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Endurance PerduranceSNAP 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
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
SPQR… entities and their SPAN realizations
function
role
plan
disposition
therapy
disease
SNAP
SPQR… entities and their SPAN realizations
expression
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
Formalizing time
F(a)
F(a,b) at t
F(a,b,t)
F(a@t,b@t)
Formalizing time
F(a) – SPAN
F(a) at t – SNAP
F(a,t) – Eternalism
F(a@t) – stage ontology
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
Principal Signatures
In the binary case:
SNAP-SNAP - (SNAPi, SNAPi), i = i
- (SNAPi, SNAPi), i < j, i > j
SPAN-SPAN
SNAP-SPANSPAN-SNAP
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
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 expression 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
expression
exercise
realization
application
course
SPAN
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
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
