VT

SNAP and SPAN

Substances

Mesoscopic reality is

divided at its natural joints

into substances:

animals, bones, rocks, potatoes

The Ontology of Substances

Substances form natural kinds

(universals, species + genera)

Processes

Processes merge into one another

Process kinds merge into one another

… few clean joints either between instances or between types

Processes

t i m e

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

Natural language

glues them together indiscriminately

substance

t i m

e

process

Substances and processes

t i m

e

process

demand different sorts of inventories

Substances demand 3-D partonomies

space

Moments demand 4D-partonomies

t i m e

Processes

a whistling, a blushing, a speech

a run, the warming of this stone

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

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

Substances have spatial parts

How do we glue these two different sorts of entities together mereologically?

How do we include them both in a single inventory of reality?

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?

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

Main problem

There is a polymorphous ontological promiscuity of the English sentence,

which is inherited also by the form ‘F(a)’

The Four-Dimensionalist Ontology

t i m e

boundaries are mostly fiat

t i m e

everything is flux

mereology works without restriction everywhere here

t i m e

clinical trial

The Time-Stamped Ontology

t1

t3

t2

here time exists outside the ontology, as an index or time-stamp

mereology works without restriction in every 3-D SNAPti ontology

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

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

Substances

can also gain and lose parts

… as an organism may gain and lose molecules

Types of relations between parts

1. Dependence relations

2. Side-by-sideness relations

3. Fusion relations

Dependence

cannot exist without a thinker

a thinking process

substance

Theory of vagueness

Side-by-sideness

found among substances and among qualities and processes

Fusion

Topology

Topology, like mereology,

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

SNAP and SPAN

Substances+qualities and processesContinuants and occurrents

In preparing an inventory of realitywe keep track of these two different categories of entities in two different ways

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

Parts of processes (1)

c

c: boundary

a

a

a: scattered part

b

b: temporal slice

Parts of processes (2)

a

a: sub-process

b

b: phase

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

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

The Parable of Little Tommy’s Christmas Present

Little Tommy’s Other Christmas Present

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

Fourdimensionalism

is right in everything it says

But incomplete

Realist Perspectivalism

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

Need for different perspectives

Not one ontology, but a multiplicity of complementary ontologies

Cf. Quantum mechanics: particle vs. wave ontologies

Two Orthogonal, Complementary Perspectives

SNAP and SPAN

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

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

SNAP vs. SPAN

1. SNAP: a SNAPshot ontology of endurants existing at a time

2. SPAN: a four-dimensionalist ontology of processes

You are a substance

Your life is a process

You are 3-dimensional

Your life is 4-dimensional

ChangeAdding 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

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

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

Three kinds of SNAP entities

1. Substances

2. SPQR… entities

3. Spatial regions, contexts, niches, environments

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

Other SPQR… entities:

functions, dispositions, plans, shapes

SPQR… entities are all dependent on substances

one-place SPQR entities: temperature, color, height

Substances and SPQR… entities

Substances are the bearers or carriers of,

SPQR… entities ‘inhere’ in their substances

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

relational SPQR… entities

John Mary

love

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

Ontological Dependence

Substances are that which can exist on their own

SPQR… entities require a support from substances in order to exist

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

SNAP ontology

many sharp boundaries

SPAN ontologymany smeered boundaries

many fiat boundaries

(more scope for gerrymandering – why?)

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

SNAP entities

provide the principles of individuation/segmentation for SPAN entities

No change without some THING or QUALITY which changes

identity-based change

Processes, too, are dependent on substances

One-place vs. relational processes

One-place processes:

getting warmer

getting hungrier

Examples of relational processes

kissings, thumps, conversations,

dances,

Such relational processes

join their carriers together into collectives of greater or lesser duration

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

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)

SNAP: Entities existing in toto at a time

Three kinds of SNAP entities

1. Substances

2. SPQR… entities

3. Spatial regions, Contexts, Niches

SNAP

SPAN: Entities extended in time

SPANEntity extended in time

Portion of Spacetime

Fiat part of process *First phase of a clinical trial

Spacetime worm of 3 + Tdimensions

occupied by life of organism

Temporal interval *projection of organism’s life

onto temporal dimension

Aggregate of processes *Clinical trial

Process[±Relational]

Circulation of blood,secretion of hormones,course of disease, life

Processual Entity[Exists in space and time, unfolds

in time phase by phase]

Temporal boundary ofprocess *

onset of disease, death

SPAN: Entities extended in time

SPAN: Entities extended in time

Relations between SNAP and SPAN

SNAP-entities participate in processes

they have lives, histories

Participation

x

y

substances x, y participate in process B

time

Bx

y

SNAP-ti.

time

SPAN

B

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

SPQR… entities and their SPAN realizations

function

role

plan

disposition

therapy

disease

SNAP

SPQR… entities and their SPAN realizations

performance

exercise

execution

realization

application

course

SPAN

problem cases

traffic jam

forest fire

anthrax epidemic

hurricane Maria

waves

shadows

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

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.

SNAP and SPAN

space

space-time

substances

SPQR entities (including functions)

processes

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

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?

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 dividethey glue SNAP and SPAN entities together

This generates a first list of formal relations,

e.g. dependence,

but we find some of these relations also within SNAP or within SNAP

The idea (modified version)

Formal relations are the relations that hold SNAP and SPAN entities/ontologies togetherand analogous relations… they come for free, they do not add anything to being = they are links between categories

Example:Individuation, segmentation

Substances

tokens separated by bona fide boundaries

form natural kinds, types

(universals, species + genera)

separated by bona fide boundaries

Processes

Process tokens merge into one another

Process kinds merge into one another

… few clean joints either between tokens or between types

boundaries are mostly fiat

t i m e

everything is flux

SNAP entities

provide the principles of individuation/segmentation for SPAN

entities

No change without some THING or QUALITY which changes

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

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)

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

Principal Signatures

In the binary case:

SNAP-SNAP - (SNAPi, SNAPi), i = i

- (SNAPi, SNAPi), i < j, i > j

SPAN-SPAN

SNAP-SPANSPAN-SNAP

Transtemporal relations

Examples:

Genidentity

(transtemporal generalization of identity/part-whole)

Successive causality

Genidentity

Also SPAN-SPAN? Is there a form of genidentity among processes?

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

Successive Causality

SNAP-SPAN: Agent causationA substance produces causally a process

SPAN-SPAN: Process causationOne process causes another process

SPAN-SNAP: Causal repercussionA process results in the modification of a substance (always mediated by process causation)

SNAP-SNAP: Causal originOne substance is the causal origin of another (mediated by other types of causal relations)

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

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)

Simultaneous causality

SPAN-SPAN

The rise in temperature causes the (simultaneous) increase in pressure

(Boyle’s law)

Substance->Process

PARTICIPATION(a species of dependence)

Participation (SNAP-SPAN)

A substance (SNAP) participates in a process (SPAN)

A runner participates in a race

A voter participates in an election

Axes of variation

activity/passivity (agentive)

direct/mediated

benefactor/malefactor (conducive to existence) [MEDICINE]

SNAP-SPAN

Participation

Perpetration (+agentive)

Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

Perpetration

A substance perpetrates an action (direct and agentive participation in a process):

The referee fires the starting-pistol

The captain gives the order

Initiation

A substance initiates a process:

The referee starts the race

The attorney initiates the process of appeal

Perpetuation

A substance sustains a process:

The singer sings the song

The charged filament perpetuates the emission of light

Termination

A substance terminates a process:

The operator terminates the projection of the film

The judge terminates the imprisonment of the pardoned convict

Influence

A substance (or its quality) has an effect on a process

The steepness of the slope affects the movement of the troopsThe politicians influence the course of the war

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

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

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

Patiency

Dual of agentive participation

John kisses [Mary] (John agent)

Mary is kissed [by John] (Mary patient)

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

2nd Family

REALIZATION

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Spatial Regions

Processuals

Processes

Events

Space-Time Regions

participation

realization

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

Realization (SNAP-SPAN)

the execution of a plan, algorithm

the performance of a function

the exercise of a role

the realization of a disposition

SPQR… entities and their SPAN realizations

plan

function

role

disposition

algorithm

SNAP

SPQR… entities and their SPAN realizations

execution

performance

exercise

realization

application

course

SPAN

Material examples:

performance of a symphonyprojection of a filmexpression of an emotionutterance of a sentenceapplication of a therapycourse of a diseaseincrease of temperature

SNAP->SPAN

Participation

Substance -> Process

Realization

SPQR -> Process

SPAN -> SNAP

Involvement

SPAN -> SNAP

Involvement

Creation

Sustaining in being

Destruction

DemarcationBlurring

Degradation

Involvement

process -> substance(sometimes the converse of participation):

Races involve racers

(but not always):

Wars involve civilians

Creation

A process brings into being a substance:

The declaration of independence creates the new state

The work of the potter creates the vase

Sustaining in being

A process sustains in being a substance:

The circulation of the blood sustains the body

Levying taxes sustains the army

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

Destruction

A process puts a substance out of existence

The explosion destroys the car

The falling of the vase on the floor breaks it

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

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

Process -> SPQR

Continuation

DegradationDestruction

Creation

Qualitative projection

Qualitative Projection

A warming process yields a rise in temperature

The tenure process yields a rise in John’s status

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.

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

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

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

Varieties of projection

Warming process series of temperature qualities

= qualitative projection

Process temporal interval

= temporal projection

Spatial Projection

A process occurs in a given place or area:

The Revolution took place in Paris

The wind blows beyond the 24th parallel

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

SNAP-SPAN

Participation

Perpetration (+agentive)

Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

SPAN-SNAP

Involvement

Creation

Sustenance

Destruction

Continuation

DegradationDestruction

Creation

DemarcationBlurring

Qualitative projection

Degradation

The idea (a closer approximation)

Formal relations are those relations which are not captured by either the SNAP or the SPAN ontologyeither because they traverse the SNAP-SPAN divideor because they traverse the granular divide

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