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Pierre Livet: Ontologies, from entities to operations.
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Pierre Livet: Ontologies, from entities to operations.

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  • 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