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The Cornucopia of Formal-Ontological Relations

Barry Smith and Pierre Grenon

Institute for Formal Ontology and Medical Information Science

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Realist Perspectivalism

There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality

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Anatomy vs. Pathology

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The Problem

The tumor developed in John’s lung over 25 years

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The Problem

____ developed in _____ over 25 years

process

state

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The Problem

The tumor developed in the lung over 25 years

substances

things

objects

continuants

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The Problem

The tumor developed in John’s lung over 25 years

PARTHOOD NOT DETERMINATE

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The Problem

The tumor developed in the lung over 25 years

substances

GLUING THESE TOGETHER YIELDS ONTOLOGICAL MONSTERS

processes

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Substances and processes exist in time in different ways

substance

t i m

e

process

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SNAP vs SPAN

Endurants vs perdurants

Continuants vs occurrents

In preparing an inventory of reality

we keep track of these two different kinds of entities in two different ways

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Need for different perspectives

Not one ontology, but a multiplicity of complementary ontologies

Cf. particle vs. wave ontologies in quantum mechanics

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Three kinds of SNAP entities

1. Substances

2. Dependents (SPQR… entities)

3. Spatial regions, contexts, niches, environments

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SPQR… entitiesStates, powers, qualities, roles …

functions, dispositions, plans, shapes, status, habitus, liabilities …

= dependent SNAP entities

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SPQR… entities:

one-place:

your temperature, color, heightmy knowledge of French

the whiteness of this cheese the warmth of this stone

the fragility of this glass

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relational SPQR… entities

John Mary

love

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

specific dependence

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Generic dependence of relational SPQR… entities

legal systems

languages (as systems of competences)

religions (as systems of beliefs)

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Three kinds of SNAP entities

1. Substances

2. Dependents (SPQR… entities)

3. Spatial regions, contexts, niches, environments

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Three kinds of SNAP entities

1. Substances

2. Dependents (SPQR… entities)

3. Spatial regions, contexts, niches, environments

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Spatial regions, contexts, niches, environments

Organism species evolve into environments

Domesticated spatial regions: rooms, nostrils, your alimentary tract

Fiat spatial regions: JFK designated airspace

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SNAP: Entities existing in toto at a time

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Substances

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SPQR …

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Spatial regions

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The SPAN Ontology

t i m e

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here time exists as part of the domain of the ontology

The SPAN ontology

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mereology works without restriction everywhere here

t i m e

clinical trial

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Processes, too, are dependent on substances

One-place vs. relational processes

One-place processes:

your getting warmer

your getting hungrier

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Examples of relational processes

kissings, thumpings, conversations,

dancings,

join their carriers together into collectives of greater or lesser duration

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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

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Two kinds of SPAN entities

1. Processes (including events: process-boundaries)

2. Spatio-temporal regions

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Processes

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Spatio-temporal regions

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4-dimensional environments

Lobsters have evolved into environments marked by cyclical patterns of temperature change

Tudor EnglandThe Afghan winterThe window of opportunity for an invasion of Iraq

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

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problem cases

forest fire

anthrax epidemic

hurricane Maria

traffic jam

ocean wave

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forest fire:

a process

a pack of monkeys jumping from tree to tree and eating up the trees as they go

the Olympic flame:

a process or a thing?

(anthrax spores are little monkeys)

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Formal-ontological concepts

come for free

do not add anything to being

are domain-independent

are expressed linguistically by closed-class items …

HOW TO GENERATE THEM?

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The idea (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

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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

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Example:Individuation, 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

t i m e

everything is flux

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SNAP entities

provide the principles of individuation/segmentation for SPAN

entities

No change without some THING or QUALITY which changes

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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

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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 < j, i > j

SPAN-SPAN

SNAP-SPANSPAN-SNAP

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Transtemporal relations

Examples:

Genidentity

(transtemporal generalization of identity/part-whole)

Successive causality

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Genidentity

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

The such-has-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

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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)

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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(holds of examples given below also)

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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

(Boyle’s law)

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Substance Process

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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Participation

x

y

substances x, y participate in process B

time

Bx

y

SNAP-ti.

time

SPAN

B

slice of x’s life

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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)

Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

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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 troopsThe 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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Facilitation

is this really a binary relation?

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Hindrance, prevention, inhibition

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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Hindrance, prevention, inhibition

Is this really a binary relation ? (What is the second term?)

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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

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

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Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

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Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

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Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

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REALIZATION

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Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Spatial Regions

Processuals

Processes

Events

Space-Time Regions

participation

realization

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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

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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

SNAP

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

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SNAP SPAN

Participation

Substance Process

Realization

SPQR Process

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SPAN SNAP

Involvement

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SPAN SNAP

Involvement

Creation

Sustaining in being

Destruction

DemarcationBlurring

Degradation

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Involvement

process 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 SPQR

Continuation

DegradationDestruction

Creation

Qualitative projection

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Qualitative Projection

A warming process yields a rise in temperature

The tenure process yields a rise in John’s 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)

Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

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SPAN-SNAP

Involvement

Creation

Sustenance

Destruction

Continuation

DegradationDestruction

Creation

DemarcationBlurring

Qualitative projection

Degradation

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Varieties of Projection

A process projects onto its temporal duration, onto the spatio-temporal region it occupiesonto the spatial region it occupies at a given time onto the sum of its participants at a time onto the sum of the SPQR… entities realized through it at a time

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Temporal Projection

of SPAN entities onto temporal intervals

of SNAP entities onto temporal intervals via their lives

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Formal relations not dealt with so far:

part-whole

instantiation

reference, intentionality

truthmaking

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Part-Whole

Basic relation exclusively intra-ontological: either SNAP-SNAP or SPAN-SPAN.

SNAP-SNAP: only if SNAPis have the same temporal index

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Relations crossing the SNAP/SPAN border are never part-relations

John’s lifesubstance John

physiological processes

sustaining in existence

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Granularity

spatial region substance

parts of substances are always substances

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Granularity

spatial region substance

parts of spatial regions are always spatial regions

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Granularity

process

parts of processes are always processes

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Intra-granular and cross-granular parthood

across SNAPs:Kevin’s arm is part of KevinKevin’s molecule is part of Kevin

across SPANs:Kevin’s leg-movement is part of Kevin’s runningKevin’s cytometabolism is part of Kevin’s running

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The idea (a further modification)

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

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Is this Kantianism?

does every ontology/perspective generate new formal-ontological relations?

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Realist Perspectivalism

There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality

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SNAP

universals and particulars

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What about

reference, intentionality,

truthmaking ?

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SNAPEnduring Entity

[Exists in space and time,

has no temporal parts]

Spatial Entity

Tunnel

Alimentary Canal

Independent Entity

Cavity

Interior of Lung

Hollow

Nostril

State

Being pregnant, being thirsty

Dependent Entity

[±Relational]

Role, Function, Power, Disposition

[Have realizations, called processes]

To circulate blood, to secrete hormones

Quality

[Sometimes form quality-

regions or scales]

Requisite

[Have determinable/

determinate structure]

Temperature. height

Optional

Diabetes

Fiat part of substance *

Extremity, upper body

Substance

Organism, organ

Unoccupied

Occupied

Spatial region of 3

dimensions

occupied by organism

Spatial region of 2

dimensions *

occupied by burn, bruise

Boundary of substance *

Surface of skin or hide

MedO Draft 0.0004

Aggregate of substances *

Family, mother and fetus

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Are there any cases of ontological dependence involving an increase in being,

analogous to the increase in being between the thought and the thinker, the charge and the conductor, the swim and the swimmer

between SPAN and SPAN entities?

(Hypothesis: all qualities of processes are essential)

Puzzle

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Co-temporality

is a requisite for most SNAP-SPAN relations (participation, realization, etc.)

Exception: the memory of a process state of memory: SNAP(vs. episodic remembering: SPAN)