The Ontology of Measurement

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The Ontology of Measurement
 
Barry Smith ONTOLOGIST.cOm
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• For individuation or delimitation of individuals,
  I think we can do better than the fig tree with
  the adventicious roots hanging down. How about a
  "sea of mountains"? That is what I usually use.
• Second, as I hope you realize, the animals in
  cages are a veal farm, not a zoo. The labels, if
  they are labels at all, would label individual
  inmates, not kinds. Incorrect details undermine
  your credibility and distract people like me from
  your main points. If you want to talk about kinds
  of animals in a zoo, with labels, why not use a
  picture of kinds of animals in a zoo, with
  labels! Lastly, some animal rights people are
  offended by veal pens, you might be doing that
  deliberately too I suppose.
• Minor point, the "road sign" is obviously (to
  me) not a "road" sign for driving, it is almost
  certainly a trail sign for hiking.

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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