Endurance Perdurance SNAP and SPAN

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Endurance PerduranceSNAP and SPAN
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Substances

• Mesoscopic reality is
• divided at its natural joints
• into substances
• animals, bones, rocks, potatoes

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The Ontology of Substances

• Substances form natural kinds
• (universals, species genera)

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Processes

• Processes merge into one another
• Process kinds merge into one another
• few clean joints either between instances or
  between types

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Processes
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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

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Natural language

• glues them together indiscriminately

substance
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Substances and processes
demand different sorts of inventories
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Substances demand 3-D partonomies
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Moments demand 4D-partonomies

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Processes

• a whistling, a blushing, a speech
• a run, the warming of this stone

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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

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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

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Substances have spatial parts
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• How do we glue these two different sorts of
  entities together mereologically?
• How do we include them both in a single
  inventory of reality?

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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?
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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

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Main problem

• There is a polymorphous ontological promiscuity
  of the English sentence,
• which is inherited also by the form F(a)

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The Four-Dimensionalist Ontology
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boundaries are mostly fiat
everything is flux
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mereology works without restriction everywhere
here
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The Time-Stamped Ontology
t3
t2
t1
here time exists outside the ontology, as an
index or time-stamp
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mereology works without restriction in every 3-D
SNAPti ontology
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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

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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

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Substances

• can also gain and lose parts
• as an organism may gain and lose molecules

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Types of relations between parts

• 1. Dependence relations
• 2. Side-by-sideness relations
• 3. Fusion relations

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Dependence
process
a thinking
cannot exist without a thinker
substance
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Theory of vagueness
Side-by-sideness
found among substances and among qualities and
processes
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Fusion
Topology
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Topology, like mereology,

• applies both in the realm of substances and in
  the realms of qualities and processes

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SNAP and SPAN

• Substancesqualities 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

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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

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Parts of processes (1)
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Parts of processes (2)
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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

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4-Dism gtThere 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

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The Parable of Little Tommys Christmas Present
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Little Tommys Other Christmas Present
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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

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Fourdimensionalism

• is right in everything it says
• But incomplete

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Realist Perspectivalism
There is a multiplicity of ontological
perspectives on reality, all equally veridical
transparent to reality
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Need for different perspectives

• Not one ontology, but a multiplicity of
  complementary ontologies
• Cf. Quantum mechanics particle vs. wave
  ontologies

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Two Orthogonal, Complementary Perspectives
SNAP and SPAN
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SNAP and SPAN

• 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

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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

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SNAP vs. SPAN

• SNAP a SNAPshot ontology of endurants existing
  at a time
• SPAN a four-dimensionalist ontology of processes

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You are a substance

• Your life is a process
• You are 3-dimensional
• Your life is 4-dimensional

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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

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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

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How do you know whether an entity is SNAP or SPAN?
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Three kinds of SNAP entities

1. Substances
2. SPQR entities
3. Spatial regions, contexts, niches, environments

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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

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Other SPQR entities

• functions, dispositions, plans, shapes
• SPQR entities are all dependent on substances
• one-place SPQR entities temperature, color,
  height

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Substances and SPQR entities

• Substances are the bearers or carriers of,
• SPQR entities inhere in their substances

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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

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• relational SPQR entities

stand in relations of one-sided dependence to a
plurality of substances simultaneously
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Ontological Dependence

• Substances are that which can exist on their own
• SPQR entities require a support from
  substances in order to exist

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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

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SNAP ontology

• many sharp boundaries
• SPAN ontology
• many smeered boundaries
• many fiat boundaries
• (more scope for gerrymandering why?)

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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

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SNAP entities

• provide the principles of individuation/segmentati
  on for SPAN entities
• No change without some THING or QUALITY which
  changes
• identity-based change

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Processes, too, are dependent on substances

• One-place vs. relational processes
• One-place processes
• getting warmer
• getting hungrier

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Examples of relational processes

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

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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

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SNAP and SPAN ontologies are partial only

• Each is a window on that dimension of reality
  which is visible through the given ontology

(Realist perspectivalism)
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SNAP Entities existing in toto at a time
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Three kinds of SNAP entities

1. Substances
2. SPQR entities
3. Spatial regions, Contexts, Niches

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SNAP
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SPAN Entities extended in time
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SPAN Entities extended in time
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SPAN Entities extended in time
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Relations between SNAP and SPAN
SNAP-entities participate in processes they have
lives, histories
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Participation
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SPQR entities and their SPAN realizations

• the expression of a function
• the exercise of a role
• the execution of a plan
• the realization of a disposition

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SPQR entities and their SPAN realizations

• function
• role
• plan
• disposition
• therapy
• disease

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SPQR entities and their SPAN realizations

• expression
• exercise
• execution
• realization
• application
• course

SPAN
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problem cases

• traffic jam
• forest fire
• anthrax epidemic
• hurricane Maria
• waves
• shadows

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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

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Formalizing time

• F(a)
• F(a,b) at t
• F(a,b,t)
• F(a_at_t,b_at_t)

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Formalizing time

• F(a) SPAN
• F(a) at t SNAP
• F(a,t) Eternalism
• F(a_at_t) stage ontology

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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.

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SNAP and SPAN

• space
• space-time
• substances
• SPQR entities (including functions)
• processes

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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

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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?

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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

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

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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

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ExampleIndividuation, segmentation
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Substances

• tokens separated by bona fide boundaries
• form natural kinds, types
• (universals, species genera)
• separated by bona fide boundaries

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Processes

• Process tokens merge into one another
• Process kinds merge into one another
• few clean joints either between tokens or
  between types

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boundaries are mostly fiat
everything is flux
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SNAP entities

• provide the principles of individuation/segmentati
  on for SPAN entities
• No change without some THING or QUALITY which
  changes

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ExampleOntological Dependence

• (SPAN, SNAP) process-gtsubstance
• The erosion of the rock necessitates the
  existence of the rock
• (SNAP, SNAP) SPQR-gtsubstance
• The token redness of the sand necessitates the
  existence of the sand

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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)

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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

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Principal Signatures

• In the binary case
• SNAP-SNAP
• - (SNAPi, SNAPi), i i
• - (SNAPi, SNAPi), i lt j, i gt j
• SPAN-SPAN
• SNAP-SPAN
• SPAN-SNAP

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Transtemporal relations

• Examples
• Genidentity
• (transtemporal generalization of
  identity/part-whole)
• Successive causality

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Genidentity
The such-as-to-have-come-forth-from relation.
Signature SNAPi-SNAPj Cut a chunk of matter in
two, the sum of the remaining pieces is
genidentical to the chunk before cutting
Also SPAN-SPAN? Is there a form of genidentity
among processes?
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Successive Causality
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-SPAN Agent causation A substance produces
causally a process
SNAP-SNAP Causal origin One substance is the
causal origin of another (mediated by other
types of causal relations)
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Successive Causality
SPAN-SPAN Process causation
SPAN-SNAP Causal repercussion
SNAP-SPAN Agent causation
SNAP-SNAP Causal origin
do not apply on all levels of granularity
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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)

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Simultaneous causality

• SPAN-SPAN
• The rise in temperature causes the
  (simultaneous) increase in pressure
• (Boyles law)

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Substance-gtProcess

• PARTICIPATION
• (a species of dependence)

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Participation (SNAP-SPAN)

• A substance (SNAP) participates in a process
  (SPAN)
• A runner participates in a race
• A voter participates in an election

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Axes of variation
activity/passivity (?agentive)
direct/mediated benefactor/malefactor
(?conducive to existence) MEDICINE
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SNAP-SPAN
Participation
Perpetration (agentive)
Influence
Patiency (-agentive)
Initiation
Termination
Facilitation
Perpetuation
Hindrance
Mediation
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Perpetration

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

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Initiation

• A substance initiates a process
• The referee starts the race
• The attorney initiates the process of appeal

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Perpetuation

• A substance sustains a process
• The singer sings the song
• The charged filament perpetuates the emission of
  light

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Termination

• A substance terminates a process
• The operator terminates the projection of the
  film
• The judge terminates the imprisonment of the
  pardoned convict

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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

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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

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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

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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

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Patiency

• Dual of agentive participation
• John kisses Mary (John agent)
• Mary is kissed by John (Mary patient)

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Signatures of meta-relations
SNAP Component
SPAN Component
Processuals
Substances
Processes
SPQR
Events
Space Regions
Space-Time Regions
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Signatures of meta-relations
SNAP Component
SPAN Component
Processuals
Substances
Processes
SPQR
Events
Space Regions
Space-Time Regions
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Signatures of meta-relations
SNAP Component
SPAN Component
Processuals
Substances
Processes
SPQR
Events
Space Regions
Space-Time Regions
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Signatures of meta-relations
SNAP Component
SPAN Component
Processuals
Substances
Processes
SPQR
Events
Space Regions
Space-Time Regions
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2nd Family

• REALIZATION

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Signatures of meta-relations
SNAP Component
SPAN Component
Processuals
Substances
Processes
SPQR
Events
Spatial Regions
Space-Time Regions
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Realization (SPQR-gtprocess)

• 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

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Realization (SNAP-SPAN)

• the execution of a plan, algorithm
• the expression of a function
• the exercise of a role
• the realization of a disposition

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SPQR entities and their SPAN realizations

• plan
• function
• role
• disposition
• algorithm

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SPQR entities and their SPAN realizations

• execution
• expression
• exercise
• realization
• application
• course

SPAN
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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

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SNAP-gtSPAN

• Participation
• Substance -gt Process
• Realization
• SPQR -gt Process

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SPAN -gt SNAP

• Involvement

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SPAN -gt SNAP
Involvement
Creation
Sustaining in being
Degradation
Destruction
Blurring
Demarcation
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Involvement

• process -gt substance
• (sometimes the converse of participation)
• Races involve racers
• (but not always)
• Wars involve civilians

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Creation

• A process brings into being a substance
• The declaration of independence creates the new
  state
• The work of the potter creates the vase

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Sustaining in being

• A process sustains in being a substance
• The circulation of the blood sustains the body
• Levying taxes sustains the army

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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

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Destruction

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

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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

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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

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Process -gt SPQR
Qualitative projection
Creation
Continuation
Destruction
Degradation
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Qualitative Projection

• A warming process yields a rise in temperature
• The tenure process yields a rise in Johns status

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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.

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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

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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

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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

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Varieties of projection

• Warming process ? series of temperature qualities
• qualitative projection
• Process ? temporal interval
• temporal projection

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Spatial Projection

• A process occurs in a given place or area
• The Revolution took place in Paris
• The wind blows beyond the 24th parallel

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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

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SNAP-SPAN
Participation
Perpetration (agentive)
Influence
Patiency (-agentive)
Initiation
Termination
Facilitation
Perpetuation
Hindrance
Mediation
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SPAN-SNAP
Qualitative projection
Creation
Involvement
Continuation
Destruction
Degradation
Creation
Sustenance
Degradation
Destruction
Blurring
Demarcation
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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

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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