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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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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