2. 1 Formal Ontology

3. 2 Schedule Sep. 4: Introduction: Mereology, Dependence and Geospatial Ontology Reading: Basic Tools of Formal Ontology Ontological Tools for Geographic Representation

4. 3 Schedule Sep. 5: (Thursday) 4pm Metaphysics talk by David Hershenov (Jointly with Philosophy Department Colloquium) Sep. 11: Talk by Peter Forrest on Mereology and Time. (Jointly with Philosophy Department Colloquium) Sep. 18: Truthmaking and the Semantics of Maps Sep. 25: Vagueness

5. 4 Schedule Oct. 2: Granularity Reading: A Theory of Granular PartitionsA Theory of Granular Partitions [Oct. 9 University Convocation: No meeting] Oct. 16: Talk by Chuck Dement on: " The Ontology of Formal Ontology" [Oct. 23 No meeting] [Oct. 30 No meeting]

6. 5 Schedule Nov. 6: 2pm “SNAP and SPAN”: Cognitive Science Colloquium Talk, 280 Park Nov 6: 4pm Discussion of "SNAP and SPAN“ Nov. 8 (Friday): 4pm Talk by Berit Brogaard

7. 6 Schedule Nov. 9 Day-long Saturday Workshop 9am Achille Varzi: " From Ontology to Metaphysics" 10.45 am Berit Brogaard 12.30 Pizza Lunch 1pm Achille Varzi: "Ontology and Logical Form" 3-5pm Barry Smith Nov. 13 Final Lecture

8. 7 IFOMIS Institute for Formal Ontology and Medical Information Science Some background

9. 8 The Manchester School Kevin Mulligan Peter Simons Barry Smith in Manchester 1973-76 working on the ontology of Edmund Husserl

10. 9 Edmund Husserl

11. 10 Logical Investigations¸1900/01 –the theory of part and whole –the theory of dependence –the theory of boundary, continuity and contact

12. 11 Formal Ontology (term coined by Husserl) the theory of those ontological structures (such as part-whole, universal-particular) which apply to all domains whatsoever

13. 12 Formal Ontology vs. Formal Logic Formal ontology deals with the interconnections of things with objects and properties, parts and wholes, relations and collectives Formal logic deals with the interconnections of truths with consistency and validity, or and not

14. 13 Formal Ontology vs. Formal Logic Formal ontology deals with formal ontological structures Formal logic deals with formal logical structures ‘formal’ = obtain in all material spheres of reality

15. 14 Formal Ontology and Symbolic Logic Great advances of Frege, Russell, Wittgenstein Leibnizian idea of a universal characteristic …symbols are a good thing

16. 15 Warning don’t confuse Logical with Ontological Form Russell Part-whole is not a logical relation

17. 16 for Frege, Russell, Lesniewski, Wittgenstein, Quine Logic is a ‘Zoology of Facts’ Formal theories are theories of reality with one intended interpretation = the world tragically after starting off on the right road

18. 17 Logic took a wrong turn

19. 18 Logic took a wrong turn

20. 19 Tarski, Carnap, Putnam, Sowa, Gruber: Forget reality! Lose yourself in ‘models’!

21. 20 IFOMIS Ontology is an ontology of reality Standard Information Systems Ontologies are ontologies of mere 'models'

22. 21 Standard Information Systems Ontologies: programming real ontology into computers is hard therefore: we will simplify ontology and not care about reality at all

23. 22 Painting the Emperor´s Palace is hard

24. 23 therefore we will not try to paint the Palace at all... we will be satisfied instead with a grainy snapshot of some other building

25. 24

26. 25 IFOMIS Strategy get real ontology right first and then investigate ways in which this real ontology can be translated into computer- useable form later NOT ALLOW ISSUES OF COMPUTER- TRACTABILITY TO DETERMINE THE CONTENT OF ONTOLOGY

27. 26 a language to map these Formal ontological structures in reality

28. 27 a directly depicting language ‘John’ ‘( ) is red’ Object Property Frege

29. 28 Wittgenstein’s Tractatus Propositions States of affairs are pictures of

30. 29 Parts and Moments in a directly depicting language all well-formed parts of a true formula are also true (The Oil-Painting Principle) A new sort of mereological inference rule – the key to the idea of a directly depicting language

31. 30 

32. 31 A directly depicting language may contain an analogue of conjunctio n p and q _______ pp

33. 32 but it can contain no negation pp _______ pp

34. 33 and also no disjunction p or q ______ pp

35. 34 The idea of a directly depicting language suggests a new method of constituent ontology: to study a domain ontologically is to establish the parts, qualities and processes of the domain and the interrelations between them

36. 35 BFO and GOL Basic Formal Ontology (BFO) BFO as an ontological theory of reality designed as a real constraint on domain ontologies (as opposed to conceptual modeling...)

37. 36 A Network of Domain Ontologies Material (Regional) Ontologies Basic Formal Ontology

38. 37 Ontology seeks an INVENTORY OF REALITY Relevance of ontology for information systems, e.g.: terminology standardization taxonomy standardization supports reasoning about reality

39. 38 Basic Formal Ontology = a formal ontological theory, expressed in a directly depicting language, of all non-intentional parts of reality (an ontology of the whole of reality but leaving aside minds and meanings) BFO

40. 39 A Network of Domain Ontologies BFO

41. 40 A Network of Domain Ontologies BFOGeO

42. 41 A Network of Domain Ontologies BFO GeOMedO

43. 42 A Network of Domain Ontologies BFO GeOMedOCellO

44. 43 A Network of Domain Ontologies BFO GeOMedOCellOGenO

45. 44 Extended formal ontology (BFO Extended by Mind) BFO BFO+Mind

46. 45 BFO Extended by Mind BFO BFO+Mind EcO

47. 46 BFO Extended by Mind BFO BFO+Mind EcO LexO

48. 47 Reality

49. 48 Reality

50. 49

51. 50 Reality

52. 51 Reality is complicated

53. 52 What is the best language to describe this complexity?

54. 53 Anglocentric Realism We have a huge amount of knowledge of reality, at many different levels of granularity, from microphysics to cosmology

55. 54 Anglocentric Realism TEE = Technically Extended English = English extended by the technical vocabularies of meteorology, chemistry, genetics, medicine, astronomy, engineering, etc.

56. 55 Anglocentric Realism Our knowledge of reality as expressed in Technically Extended English is increasing by the hour

57. 56 Unfortunately … there are problems with TEE as a formal representation language (cf. Tarski)

58. 57 Nouns and verbs Substances and processes Continuants and occurrents In preparing an inventory of reality we keep track of these two different categories of entities in two different ways

59. 58 Natural language glues them together indiscriminately substance t i m e process

60. 59 Snapshot vs. Video substance t i m e process

61. 60 Substances Mesoscopic reality is divided at its natural joints into substances: animals, bones, rocks, potatoes

62. 61 The Ontology of Substances Substances form natural kinds (universals, species + genera)

63. 62 Processes Processes merge into one another Process kinds merge into one another … few clean joints either between instances or between types

64. 63 Processes t i m e

65. 64 Substances and processes t i m e process demand different sorts of inventories

66. 65 Substances demand 3-D partonomies space

67. 66 Processes demand 4D-partonomies t i m e

68. 67 Processes a whistling, a blushing, a speech a run, the warming of this stone

69. 68 Processes may have temporal parts The first 5 minutes of my headache is a temporal part of my headache The first game of the match is a temporal part of the whole match

70. 69 Substances do not have temporal parts The first 5-minute phase of my existence is not a temporal part of me It is a temporal part of that complex process which is my life

71. 70 Substances have spatial parts

72. 71

73. 72

74. 73 How do we glue these two different sorts of entities together mereologically? How do we include them both in a single inventory of reality?

75. 74 How do we fit these two entities together within a single system of representations? within a directly depicting language?

76. 75 You are a substance Your life is a process You are 3-dimensional Your life is 4-dimensional

77. 76 Substances and processes form two distinct orders of being Substances exist as a whole at every point in time at which they exist at all Processes unfold through time, and are never present in full at any given instant during which they exist. When do both exist to be inventoried together?

78. 77 Main problem English swings back and forth between two distinct depictions of reality … imposing both 3-D partitions (yielding substances) and 4-D partitions (yielding processes) at the same time

79. 78 Main problem There is a polymorphous ontological promiscuity of the English sentence, which is inherited also by the form ‘F(a)’

80. 79 Two alternative basic ontologies SNAP and SPAN SNAP = substances plus qualities SPAN = processes

81. 80 These represent two views of the same rich and messy reality, the reality captured promiscuously by TEE

82. 81 The Four-Dimensionalist Ontology t i m e

83. 82 boundaries are mostly fiat t i m e everything is flux

84. 83 mereology works without restriction everywhere here t i m e clinical trial

85. 84 The Time-Stamped Ontology t1t1 t3t3 t2t2 here time exists outside the ontology, as an index or time-stamp

86. 85 mereology works without restriction in every instantaneous 3-D section through reality

87. 86 Three views/partitions of the same reality

88. 87 all contain huge amounts of knowledge of this reality against Kant

89. 88 Ontological Zooming The dimension of granularity

90. 89

91. 90 Part 2 Tools of Ontology: Mereology, Topology, Dependence

92. 91 Ontological Dependence processes + qualities substances

93. 92 Ontological Dependence How to link together the domain of substances and the domain of processes?

94. 93 Ontological Dependence Substances are that which can exist on their own Processes require a support from substances in order to exist This holds for qualities, too

95. 94 Specific Dependence O := overlap  x := x is necessarily such that E! := existence SD(x, y) :=  O(x, y)   x (E!x  E!y)

96. 95 Mutual specific dependence Each token of visual extension is mutually dependent on a token color quality The north pole of a magnet is mutually dependent on the south pole MSD(x, y) := SD(x, y)  SD(y, x)

97. 96 One-Sided Specific Dependence OSD(x, y) := SD(x, y)   MSD(x, y) My headache is one-sidedly specifically dependent on me.

98. 97 Substances, Qualities, Processes Substances are the bearers or carriers of qualities and processes, … the latter are said to ‘inhere’ in their substances

99. 98 Ontological Dependence Substances are such that, while remaining numerically one and the same, they can admit contrary qualities at different times … I am sometimes hungry, sometimes not

100. 99 Substances can also gain and lose parts … as an organism may gain and lose molecules

101. 100 Types of relations between parts 1. Dependence relations 2. Side-by-sideness relations 3. Fusion relations

102. 101 Dependence cannot exist without a thinker a thinking process substance

103. 102 Theory of vagueness Side-by-sideness found among substances and among qualities and processes

104. 103 Fusion Topology

105. 104 Topology, like mereology, applies both in the realm of substances and in the realms of qualities and processes

106. 105 Mereotopology = topology on a mereological basis

107. 106 Substances, Undetached Parts and Heaps Substances are unities. They enjoy a natural completeness in contrast to their undetached parts (arms, legs) and to heaps or aggregates … these are topological distinctions

108. 107 substance undetached part collective of substances

109. 108 special sorts of undetached parts ulcers tumors lesions …

110. 109 Fiat boundaries physical (bona fide) boundary fiat boundary

111. 110 Examples of bona fide boundaries: an animal’s skin, the surface of the planet of fiat boundaries: the boundaries of postal districts and census tracts

112. 111 Mountain bona fide upper boundaries with a fiat base:

113. 112 Architects Plan for a House fiat upper boundaries with a bona fide base:

114. 113 where does the mountain start ?... a mountain is not a substance

115. 114 nose...and it’s not a quality, either

116. 115 A substance has a complete physical boundary The latter is a special sort of part of a substance … a boundary part something like a maximally thin extremal slice

117. 116 interior substance boundary

118. 117 A substance takes up space. A substance occupies a place or topoid (which enjoys an analogous completeness or rounded-offness) A substance enjoys a place at a time

119. 118 A substance has spatial parts … perhaps also holes

120. 119 Each substance is such as to have divisible bulk: it can in principle be divided into separate spatially extended substances

121. 120 By virtue of their divisible bulk substances compete for space: (unlike shadows and holes) no two substances can occupy the same spatial region at the same time.

122. 121 Substances vs. Collectives Collectives = unified aggregates: families, jazz bands, empires Collectives are real constituents of reality (contra sets) but still they are not additional constituents, over and above the substances which are their parts.

123. 122 Collectives inherit some, but not all, of the ontological marks of substances They can admit contrary qualities at different times.

124. 123 Collectives, like substances, may gain and lose parts or members may undergo other sorts of changes through time.

125. 124 Qualities and processes, too, may form collectives a musical chord is a collective of individual tones football matches, wars, plagues are collectives of actions involving human beings

126. 125 One-place qualities and processes depend on one substance (as a headache depends upon a head)

127. 126 Relational qualities and processes John Mary kiss stand in relations of one-sided dependence to a plurality of substances simultaneously

128. 127 Examples of relational qualities and processes kisses, thumps, conversations, dances, legal systems Such real relational entities join their carriers together into collectives of greater or lesser duration

129. 128 Mereology ‘Entity’ = absolutely general ontological term of art embracing at least: all substances, qualities, processes, and all the wholes and parts thereof, including boundaries

130. 129 Primitive notion of part ‘x is part of y’ in symbols: ‘x ≤ y’

131. 130 We define overlap as the sharing of common parts: O(x, y) :=  z(z ≤ x  z ≤ y)

132. 131 Axioms for basic mereology AM1 x ≤ x AM2x ≤ y  y ≤ x  x = y AM3x ≤ y  y ≤ z  x ≤ z Parthood is a reflexive, antisymmetric, and transitive relation, a partial ordering.

133. 132 Extensionality AM4  z(z ≤ x  O(z, y))  x ≤ y If every part of x overlaps with y then x is part of y cf. status and bronze

134. 133 Sum AM5  x(  x)   y(  z(O(y,z)   x(  x  O(x,z)))) For every satisfied property or condition  there exists an entity, the sum of all the  -ers

135. 134 Definition of Sum  x(  x) :=  y  z(O(y,z)   x(  x  O(x,z))) The sum of all the  -ers is that entity which overlaps with z if and only if there is some  -er which overlaps with z

136. 135 Examples of sums electricity, Christianity, your body’s metabolism the Beatles, the population of Erie County, the species cat

137. 136 Other Boolean Relations x  y :=  z(z ≤ x  z ≤ y) binary sum x  y :=  z(z ≤ x  z ≤ y)product

138. 137 Other Boolean Relations x – y :=  z (z ≤ x  O(z, y)) difference –x :=  z (  O(z, x)) complement

139. 138 What is a Substance? Bundle theories: a substance is a whole made up of tropes as parts. What holds the tropes together?... problem of unity

140. 139 Topology How can we transform a sheet of rubber in ways which do not involve cutting or tearing?

141. 140 Topology We can invert it, stretch or compress it, move it, bend it, twist it. Certain properties will be invariant under such transformations – ‘topological spatial properties’

142. 141 Topology Such properties will fail to be invariant under transformations which involve cutting or tearing or gluing together of parts or the drilling of holes

143. 142 Examples of topological spatial properties The property of being a (single, connected) body The property of possessing holes (tunnels, internal cavities) The property of being a heap The property of being an undetached part of a body

144. 143 Examples of topological spatial properties It is a topological spatial property of a pack of playing cards that it consists of this or that number of separate cards It is a topological spatial property of my arm that it is connected to my body.

145. 144 Topological Properties Analogous topological properties are manifested also in the temporal realm: they are those properties of temporal structures which are invariant under transformations of slowing down, speeding up, temporal translocation …

146. 145 Topological Properties

147. 146 Topology and Boundaries Open set: (0, 1) Closed set: [0, 1] Open object: Closed object:

148. 147 Closure = an operation which when applied to an entity x yields a whole which comprehends both x and its boundaries use notion of closure to understand structure of reality in an operation- free way

149. 148 Axioms for Closure AC1: each entity is part of its closure AC2: the closure of the closure adds nothing to the closure of an object AC3: the closure of the sum of two objects is equal to the sum of their closures

150. 149 Axioms for Closure AC1x ≤ c(x) expansiveness AC2 c(c(x)) ≤ c(x) idempotence AC3 c(x  y) = c(x)  c(y) additivity

151. 150 Axioms for Closure These axioms define in mereological terms a well-known kind of structure, that of a closure algebra, which is the algebraic equivalent of the simplest kind of topological space.

152. 151 Boundary b(x) := c(x)  c(–x) The boundary of an entity is also the boundary of the complement of the entity

153. 152 Interior i(x) := x – b(x) boundary interior x

154. 153 An entity and its complement -x x

155. 154 The entity alone x

156. 155 The complement alone -x

157. 156 Closed and Open Objects x is closed := x is identical with its closure x is open := x is identical with its interior The complement of a closed object is open The complement of an open object is closed Some objects are partly open and partly closed

158. 157 Definining Topology Topological transformations = transformations which take open objects to open objects e.g. moving, shrinking x

159. 158 Closed Objects A closed object is an independent constituent of reality: It is an object which exists on its own, without the need for any other object which would serve as its host

160. 159 Contrast holes a hole requires a host

161. 160 A closed object need not be connected

162. 161 …. nor must it be free of holes

163. 162 …. or slits

164. 163 Connectedness Definition An object is connected if we can proceed from any part of the object to any other and remain within the confines of the object itself

165. 164 Connectedness A connected object is such that all ways of splitting the object into two parts yield parts whose closures overlap Cn(x) :=  yz(x = y  z   w(w ≤ (c(y)  c(z))))

166. 165 Connectedness* A connected* object is such that, given any way of splitting the object into two parts x and y, either x overlaps with the closure of y or y overlaps with the closure of x Cn*(x) :=  yz(x = y  z  (  w(w ≤ x  w ≤ c(y))   w(w ≤ y  w ≤ c(x)))

167. 166 Problems

168. 167 Problem A whole made up of two adjacent spheres which are momentarily in contact with each other will satisfy either condition of connectedness Strong connectedness rules out cases such as this

169. 168 Strong connectedness Scn(x) := Cn*(i(x)) An object is strongly connected if its interior is connected*

170. 169 Definition of Substance A substance is a maximally strongly connected non-dependent entity: S(x) := Scn(x)   y(x ≤ y  Scn(y)  x = y)   zSD(x, z)

171. 170 More needed Substances are located in spatial regions

172. 171 More needed Some substances have a causal integrity without being completely disconnected from other substances: heart lung Siamese twin

173. 172 Time Substances can preserve their numerical identity over time Full treatment needs an account of: spatial location transtemporal identity causal integrity, matter internal organization