The Ontology of Holes. Temple at Corinth Pipe The Ontology of Places

The Ontology of Holes

Temple at Corinth

Pipe

The Ontology of Places

Towards an Ontology of Places

Aristotle

Ontology of the place (topos) of an individual substance (ousia)

What is it for a substance to be (or to fit snugly) in a location or context?

Aristotle

Place

has size but not matter.

It has shape or form—exactly the shape or form of the thing that is located in it—but it lacks bulk.

Aristotle

We say that a thing is … in the air

because of the surface of the air which surrounds it;

for if all the air were its place, the place of a thing would not be equal to the thing —

which it is supposed to be. (211a24-28)

A place contains its body.

The body relates to its place in something like the way the liquid in an urn relates to the urn, or the hand relates to the glove.

Aristotle: A place

exactly surrounds the thing,

but the place does not depend specifically upon the thing, since the latter can be replaced by another thing, which is then said to be

in the same place.

When a thing is in a surrounding body of air or water

‘it is primarily in the inner surface of the surrounding body.’ The boundaries of the two—the outer surface of the thing and the inner surface of its surrounding body—exactly coincide (211a30-33): the place of a substance is the inner boundary of the immediately surrounding or containing body.

Places are holes

Places are holes

Places are holes

A hole in the ground

Solid physical boundaries at the floor and walls

but with a fiat lid:

hole

Holes involve two kinds of boundaries

bona fide boundaries which exist independently of our demarcating acts

fiat boundaries which exist only because we put them there

niches, environments are holes

and some holes can move

Where are Places?Concrete Entity

[Exists in Space and Time]Concrete Entity

[Exists in Space and Time]

Entity in 3-D Ontology[Endure. No Temporal Parts]


Entity in 4-D Ontology[Perdure. Unfold in Time]Entity in 4-D Ontology

[Perdure. Unfold in Time]

Processual EntityProcessual EntitySpatio-Temporal Region

Dim = T, T+0, T+1, T+2, T+3Spatio-Temporal Region

Dim = T, T+0, T+1, T+2, T+3

Spatial Regionof Dimension 0,1,2,3

Spatial Regionof Dimension 0,1,2,3 Dependent EntityDependent Entity

Independent EntityIndependent Entity

Quality (Your Redness, My Tallness)[Form Quality Regions/Scales]


Role, Function, PowerHave realizations (called: Processes)


Substance[maximally connected causal unity]


Boundary of Substance *Fiat or Bona Fide or MixedBoundary of Substance *

Fiat or Bona Fide or Mixed

Aggregate of Substances * (includes masses of stuff? liquids?)


Fiat Part of Substance * Nose, Ear, Mountain


Process [Has Unity]Clinical trial; exercise of role


Fiat Part of Process*Fiat Part of Process*

Aggregate of Processes*Aggregate of Processes*

Instantaneous Temporal Boundary of Process (= Ingarden’s 'Event’)*


Quasi-ProcessJohn’s Youth. John’s Life


Quasi-Quality Prices, Values, Obligations


Quasi-SubstanceChurch, College, Corporation


Quasi-Role/Function/PowerThe Functions of the PresidentQuasi-Role/Function/Power

The Functions of the President

Where are Places (Holes)?Concrete Entity









Dim = T, T+0, T+1, T+2, T+3

Spatial Regionof Dimension 0,1,2,3

Spatial Regionof Dimension 0,1,2,3 Dependent EntityDependent Entity








Boundary of Substance *Fiat or Bona Fide or MixedBoundary of Substance *

Fiat or Bona Fide or Mixed







Fiat Part of Process*Fiat Part of Process*

Aggregate of Processes*Aggregate of Processes*









Quasi-Role/Function/PowerThe Functions of the PresidentQuasi-Role/Function/Power

The Functions of the President

Where are Places?Concrete Entity









Dim = T, T+0, T+1, T+2, T+3

Spatial Regionof Dimension

0,1,2,3

Spatial Regionof Dimension

0,1,2,3

Dependent EntityDependent Entity


Types of PlacesConcrete Entity









Dim = T, T+0, T+1, T+2, T+3

Generalized Spatial Regionof Dimension

0,1,2,3

Generalized Spatial Regionof Dimension

0,1,2,3

Dependent EntityDependent Entity


StationaryStationaryMobileMobile

Armchair Ontology

Armchair Ontology

artefacts and niches

Positive and negative parts

positivepart

negativepartor hole

(made of matter)

(not made of matter)

Formal Ontology

atomism vs. holism

set theory

mereology

Environments a Neglected Major Category

Substances

Qualities

Processes

Environments

Accidents

environmentplaceniche

habitatsettinghole

spatial regioninterior

Applications of these concepts

in biology, ecologyin anthropologyin lawin politicsin medicinein embryology

Ecological Niche Concepts

niche as particular place or subdivision of an environment that an organism or population occupies

vs.

niche as function of an organism or population within an ecological community

Elton

the ‘niche’ of an animal means its place in the biotic environment, its relations to food and enemies. [...] When an ecologist says ‘there goes a badger’ he should include in his thoughts some definite idea of the animal’s place in the community to which it belongs, just as if he had said ‘there goes the vicar’ (Elton 1927, pp. 63f.)

The Niche as Hypervolume

temperature

hum

idity

foli

age

den

sity


temperature

hum

idity

foli

age

den

sity


temperature

hum

idity

foli

age

den

sity


temperature

hum

idity

foli

age

den

sity

Hypervolume niche is a location in an attribute space

defined by a specific constellation of environmental variables such as degree of slope, exposure to sunlight, soil fertility, foliage density...

… John found his niche as a mid-level accounts manager in a small-town bank …

But every hypervolume niche must be realized in some specific spatial

location

Niche type must be tokenized in space

J. J. Gibson’s Ecological Psychology

The terrestrial environment is [best] described in terms of a medium, substances, and the surfaces that separate them. (Gibson 1979, p. 16)

Affordances

J. J. Gibson has provided a valuable account of the perceived world, which he presented as a prelude to his accounts of human visual perception

A key part of his account is the concept of affordances

Affordances

“The affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or evil.”

James J. Gibson, The Ecological Approach to Visual Perception

Affordances

“The verb to afford is found in the dictionary, but affordance is not. I have made it up.”

“I mean by it something that refers both to the animal and the environment in a way that no existing term does.” (p. 127)

Gibson’s theory of surface layout

‘a sort of applied geometry that is appropriate for the study of perception and behavior’ (1979, p. 33)

ground, open environment, enclosure, detached object, attached object, hollow object, place, sheet, fissure, stick, fiber, dihedral, etc.

Gibson’s theory of surface layout

systems of barriers, doors, pathways to which the behavior of human beings is specifically attuned,

temperature gradients, patterns of movement of air or water molecules

positive and negative features of the environment

(Casati-Varzi theory of holes)

Monadology

Monadological Niche-Concepts

(niche as small world)

Uexküll

Cf. the ‘first principle’ of Jakob von Uexküll’s Umweltlehre:

all animals, from the simplest to the most complex, are fitted into their unique worlds with equal completeness.

A simple world corresponds to a simple animal, a well-articulated world to a complex one (p. 10).

Uexküll

Theoretical Biology (1928, p. 2): “All reality is subjective appearance -- this must serve as the fundamental insight of biology, too.”

Uexküll

I am afraid that if I publicly proclaim this perspective, that they will treat me à la Galileo,

and either lock me up in a madhouse or else ridicule me as an arch-reactionary.

Uexküll

However I must just once say my piece. Perhaps no one will understand me. Nevertheless, it remains a fact: ‘Epur non si move.’I do not move around the sun, but rather the sun rises and sets in my arch of the sky. It is always another sun, always a new space in which it moves.

Uexküll

the real world is much richer than the naïve person suspects

because there is spread out around every living thing its own world of appearance, …

which manifests so many variations that he could devote his whole life to the study of these worlds without there ever being an end in sight.

Uexküll

when once we have made a beginning in showing in regard to a few animals what environments surround them like solid but invisible glass houses, then we will soon be able to people the world around us with numberless other shimmering worlds, which will intensify the riches of our world a further thousandfold.

Uexküll

In this way biology offers to the naive man an unlimited enrichment of his world,

while the physicist makes of him a beggar. (Uexküll 1928, p. 62)

Gestalt Psychology

Psychological Environment vs. Geographical Environment

Koffka

The Ride Across Lake Constance

On a winter evening amidst a driving snowstorm a man on horseback arrived at an inn, happy to have reached shelter after hours of riding over the wind-swept plain on which the blanket of snow had covered all paths and landmarks.


The landlord who came to the door viewed the stranger with surprise and asked him whence he came. The man pointed in the direction straight away from the inn, whereupon the landlord, in a tone of awe and wonder, said: ‘Do you know that you have just ridden across the Lake of Constance?’ At which the rider dropped stone dead at his feet.


Koffka: In what environment, then, did the behaviour of the stranger take place? The Lake of Constance.

Certainly [... and it is] interesting for the geographer that this behaviour took place in this particular locality.

But not for the psychologist as the student of behaviour


[the latter] will have to say: There is a second sense to the word environment according to which our horseman did not ride across the lake at all, but across an ordinary snow-swept plain.His behaviour was a riding-over-a-plain, but not a riding-over-a-lake. (Koffka 1935, pp. 27f.)

Psychologists’ Confusion

What we experience, according to Gestaltists such as Koffka, are not objects in physical reality (objects in the geographic environment). Rather, we experience, precisely, Gestalten, created objects, which differ from objects in physical reality inter alia because they arise through the application of special Gestalt ‘laws of organization’.

Same confusion in Scheler

Scheler’s theory of the milieu of practical life (influenced Heideggers writings on being-in-the-world)


The ‘things’ which are relevant to our acting, what we always refer to when, for example, we trace certain deeds of human beings (or dispositions towards such deeds) to their ‘milieu’, have of course not the slightest to do either with Kant’s ‘thing in itself’ or with the objects conceived by science (through the supposition of which science ‘explains’ natural facts).


The sun of the milieu of human beings is not the sun of astronomy. The meat that is stolen, bought, or what have you, is not a sum of cells and tissues with the chemicophysical processes which take place within them. The sun of the milieu is different at the North Pole, in moderate zones, and at the equator, and its beams are felt as different beams.


] A ‘milieu-thing’ belongs to an ‘intermediate realm’ lying between our perceptual content and its objects on the one hand and those objectively thought objects on the other. (Scheler 1954, p. 159, Eng. trans. p. 140)

Husserl, Scheler, Heidegger ...

Niche as Lebenswelt

Roger Barker: Niche as Behavioral Setting

Niches are recurrent settings which serve as the environments for our everyday activities:

my swimming pool,

your table in the cafeteria,

the 5pm train to Long Island.

Each setting is associated with certain standing patterns of behavior.

Niches, for Barker,

are natural units in no way imposed by an investigator.

To laymen they are as objective as rivers and forests

— they are parts of the objective environment that are experienced as directly as rain and sandy beaches are experienced. (Barker 1968, p. 11)

Settings

Each setting has a boundary which separates an organized internal (foreground) pattern from a differing external (background) pattern.

Nesting

Many settings occur in assemblies:

A unit in the middle range of a nesting structure is simultaneously both circumjacent and interjacent,

both whole and part,

both entity and environment.

NestingAn organ—the liver, for example—is a whole in relation to its own component pattern of cells,

and is a part in relation to the circumjacent organism that it, with other organs, composes;

it forms the environment of its cells, and is, itself, environed by the organism. (Barker 1968, p. 154)

Ontological Clarification of Barker

Two notions of ‘spaceship’

John is in the spaceship

Marks of (bodily) substance

i. Rounded-offness

ii. Occupies space

iii. Complete boundary

iv. May have substantial parts (nesting)

v. May be included in larger substances

vi. Has a life (manifests contrary accidents at different times)

Marks of Niches

(i) A niche enjoys a certain natural completeness or rounded-offness,

being neither too small nor too large

—in contrast to the arbitrary undetached parts of environmental settings and to arbitrary heaps or aggregates of environmental settings.

(ii) A niche takes up space,

it occupies a physical-temporal locale,

and is such as to have spatial parts.

Within this physical-temporal locale is a privileged locus—a hole—

into which the tenant or occupant of the setting fits exactly.

(iii) A niche

has an outer boundary:

there are objects which fall clearly within it,

and other objects which fall clearly outside it.

(The boundary itself need not be crisp.)

(iv) An environmental setting

may have actual parts which are also environmental settings.

(v) An environmental setting

may similarly be a proper part of larger, circumcluding environmental settings.

(vi) Niche has a life

is now warm, now cold

now at peace, now at war ….

Marks of (bodily) substance

i. Rounded-offness

ii. Occupies space

iii. Complete boundary

iv. May have substantial parts (nesting)

v. May be included in larger substances

vi. Has a life; is now warm, now cold

Double Hole Structure

Medium (filling the environing hole)

Tenant (occupying the central hole)

Retainer (a boundary of some surrounding structure)

The Structure of Niches

media and retainers

the medium of the bear’s niche is a

circumscribed body of air

Two Types of Boundary

Fiat boundary Physical boundary

Four Basic Niche Types

1 2 3 4

1: a womb;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the niche around a buzzard

Types of Niches

a pond, a nest, a cave, a hut, an air-conditioned apartment building

the history of evolution as a history of the development of niches

all vacant niches must have a retainerdependence of niche on tenant(s) the armchair nichetransforming niches of type 2 into niches of type 1


1 2 3 4

1: a house;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the earth’s atmosphere

stationary niches

1: your office when the door is closed; 2: a rabbit hole; 3: a seat at Yankee stadium; 4: the Klingon Empire

Niche as territory (home range)

nested hierarchy of stationery niches

Robert Ardrey, The Territorial Imperative

mobile niches


1 2 3 4

1: a womb;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the niche around a buzzard

Niche Construction

Lewontin: niches normally arise in symbiosis with the activities of organisms or groups of organisms;

they are not already there, like vacant rooms in a gigantic evolutionary hotel, awaiting organisms who would evolve into them.

“ecosystem engineering”

maintenance of niches (screwdrivers, paintings)

niches on different levels of the food chain

a. at the bottom of the hiearchy is the saprophytic chain, in which micro-organisms live on dead organic matter;

b. above this is the primary relation between animals and the plants they consume;

c. above this is the predator chain, in which animals of one sort eat smaller animals of another sort;

d. crosscutting all of these is the parasite chain, in which a smaller organism consumes part of a larger host organism.

Token Science

selection theory is concerned with phenomena at the level of populations; it is ‘concerned with what properties are selected for and against in a population. We do not describe single organisms and their physical constituents one by one.’ genotypes vs. genotokens

niche theory and set theory

Fiat Boundaries

fish and bird niches as volumes of space

demarcatory vs. behavioral fiat boundaries

trade-off between security/comfort and freedom of movement

Varieties of Controlled Airspace

Apertures, Mouths, and Sphincters

security vs. freedom of movement plantsbarnacles and snails fish and birdsskin or hide

Security vs. Freedom

the mouth of the bear, the threshold of your office

freedom of movement and fiat boundaries (of niches and of organisms)

the alimentary canal: hole or part ?

Double Hole Structure

Medium (filling the environing hole)

Tenant (occupying the central hole)

Retainer (a boundary of some surrounding structure)

The Medium for Life

a medium is a medium only relative to a given type of niche

a medium requires either a retainer (in the case of a vacant niche) or a tenant (in the case of an occupied niche)

when a tenant leaves its niche the gap left by the tenant is filled immediately by the surrounding mediumMichelangelo’s Davidexamples of media: air, smoke, water

Mixed Media

mixed media (including radioactive impurities, as well as as vitamins, amino acids, salts, and sugars)

Scrooge, crowds, plastic balls

every medium is maximal

what does the job of filling out the niche whose medium is made of air or water? Answer: bodies of vacuum

Vacuum

vacuum satisfies our operational test for being a medium.

vacuum = a volume of space which contains no particlesvacuum = fiat extensionbodies of vacuum are made of: nothing. vacuum is thus impenetrablevacuum contains no boundaries of the bona fide sort

application of niche concept

to formal theories of computer security (niches as ambients, firewalls as ambient boundaries)

to theories of situatedness, situation semantics, context-based semantics, information as context-dependent

in theories of planning (the meaning of life)

Beyond Biology

stacked retainers 1. underground nuclear shelters, 2. soccer

stadiums, 3. heliports, 4.bodies of controlled air space around airports. the niche of the astronaut is the interior of her spacesuitthe niche of the astronaut-plus-spacesuit is the interior of the spaceshipthe niche of the spaceship is the relevant region of spacetenants and niches are categorially disjoint

Lexical Semantics

the fruit is in the bowlthe bird is in the nestthe lion is in the cagethe pencil is in the cupthe fish is in the riverthe river is in the valleythe water is in the lakethe car is in the garagethe fetus is in the cavity in the uterine liningthe colony of whooping crane is in its breeding grounds

Lexical Semantics

‘She swam across the bay in which the submarine was buried and which supplied oysters for the local population.’

The Aristotle-Brentano Principle:

boundaries are ontologically parasitic on (i.e., cannot exist in isolation from) their hosts

The Touching Principle: two entities can be in contact (externally connected) only if one of them is not closed

The niche around the sleeping bear

There are relations of spatial overlap which do not imply corresponding relations of mereological overlap.

Niches are bounded not just spatially, and not just via physical material (the walls of the cave), but also via thresholds in quality-continua (for instance, temperature).

Hence:

distinct niches, may occupy the same spatial region.

Niches are exclusive environments: they cannot be shared by distinct entities (though distinct entities may have overlapping niches, both in the mereological and in the spatial sense of ‘overlap’).

bowling balls inside a closed velvet-lined case

twin fetuses inside a mother’s womb

Vagueness

A niche for an entity y may have proper parts that are not niches for y

What of the outer boundaries of niches?

Indoor vs. outdoor niches

Ecological subjects

A niche for a sum y+z is not ipso facto a niche for each of the summed parts. y+z = John’s head the head plus the rest of John’s body

Not every entity has its own niche. Those which do are natural units:

A substance (body, thing) is a maximally connected tenant, a tenant which is such that no larger connected tenant includes it as a proper part.

You are a substance, but your heart is only a connected tenant within your interior.

A group is a tenant including substances as proper parts.

Extending Mereology

mereology, formalized in terms of the single primitive relation: part of

mereotopology, obtained by adding extra primitive relation boundary for

theory of location, obtained by adding extra primitive relation located at

formal ecology, obtained by adding extra primitive relation niche for

Aim

To define structural properties such as:

open, closed, connected, compact, spatial coincidence, integrity, aggregate, boundary

Primitives

mereological predicate

P(x, y) (read: “x is part of y”), a

topological predicate

B(x, y) (“x is a boundary for y”),

locational predicate

L(x, y) (“x is located at y”).

For: exact location.

Some theorems:

T1 B(x, y) B(x, –y).

T2 B(x, y) B(y, z) B(x, z).

T3 P(x, y) B(y, z) B(x, z).

Defined Terms

D1 O(x, y)=df z (P(z, x) P(z, y))overlap

D2 xx =df xy (O(y, x) z (z O(z, y))) sum

D3 x+y =df z (P(z, x) P(z, y)) sum of x and y

D4 x–y =df z (P(z, x) O(z, y)) difference

D5 l(x) =df x(L(y, x)) location of x

Defined Terms

D6 b(x) =df z B(z, x) boundary of x

D7 i(x) =df x–b(x) interior of x

D8 c(x) =df x+b(x) closure of x

D9 Cl(x) =df x=c(x) closedness

D10 Rg(x) =df c(x) = c(i(x)) i(x) = i(c(x))regularity

Defined Terms

D11 C(x, y) =df O(x, y) O(c(x), y) O(x, c(y))

connection

D12 EC(x, y) =df C(x, y) O(x, y)

external connection

D13 IP(x, y) =df P(x, y) z(B(z, y) O(x, z))

interior parthood

D14 Cn(x) =df yz (x=y+z C(y, z))

self-connectedness

niche predicates

N(x, y), read: “x is a niche for y”.

N(x), read: “x is a niche”. This could be defined in terms of the binary predicate, but only if every niche has a tenant

‘N(x, y)’ and ‘N(x)’, where ‘’ ranges over organism-types.

medium and retainer

M(x, y)

“x is a medium for y”

R(x, y)

“x is a retainer for y”

free niche

D15 N*(x, y) =df N(x, y) zR(z, x)free niche for y

D16 N*(x) =df N(x) zR(z, x)

Every niche is either a free niche, in this sense, or else it has a retainer—

which will imply that it has a solid physical boundary for at least a portion of its exterior surface.

further definitions

D17 t(x) =df y N(x, y) tenant of x

D18 r(x) =df z R(z, x) retainer of x

D19 m(x) =df z M(z, x) medium of x

The Axioms

A1 N(x, y) O(l(x), l(y)) disjointness

A2 N(x, y) IP(l(y), l(x+y)) spatial containment

A3 N(x, y) C(x, y) connection of niche

A4 N(x, y) Cl(y) closure of tenant

A5 N(x, y) Cn(x) connectedness of niche

A6 N(x, y) Rg(y) regularity of tenant

A7 N(x, y) Rg(x) regularity of niche

A8 N(x, y) N(x, z) y = z functionality

Every occupied niche is a niche.

A9 yN(x, y) N(x)

There are no vacant fiat niches

A10 N*(x) yN(x, y)

Every fiat niche is a niche for something.

Media and retainers

A11 M(x, y) N(y)

A12 R(x, y) N(y)

Media are media of niches and retainers are retainers of niches.

Parts

A13 M(x, y) P(z, x) M(z, y)A14 R(x, y) P(z, x) R(z, y)

The parts of a medium for a given niche are themselves media for that niche and the parts of a retainer are themselves retainers.

A15 N(x) x = z(M(z, x) R(z, x))

Niches have no parts other than media and retainers.

Retainers and boundaries

A16 R(z, x) B(z, x)

Retainers are boundaries of niches (though not all boundaries of niches are retainers).

A17 N(x) zM(z, x)

Every niche has a medium (though a niche may lack a retainer).

A18 m(x) = m(y) x = y

No two niches have the same medium (though we leave it open whether two niches can have the same retainer).

Retainers and tenants

A19 N(x, y) R(z, x) C(z, y)

Retainers and tenants are not connected to each other, i.e., they do not share any physical parts or boundaries (for they are in every case separated by a medium.)

A20 M(z, x) R(w, x) EC(l(z), l(w))

The location of a retainer is externally connected (i.e., connected without overlap) to the location of the medium.

Axioms

A2' N(x, y) IP(l(y), l(m(x) + y))It is the medium of an occupied niche that surrounds

the tenant.

A3' N(x, y) C(m(x), y)It is the medium of an occupied niche that is connected

to the tenant. This actually follows from A3 in view of A19.

Axioms

A5' N(x) Cn(m(x))The medium of a niche is self-connected (though it

need not be compact, i.e., fill the entire environing hole: consider the bat flying in the bear’s cave).

A7' N(x) Rg(m(x))The medium of a niche is regular.

Theorems

T1 N(x) y(N(x, y) R(y, x))Every niche has either a tenant or a retainer. This is a

consequence of A10.

T2 M(x, y) z(N(y, z) R(z, y))Every medium requires either a tenant or a retainer.

This follows from T1 via A12.

Theorems

T3 M(z, x) P(z, x)

T4 R(z, x) P(z, x) Media and retainers are parts of niches. More

generally:

T5 M(x, y) P(z, x) P(z, y)

T6 R(x, y) P(z, x) P(z, y) All parts of a medium and all parts of a retainer are

parts of the relevant niche.

Theorems

T7 N(x, y) M(y, x)

T8 N(x, y) R(y, x)The tenant of a niche is neither a medium nor a retainer

thereof.

T9 M(z, x) R(w, x) EC(z, w)

The retainer of a niche is externally connected to the medium.

T10 R(z, x) B(z, m(x))

Retainers are boundaries of media.

Against multiplication of niches

T11 R(x, y) N(y – x)

A niche minus (part of) its retainer is not a niche.

This excludes the possibility that the difference between two niches might lie entirely in their retainers, which would result in an undue multiplication of niches with what are putatively the same boundaries.

Open Problems

X1 N(x, y) N(x', y') N(x + x', y + y') Mereological summing of niches is never additive.

cats whose niches come together to form a new, fused niche: the new niche is not just the mereological sum of the two separate niches;

for even assuming that the fiat boundaries of the two niches survive the fusion and continue to exist within the interior of the new niche, they are still not a part of it but are rather extrinsic to it.

Open Problems

X2 M(x, y) B(z, x) R(z, y) B(z, t(x))The boundaries of a medium are either retainers of the niche or boundaries of the tenant.

This would only be true if ‘B’ were understood as standing for physical boundaries, and only if one assumed that a medium has no holes except for the central holes occupied by the tenants.

(But consider again the bat in the bear’s cave, or a cage floating in the sea through which fish can swim.)

Open Problems

X3 M(x, y) B(z, x) EC(z, x)A medium never contains its own physical boundaries.

X4 B(b(m(x)), x)

Any boundary of the medium of a niche is a boundary of the niche itself.

This is false if we consider that the medium need not fill the environing hole completely. (The bat flying in the cave would not be part of the medium of the bear’s niche, yet the surface of the bat would not be part of the retainer either.)

Documents

The Ontology of Holes. Temple at Corinth Pipe The Ontology of Places