1. VT

2. SNAP and SPAN

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

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

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

6. Processes t i m e

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

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

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

10. Substances demand 3-D partonomies space

11. Moments demand 4D-partonomies t i m e

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

13. 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

14. 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 moment which is my life

15. Substances have spatial parts

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

18. 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?

19. 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

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

21. The Four-Dimensionalist Ontology t i m e

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

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

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

25. mereology works without restriction in every 3-D SNAP ti ontology

26. 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

27. 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

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

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

30. Dependence cannot exist without a thinker a thinking process substance

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

32. Fusion Topology

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

34. SNAP and SPAN Substances+qualities 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

35. Fourdimensionalism denies this – time is just another dimension, analogous to the three spatial dimensions – only processes exist – substances are analyzed away as worms/fibers within the four-dimensional process plenum

36. Parts of processes (1) c c: boundary a a a: scattered part b b: temporal slice

37. Parts of processes (2) a a: sub-process b b: phase

38. There are no substances Bill Clinton does not exist Rather: there exists within the four- dimensional plenum a continuous succession of processes which are similar in Billclintonizing way

39. 4-Dism –>There is no change That the water boils means: Not: the water is colder at one time and hotter at another time Rather: that one phase of the boiling process is cold and another hot as one part of a colored ribbon is red and another blue

40. The Parable of Little Tommy’s Christmas Present

41. Little Tommy’s Other Christmas Present

42. Fourdimensionalism rests on a misunderstanding of physics (both of relativity theory and of quantum mechanics) and on a misunderstanding of the status of Newtonian physics

43. Fourdimensionalism is right in everything it says But incomplete

44. Realist Perspectivalism There is a multiplicity of ontological perspectives on reality, all equally veridical = transparent to reality

45. Need for different perspectives Not one ontology, but a multiplicity of complementary ontologies Cf. Quantum mechanics: particle vs. wave ontologies

46. Two Orthogonal, Complementary Perspectives SNAP and SPAN

47. the tumor and its growth the surgeon and the operation the virus and its spread the temperature and its rise the disease and its course the therapy and its application

48. SNAP and SPAN SNAP entities - have continuous existence in time - preserve their identity through change - exist in toto if they exist at all SPAN entities - have temporal parts - unfold themselves phase by phase - exist only in their phases/stages

49. SNAP vs. SPAN 1.SNAP: a SNAPshot ontology of endurants existing at a time 2.SPAN: a four-dimensionalist ontology of processes

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

51. Change Adding SNAP to the fourdimensionalist perspective makes it possible to recognize the existence of change (SNAP entities are that which endure, thus providing identity through change) SNAP ontologies provide perspective points – landmarks in the flux – from which SPAN processes can be apprehended as changes

52. 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

53. How do you know whether an entity is SNAP or SPAN?

54. Three kinds of SNAP entities 1.Substances 2.SPQR… entities 3.Spatial regions, contexts, niches, environments

55. SPQR… entities States, powers, qualities, roles … Substances are independent SPQR entities are dependent on substances, they have a parasitic existence: a smile smiles only in a human face

56. Other SPQR… entities: functions, dispositions, plans, shapes SPQR… entities are all dependent on substances one-place SPQR entities: temperature, color, height

57. Substances and SPQR… entities Substances are the bearers or carriers of, SPQR… entities ‘inhere’ in their substances

58. one-place SPQR… entities tropes, individual properties (‘abstract particulars’) a blush my knowledge of French the whiteness of this cheese the warmth of this stone

59. relational SPQR… entities John Mary love stand in relations of one-sided dependence to a plurality of substances simultaneously

60. Ontological Dependence Substances are that which can exist on their own SPQR… entities require a support from substances in order to exist

61. 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

62. SNAP ontology many sharp boundaries SPAN ontology many smeered boundaries many fiat boundaries (more scope for gerrymandering – why?)

63. SPAN ontology also smeered in that it forms layers of spatio-temporally coincident entities Cf. the relation between application of therapy and course of disease These overlap spatio-temporal, but belong to different layers Need for Layered Mereotopology

64. SNAP entities provide the principles of individuation/segmentation for SPAN entities No change without some THING or QUALITY which changes identity-based change

65. Processes, too, are dependent on substances One-place vs. relational processes One-place processes: getting warmer getting hungrier

66. Examples of relational processes kissings, thumps, conversations, dances, Such relational processes join their carriers together into collectives of greater or lesser duration

67. Processes, like substances, are concrete denizens of reality My headache, like this lump of cheese, exists here and now, and both will cease to exist at some time in the future. But they exist in time in different ways

68. Each is a window on that dimension of reality which is visible through the given ontology SNAP and SPAN ontologies are partial only (Realist perspectivalism)

69. SNAP: Entities existing in toto at a time

70. Three kinds of SNAP entities 1.Substances 2.SPQR… entities 3.Spatial regions, Contexts, Niches

73. SNAP

74. SPAN: Entities extended in time

77. Relations between SNAP and SPAN SNAP-entities participate in processes they have lives, histories

78. Participation x y substances x, y participate in process B time B x y SNAP-t i. time SPAN B

79. SPQR… entities and their SPAN realizations the performance of a function the exercise of a role the execution of a plan the realization of a disposition

80. SPQR… entities and their SPAN realizations function role plan disposition therapy disease SNAP

81. SPQR… entities and their SPAN realizations performance exercise execution realization application course SPAN

82. problem cases traffic jam forest fire anthrax epidemic hurricane Maria waves shadows

83. forest fire: a process a pack of monkeys jumping from tree to tree the Olympic flame: a process or a thing? anthrax spores are little monkeys

84. Two alternative basic ontologies both of which are able to sustain a directly depicting language plus a system of meta-relations for building bridges between the two ontologies via: dependence participation initiation etc.

85. SNAP and SPAN space space-time substances SPQR entities (including functions) processes

86. Gene Ontology Cellular Component Ontology: subcellular structures, locations, and macromolecular complexes; examples: nucleus, telomere SNAP-INDEPENDENT Molecular Function Ontology: tasks performed by individual gene products; examples: transcription factor, DNA helicase SNAP-DEPENDENT (SPQR) Biological Process Ontology: broad biological goals accomplished by ordered assemblies of molecular functions; examples: mitosis, purine metabolism SPAN

87. Special role of formal relations Only they are represented by predicates in the first-order logic representation of our ontology But what are formal relations?

88. A hypothesis (first rough version) Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP-SPAN divide they glue SNAP and SPAN entities together

89. This generates a first list of formal relations, e.g. dependence, but we find some of these relations also within SNAP or within SNAP

90. The idea (modified version) Formal relations are the relations that hold SNAP and SPAN entities/ontologies together and analogous relations … they come for free, they do not add anything to being = they are links between categories

91. Example: Individuation, segmentation

92. Substances tokens separated by bona fide boundaries form natural kinds, types (universals, species + genera) separated by bona fide boundaries

93. Processes Process tokens merge into one another Process kinds merge into one another … few clean joints either between tokens or between types

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

95. SNAP entities provide the principles of individuation/segmentation for SPAN entities No change without some THING or QUALITY which changes

96. Example: Ontological Dependence (SPAN, SNAP): process->substance The erosion of the rock necessitates the existence of the rock (SNAP, SNAP): SPQR->substance The token redness of the sand necessitates the existence of the sand

97. Generating a typology Two main types of formal relations: meta-ontological: obtain between entities of different ontologies intra-ontological: obtain between entities of the same ontology (intra-SNAP, intra- SPAN)

98. Three parameters: - the arity of the relation - the types of the relata, expressed as an ordered list, called the signature of the relation - the formal nature of the relation

99. Principal Signatures In the binary case: SNAP-SNAP - (SNAP i, SNAP i ), i = i - (SNAP i, SNAP i ), i j SPAN-SPAN SNAP-SPAN SPAN-SNAP

100. Transtemporal relations Examples: Genidentity (transtemporal generalization of identity/part-whole) Successive causality

101. Genidentity Also SPAN-SPAN? Is there a form of genidentity among processes? The such-as-to-have-come-forth-from relation. Signature: SNAP i -SNAP j Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting

102. Successive Causality SNAP-SPAN: Agent causation A substance produces causally a process SPAN-SPAN: Process causation One process causes another process SPAN-SNAP: Causal repercussion A process results in the modification of a substance (always mediated by process causation) SNAP-SNAP: Causal origin One substance is the causal origin of another (mediated by other types of causal relations )

103. Successive Causality SNAP-SPAN: Agent causation SPAN-SPAN: Process causation SPAN-SNAP: Causal repercussion SNAP-SNAP: Causal origin do not apply on all levels of granularity

104. Our main target: Temporally extended relations Simultaneous Causality Participation (holds between a substance and a process such as an action or a life or history) Realization (holds between SPQR… entities and their SPAN expressions)

105. Simultaneous causality SPAN-SPAN The rise in temperature causes the (simultaneous) increase in pressure (Boyle’s law)

106. Substance->Process PARTICIPATION (a species of dependence)

107. Participation (SNAP-SPAN) A substance (SNAP) participates in a process (SPAN) A runner participates in a race A voter participates in an election

108. Axes of variation activity/passivity (  agentive) direct/mediated benefactor/malefactor (  conducive to existence) [MEDICINE]

109. SNAP-SPAN Participation Perpetration (+agentive) Initiation Perpetuation Termination Influence Facilitation Hindrance Mediation Patiency (-agentive)

110. Perpetration A substance perpetrates an action (direct and agentive participation in a process): The referee fires the starting-pistol The captain gives the order

111. Initiation A substance initiates a process: The referee starts the race The attorney initiates the process of appeal

112. Perpetuation A substance sustains a process: The singer sings the song The charged filament perpetuates the emission of light

113. Termination A substance terminates a process: The operator terminates the projection of the film The judge terminates the imprisonment of the pardoned convict

114. Influence A substance (or its quality) has an effect on a process The steepness of the slope affects the movement of the troops The politicians influence the course of the war

115. Facilitation A substance plays a secondary role in a process (for example by participating in a part or layer of the process) The catalyst provides the chemical conditions for the reaction The traffic-police facilitate our rapid progress to the airport

116. Hindrance, prevention A substance has a negative effect on the unfolding of a process (by participating in other processes) The drug hinders the progression of the disease The strikers prevent the airplane from departing

117. Mediation A substance plays an indirect role in the unfolding of a process relating other participants: The Norwegians mediate the discussions between the warring parties

118. Patiency Dual of agentive participation John kisses [Mary] (John agent) Mary is kissed [by John] (Mary patient)

119. Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

120. Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

121. Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

122. Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

123. 2nd Family REALIZATION

124. Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Spatial Regions Processuals Processes Events Space-Time Regions participation realization

125. Realization (SPQR->process) The most general relation between a dependent (SPQR…) entity and a process The power to legislate is realized through the passing of a law The role of antibiotics in treating infections is via the killing of bacteria

126. Realization (SNAP-SPAN) the execution of a plan, algorithm the performance of a function the exercise of a role the realization of a disposition

127. SPQR… entities and their SPAN realizations plan function role disposition algorithm SNAP

128. SPQR… entities and their SPAN realizations execution performance exercise realization application course SPAN

129. Material examples: performance of a symphony projection of a film expression of an emotion utterance of a sentence application of a therapy course of a disease increase of temperature

130. SNAP->SPAN Participation Substance -> Process Realization SPQR -> Process

131. SPAN -> SNAP Involvement

132. SPAN -> SNAP Involvement Creation Sustaining in being Destruction Demarcation Blurring Degradation

133. Involvement process -> substance (sometimes the converse of participation): Races involve racers (but not always): Wars involve civilians

134. Creation A process brings into being a substance: The declaration of independence creates the new state The work of the potter creates the vase

135. Sustaining in being A process sustains in being a substance: The circulation of the blood sustains the body Levying taxes sustains the army

136. Degradation A process has negative effects upon a substance Eating sugar contributes to the deterioration of your teeth. The flow of water erodes the rock

137. Destruction A process puts a substance out of existence The explosion destroys the car The falling of the vase on the floor breaks it

138. Demarcation A process creates (fiat or bona fide) boundaries of substances. The signing of the treaty establishes fixed borders between the two nations The tracing of the area of operation by the surgeon defines a boundary, the incision performed by the surgeon yet another one

139. Blurring A process destroys boundaries of substances: The military stand-off creates the no man's land The successful transplant obliterates the boundary between original and grafted tissue

140. Process -> SPQR Continuation Degradation Destruction Creation Qualitative projection

141. Qualitative Projection A warming process yields a rise in temperature The tenure process yields a rise in John’s status

142. Creation A process brings into being a dependent entity The accident reshapes the car. The baking of the clay gives the vase its rigidity and color.

143. Continuation A process sustains the existence of an SPQR entity The firing of the fireworks maintains the coloration of the sky The intake of alcohol sustains the rosiness of his cheeks

144. Degradation A process affects a substance's quality or status by lowering its degree The opening of the window diminishes the temperature in the room

145. Destruction A process destroys/changes an SPQR… entity The accident destroys the car's shape The burning of the vase destroys its color The demotion relieved him of his rank as an officer

146. Varieties of projection Warming process  series of temperature qualities = qualitative projection Process  temporal interval = temporal projection

147. Spatial Projection A process occurs in a given place or area: The Revolution took place in Paris The wind blows beyond the 24th parallel

148. Starts in / ends at (spatial projection of process boundaries) A process begins/ends at a location The race started in Paris The race ended in Roubaix

149. SNAP-SPAN Participation Perpetration (+agentive) Initiation Perpetuation Termination Influence Facilitation Hindrance Mediation Patiency (-agentive)

150. SPAN-SNAP Involvement Creation Sustenance Destruction Continuation Degradation Destruction Creation Demarcation Blurring Qualitative projection Degradation

151. The idea (a closer approximation) Formal relations are those relations which are not captured by either the SNAP or the SPAN ontology either because they traverse the SNAP- SPAN divide or because they traverse the granular divide

152. Types of Formal Relation Intracategorial –Mereological (part) –Topological (connected, temporally precedes) –Dependency (e.g. functional ?) Intercategorial –Inherence (quality of) –Location –Participation (agent) –Dependency (of process on substance) Transcendentals