The Ontology of Measurement

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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
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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 realism

Different 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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bona fide objects

• objects which exist independently of our
  partitions
• (objects with bona fide boundaries)

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bona fide partition of individuals
John Paul George Ringo
bona fide partition of types
... up down charm strange ...
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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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Artists 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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fiat partition at the level of types
mild hypertension moderate hypertension severe hypertension
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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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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
a map is a mapping between points in reality and
the types represented in a legend
x
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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
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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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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