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The Ontology of Measurement

Barry Smith

ONTOLOGIST.cOm

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The world knows colour

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The world knows no redness, greenness, blueness, …

These types do not reflect joints in reality

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The world knows no mild hypertension, moderate hypertension,

severe hypertension, …

These do not reflect joints in reality

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The world knows no Poland, Belgium, Utah, Bavaria, …

These do not reflect joints in reality

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The world knows no nation-state, parish, census tract, township, legal

jurisdiction …

These types do not reflect joints in reality

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what the world knows

what we know

what we think we know

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The world is largely a system of continua, both on the level of instances and on the level of types

But what we know (at least as expressed in language) is always in a sense digital rather than analogue

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All of the mentioned entities arises because of our parcellings, griddings,

apportionments, segmentations, ...

= partitions

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Partition

Partitions

A partition is the result of drawing a (typically complex) fiat boundary over a certain domain

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GrGr

A simple partition on the level of individuals

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GrGr

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GrGr

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partitions can be extended

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partitions can be split and merged

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partitions can be split and merged

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partitions can be split and merged

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A partition can be more or less refined

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one partition can be skew to another

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Perspectivalism

Perspectival realismDifferent partitions which are skew to each other may be equally veridical representations of the same reality

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Cerebral Cortex

We can apply partitions to other partitions

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Mereotopology of Neuronal Partitions

Advanced Database Methodology for the Collation of Connectivity Data on the Macaque Brain

Klaas E. Stephan, et al., Phil. Trans. Royal Society London B, 2001

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link: Granular partitions

http://ontologist.com

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An ontology is a partition, or a complex partitions, on the level of types

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Types and instances

Partitions can be created both at the level of instances (Poland vs. Germany) and at the level of types (nation-state vs. colony)

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An ontology is a partition at the level of types

focusing primarily on types (dog, nation, leaf, cell, lung, lake …) whose instances have their own complete bona fide boundaries

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= objects which exist independently of our partitions

(objects with bona fide boundaries)

bona fide objects

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John Paul George Ringo

... up down charm strange ...

bona fide partition of individuals

bona fide partition of types

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a bona fide type classification

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But there are also fiat partitions

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Fiat partitions are artefacts of our cognition

= of our referring, perceiving, classifying, counting, measuring, mapping activity

GRIDDING ACTIVITY

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Artist’s Grid

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e.g. they are artefacts for counting

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Frege: “Numbers belong to the realm of concepts”

Better: Numbers belong to the realm of partitions

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Without partitions

how many numbers?

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Partitions can sometimes create objects

fiat objects = objects created by partitions

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mild hypertension

moderate hypertension

severe hypertension

fiat partition at the level of types

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fiat partition at the level of individuals

this

tail

this

torso

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Kansas

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Ontology of Maps

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types represented in an ontology

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domestic cow breed: Brahman

domestic cow breed: HOLSTEIN

species: Bos TAURus

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A label in the zoo is a mapping between an animal instance and an

animal type

(all scientific language is built around mappings of this sort between instances and types)

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California Land Cover

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California Land Cover

x

a map is a mapping between points in reality and the types represented

in a legend

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A Map

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A Portion of Reality

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A Mapping

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A Map is a Mapping

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The Ontology of Measurement

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The world knows no Poland, Belgium, Utah, Bavaria, …

These do not reflect joints in reality

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The world knows no inches, feet, centimeters, seconds, grams, pascals, joules, ohms, teslas, volts, kg/m3 …

These, too, do not reflect joints in reality

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Measurement belongs to the realm of partitions

... -20-10 -10 0 0 10 10 20 ...

massivelyincreased... normal increased chronic ...

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Partitions can be skew to each other

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Partitions can be more and less refined

and thereby yield measurements which are more or less vague

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Units of measurement are fiat types

Each inch long thing has a length which is an instance of the fiat type inch

(the fiat type inch is like the fiat type blue)

Each case of mild hypertension has a disorder which is an instance of the fiat type mild hypertension

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Length is a bona fide universal

But the different ways of slicing up length (creating a set of quasi-discrete portions out of a continuum) create fiat universals

Is there a way of slicing up the universal length into minima? (infinitesimal portions?)

Is Planck length a bona fide unit type?

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in the everyday world

all the measurements (lengths, temperatures ...) with which we have to deal are socially created artefacts subject to phenomena of vagueness, technology-dependence, and using fiat units of measure

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Phenomenon of vagueness

every measurement is vague, to a degree determined by the measuring rod/standard used

vagueness is the other side of the coin from granularity

every measuring rod (scale) does not recognize differences beneath a certain size

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Measurement: we lay a grid upon a specific portion of physical reality with a gridding

determined by a given unit type, map endpoints to endpoints and count the number

of cells between the endpoints

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An Act of Measurement

portion of reality:

dependent magnitude (here: distance)

+ independent bearer

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The Act of Measurement

tape measure (grid) projected onto reality with endpoints mapped to endpoints

l l l l

l l l l

l l l l

l l l l

l l l l

l l l

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1 2 3 4

then you count the cells in the grid

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Ontological assay of the act of measuring length

• act of counting• cells • in a grid• determined by the fiat type which is the pertinent

unit of measurement • and by a certain portion of reality• consisting of some independent continuant bearer

together with• a dependent feature, here: a certain distance • between two endpoints

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THE END

THE END