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Resemblance: a Logico-Philosophical Analysis RESEMBLANCE: A LOGICO-PHILOSOPHICAL ANALYSIS ISKENDER_ TAS»DELEN NOVEMBER 2005 RESEMBLANCE: A LOGICO-PHILOSOPHICAL ANALYSIS A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF SOCIAL SCIENCES OF THE MIDDLE EAST TECHNICAL UNIVERSITY BY ISKENDER_ TAS»DELEN IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE DEPARTMENT OF PHILOSOPHY NOVEMBER 2005 Approval of the Graduate School of Social Sciences Prof. Dr. Sencer Ayata Director I certify that this thesis satis¯es all the requirements as a thesis for the degree of Doctor of Philosophy. Prof. Dr. Ahmet Inam_ Head of Department This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Doctor of Philosophy. Assoc. Prof. Dr. David GrÄunberg Supervisor Examining Committee Members Assoc. Prof. Dr. David GrÄunberg (METU, PHIL) Assoc. Prof. Dr. Erdin»cSayan (METU, PHIL) Assoc. Prof. Dr. Ayhan Sol (METU, PHIL) Assoc. Prof. Dr. Erdal Cengiz (DTCF, PHIL) Assoc. Prof. Dr. Zekiye Kutlusoy (Uluda¸g U,Ä PHIL) I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last name : Iskender_ Ta»sdelen Signature : iii Abstract Resemblance: A Logico-Philosophical Analysis Ta»sdelen, Iskender_ Ph.D., Department of Philosophy Supervisor: Assoc. Prof. Dr. David GrÄunberg November 2005, 101 pages Indiscernibility, interchangeability and resemblance relations may be named as weak identity relations or identity-like relations. Indeed, identical objects can be thought to satisfy all these three relations. According to the realist view, these relations are de¯ned on the basis of properties of objects. While indiscernibility is a context- independent relation (for it is de¯ned in terms of all properties of objects), inter- changeability and resemblance relations are de¯ned in terms of some signi¯cant prop- erties of objects and thus they should be regarded as context-dependent. We should consider the following points while comparing rivalling theories of resemblance: 1. The theory explaining resemblance relations between objects should cover as many domains as possible. Instead of simply admitting that objects of a given type may resemble each other, the theory should explain how these relations are possible. 2. Objects do not just resemble or not; resemblance is a relation that admits degrees. Thus, the theory providing a ¯ner analysis of close and weak resem- blances should be preferred. In comparison to resemblance nominalism, the realist theory of resemblance is stronger with respect to both points. The criticism that the realist view may not iv explain degrees of resemblance can be rejoined by removing the indeterminacy as to the nature of this notion. Among knowledge representation systems, property and attribute systems provide a simple but strong models for analytic ontology. Weak identity relations can easily be de¯ned in these systems and the results following from these de¯nitions can be seen to conform to our intuitions about weak identity relations. Keywords: Ontology, Identity, Indiscernibility, Resemblance, Knowledge Represen- tation System, Tolerance Relation, Model Theory. v OzÄ Benzes»me: Mant³ksal-FelsefI_ BI_r C» ozÄ umlemeÄ Ta»sdelen, Iskender_ Doktora, Felsefe BÄolÄumÄu Tez YÄoneticisi:Do»c.Dr. David GrÄunberg Kas³m 2005, 101 sayfa Ay³rdedilemezlik, kar»s³l³kl³-de¸gi»stirilebilirlik(ya da muadiliyet) ve benzerlik ba¸g³nt³la- r³ \zay³f Äozde»slikba¸g³nt³lar³" ya da \Äozde»slik-benzeri varl³kbilimsel ba¸g³nt³lar" olarak adland³r³labilir. Ger»cektende, Äozde»snesneler i»cinher Äu»cba¸g³nt³n³n da sa¸gland³¸g³ dÄu»sÄunÄulebilir.Ger»cek»cigÄorÄu»segÄorebu ba¸g³nt³lar nesnelerin Äozellikleriile tan³mlan³r. Ay³rdedilemezlik ba¸g³nt³s³ nesnelerin tÄumÄozellikleriile tan³mland³¸g³i»cinba¸glam- ba¸g³ls³zbir ba¸g³nt³ iken, kar»s³l³kl³-de¸gi»stirilebilirlikve benzerlik ba¸g³nt³lar³ nesnelerin kimi Äozellikleriile tan³mland³¸g³ndanba¸glam-ba¸g³lba¸g³nt³lar olarak dÄu»sÄunÄulmelidir. Benzerlik ba¸g³nt³s³na dair varl³kbilimsel kuramlar³n k³yaslanmas³nda gÄozÄonÄune al³nmas³ gerekenler aras³nda »sunlar³sayabiliriz: 1. Kuram mÄumkÄunoldu¸guncafazla say³da ve tipte nesnelerin aras³ndaki ben- zerlik ili»skilerinia»c³klayabilmelidir. Belirli tipteki nesneler aras³ndaki benzerlik ili»skilerininolabilece¸ginisadece ilkece kabul etmek yerine bu ili»skilerinnas³l mÄumkÄunoldu¸gunu a»c³klayan bir kuram tercih edilmelidir. 2. Benzerlik ya var ya da yok denebilecek bir ba¸g³nt³ olmay³p derecelerle or- taya »c³kabilen bir ba¸g³nt³ oldu¸gundan,daha yak³n ya da daha uzak benzerlik ba¸g³nt³lar³n³n olabildi¸ginceayr³nt³l³ bir »sekildeincelenmesine olanak sa¸glayan bir kuram tercih edilmelidir. Benzerlik adc³l³¸g³nak³yasla, ger»cek»cikuram bu iki a»c³danda gÄu»clÄudÄur.Ger»cek»ci vi kuram³n benzerlik derecelerini a»c³klayamad³¸g³iddias³ ise benzerlik derecelerine ili»skin belirsizli¸gingiderilmesi ile yan³tlanabilir. Bilgi temsili sistemleri aras³nda say³lan Äozellikve nitelik sistemleri »cÄozÄumleyici varl³kbilim i»cinbasit ve gÄu»clÄumodeller sa¸glamaktad³r.Bu sistemlerde zay³f Äozde»slik ba¸g³nt³lar³ kolayca tan³mlanabilir ve bu tan³mlardan elde edilen sonu»clar³nsezgileri- mizle uygunluk i»cindeoldu¸gugÄorÄulebilir. Anahtar Kelimeler: Varl³kbilim, Ozde»slik,Ay³rdedilemezlik,Ä Kar»s³l³kl³-de¸gi»stirilebilir- lik, Benzerlik, Bilgi Temsili Sistemi, Tolerans Ba¸g³nt³s³, Model Kuram³. vii In Memory of Anneanne and Efendibaba viii Acknowledgments I would like to express my sincere gratitude to my supervisor Assoc. Prof. Dr. David GrÄunberg for his friendly encouragement, his helpful criticisms and suggestions. I am deeply grateful to Prof. Dr. Teo GrÄunberg, the father of modern logic in Turkey, for teaching me logic and for his insistence that I should also study philosophical applications of logic. I deeply thank the members of the examining committee specially for providing me some suggestions for my future work. I am grateful to the METU Department of Philosophy for the friendly atmosphere. I have always enjoyed and bene¯ted from our conversations with Assoc. Prof. Dr. Erdin»cSayan. I could not complete this thesis without the support of my family including Woody. ix Table of Contents Plagiarism ............................................................ iii Abstract .............................................................. iv OzÄ ...................................................................... vi Acknowledgments ................................................... ix Table of Contents ................................................... x CHAPTER 1 Introduction ...................................................... 1 2 Prelude ............................................................ 6 3 Identity, Indiscernibility, Interchangeability ............... 9 4 Resemblance ....................................................... 15 4.1 Criticisms of Resemblance Nominalism . 16 4.2 Some Preliminary Remarks on Possible Formalisms of Resemblance . 18 4.3 Real Resemblances . 19 5 Set Theoretic First-Order Structures ....................... 25 6 Identity-like Relations in Set-Theoretic Models . 30 x 6.1 Preservation of Identity-Like Relations . 33 7 Formal Properties of Resemblance and Tolerance Spaces 37 8 Identity-like Relations in Information Systems . 43 8.1 Property and Relation Systems . 43 8.2 Identity-like Relations in Property and Relation Systems . 46 8.3 Attribute Systems . 47 8.4 Identity-like Relations in Attribute Systems . 52 9 Deutsch's Problem ............................................... 58 9.1 Deutsch's System . 61 9.2 General Similarity Relations and Indiscernibility Properties in Information Systems . 64 10 Infinite Regress Arguments and Resemblance . 66 10.1 The Way to In¯nite Regress . 68 10.2 Viciousness . 72 10.3 Resemblance and In¯nite Regresses . 74 11 Conclusion ......................................................... 76 References ............................................................ 78 Appendices Appendix A. Set-Theoretic Preliminaries ..................... 80 Appendix B. Turkish Summary .................................. 88 Vita ....................................................................101 xi Chapter 1 Introduction This is a study of identity-like ontological relations: indiscernibility, interchange- ability and resemblance. I devoted special attention to the relation of resemblance. The thesis is roughly divided into two parts. Not in form (since, e.g., philosophical remarks invaded most of chapters 2, 3, 4 and 10) but in spirit. First I presented some philosophical remarks as to the nature of these relations. This part is not an overall philosophical discussion of the topic. However, it serves to provide, at least for myself, a philosophical motivation for the next part in which I examined some formalisms of identity-like relations. In the second part of the thesis, I presented some structures and how statements concerning identity-like relations can be interpreted in these structures. The last example, that of information systems seems to me to be the most e®ective way of explicating identity-like relations. I will now give a little more detailed outline of these parts. I In the ¯rst part, I discussed my philosophical contentions. I have two main philosophical contentions regarding identity-like relations:
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