitutive relations….
• Distinctions, and operations that make distinctions are more
important than entities,
• Still things have remain distinguable

3. Fonction et relations
How to find the function given the table of correspondences between values of m,
n, and values of F(m,n)???? We need the recursive form:
a) F(m,n) = n+1 if m = 0 ;
b) F(m,n) = F(m-1, 1) if m >0 and n= 0
c) F(m,n) = F(m-1,F(m,n-1)) if m>0 et n>0
Example: F(1,1)=?
We start from m-1= 0, n-1= 0, we have (m-1,F(m,n-1))= (0, F(1,0)) ;
F(1,0) [by(b)] = F(0,1)
F(m,n) where m= 0 and n= 1 gives , [by a] : n+1 = 2
F(m-1,F(m,n-1)) = F(0, 2) = 2+1= 3.

4. Ontology of the recursion process
• 0 is the basis. We can generate numbers a) by applying the
successor function to 0: 0’’’… (denumerable)
• b) by reapplying the set operation on 0: {0,{0} }, etc. applying the
same process to each 0! (non denumerable.)
• 0 is a distinguished element, but only as a basis for other
distinctions : the ‘, the {}.
• In a sense, it is a reserve of still undistinguished distinctors for
future distinctions
• (as starting from one 0 we can repeat 0 ad libitum in step b)
• A kind of unspecified dot (.) that could be extended as (.(.)) etc.
• Once{0} have been distinguished from 0, the distinctor {.}, implicit
in 0 as a reserve, has been used (and, in addition, is distinguished).
• As long as we dispose of unused and undistinguished distinctors,
we can cumulate distinguished elements
• The structure of the succession or embedding of the used distinctors
is the signature of the complex of distinguished elements,
• (leaving still undistinguished other possible distinctors )

5. Functions and predicates?
• In: a) F(m,n) = n+1 if m = 0 ;
• b) F(m,n) = F(m-1, 1) if m >0 and n= 0
• c) F(m,n) = F(m-1,F(m,n-1)) if m>0 et n>0
• ‘(‘ is the operation of a distinctor,
• m and n as variables are reserve of distinctors,
• 0 is the basis for the sequence of distinctions, and an implicit
reserve of distinctors
•
• F =predicate? x , or a, = substance or substrate?
• No: ‘F(‘ is the operation of a distinctor or several ones
• x a stock of distinctors,
• F(xi), the value of the function for a value xi of x, is the result of one
distinction, distinguishing the result of this distinctor from another
one
• ( but we still leave the distinctor itself undistinguished in the value
xi, while it is distinguished and made explicit in F).

6. A being = one being?
• Distinctors are need in order for entities to be distinguished
and identifiable.
• We cannot exclude that some beings, having no distinctors, are
not distinguished, that not every being is one being.
• Leibniz Principle: “if a exists, then a has discernible
properties“ becomes disputable!
• Identity of Indiscernibles (if a is not b, then a has at least a
different property that b has not), in a weak version, asserts
that “in order to be a being, a has to be distinguished” (not
disputable!)
• Distinctors are often presupposed, but not themselves
distinguished.

7. Signatures of classical entities
• Substrate or substance (particulars): an entity distinguished
from another entity (type e)
• Quality (particular property): distinguished relatively to one
entity of type e and to an entity distinguished relatively to an
entity of type e; type q
• Internal relation: (having a bigger size than); the complex of
entity of type e and type q is distinguished relatively to either
an entity e or a complex (e,q). Relational complex R
• Constitutive relation (being the father of, in the social sense):
the relational complex R is a distinctor, distinguishing new
entities of type qc (new qualities) supervening on previous
qualities.
• External relation (being 200m from point P): distinguished
using qualities of the relational complex, and not qualities of
entities e.

8. Change
• Constitutive relation simply adds new distinctions.
• Change implies that some new distinctions are added and
some old distinctions are lost:
• change implies that distinguished entities become
indistinguishable.
• (think of measurement in quantum mechanics; previous
coherences or interactions between states are lost)
• Web: creating new nodes, new labels, new links is creating
constitutive relations – new network and new qualities -
• At the same time it might make access to previous nodes, etc.
less frequent and decrease the strength of the previous links
• (but still distinguishable)

9. Quasi-explicit ontology
• Web ontology includes not only the distinguished entities
(referents, localisation, labels, type of links)
• But also the distinguishing operations (distinctors).
• The distinctors themselves are distinguished by architects of
networks:
• algorithms for building the network, for updating the referents,
the labels, for inferring new links from previous ones,
• for taking into account the visited nodes and by what paths,
inferring the visitor’s profile (her own distinctors!)
• But most of the time, the real distinctors of the network are
hidden and indistinguishable from the user’s point of view.
• They have to be at least distinguishable for users

10. Quasi-explicit ontology
• Web ontology includes not only the distinguished entities
(referents, localisation, labels, type of links)
• But also the distinguishing operations (distinctors).
• The distinctors themselves are distinguished by architects of
networks:
• algorithms for building the network, for updating the referents,
the labels, for inferring new links from previous ones,
• for taking into account the visited nodes and by what paths,
inferring the visitor’s profile (her own distinctors!)
• But most of the time, the real distinctors of the network are
hidden and indistinguishable from the user’s point of view.
• They have to be at least distinguishable for users