PH 221 Week 7: Measurement
Cartwright and Bradburn1
Measurement module: this week we focus on theory, next week on application to the CPI.
We will look at three parts of (philosophical) measurement theory this week: characterisation,
representation and application (or procedures) and focus on values and application next
week.
Characterisation
1. Characterisation
part one
What it is
Characterisation
Way of picking out a concept from another, drawing its boundaries, identifying
its referents.
Family resemblance concepts
i) games
with either i) no essential
(necessary) conditions or ii)
ii) exploitation
no necessary and sufficient
conditions.
iii) social status
Ideal concepts with no real
i) homo economicus
referents, somewhat like
platonic forms.
A. Ballung concepts
B. Concepts of Pure
Understanding
C. ‘Classical’
Cocnepts


An example
Refer to a single quantity or
category that can be precisely
defined.
i) cup
ii) heat
iii) square
Some argue all concepts are ballung concepts.
If a concept is ballung then it can’t be classically defined
2. Characterisation
part two
What it is
Definition
Providing a characterisation
A. explicit
An example
Direct definition of the
concept without reference to
other concepts from within the
theory.
Definition of concept wrt
other concepts in the theory.
i) square is a four sided figure with equal sides
and equal angles
Defined by measurement
procedures—concept
is
characterised by whatever
measurement picks out.
Arbitrary definition of concept
that is (usually) sharper than
concept is in ordinary use.
Makes concept ‘workable’.
i) IQ
i) income effect: change in demand brought
about by change in real income.
B. implicit
C. operational
D. conventional



1
i) exploitation as diff b/w real wages and MPL
ii) rationality as consistent maximisation.
All definitions are implicit in some way.
Operational definitions are a subset of conventional definitions.
Does this categorisation seem right?
Sam, June.
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PH 221 Week 7: Measurement
Representation
3. Representation
What it is
Representation
Mapping of features of a concepts instances. Representation theorems show us
that our measurement scales are isomorphic to our concepts.
List or index of values with no i) instances of exploitation
specified aggregation.
ii) EU measures on social exclusion
Enumeration of examples or
instances
Indicators
An example
Metric systems
Ordinal
A function that assigns numbers to subsets of sets in a systematic way.
Ordered ranking. Strength
i) mohs scale (mineral scratches another)
doesn’t matter.
ii) good, medium, bad
Cardinal
Numerical ranking, no true 0
point. (ratios are meaningless,
ratios of differences aren’t
though)
Non-arbitrary 0 value
Ratio



i) utilities (VNM, savage)
i) loudness
ii) temperature
Representation must match the properties of our concept.
We want it represented correctly—sub-additive length is a mistake.
Ballung concepts are hard to represent. What are the pros of aggregation? Cons of not?
Application (procedures)
3. Application
(procedures)
What it is
An example of failure
Application
(2 desiderata)
Accuracy
The way by which we actually
tools and methods we adopt.
Whether measurement agrees
with true values
Degree of specificity
Accurage representation of
our concept
put our representation scale into practice, the
Precision
Good representation
Problem of nomic
measurement


To know whether or not our
measurement is ‘true’ we need
either more precise measure
or more general theory.
I look in the room and say it is 40% men 60%
women. It is really 32% women, 68% men
She is 5 feet tall. She is 5’11’’ she is 5’11.476…’’
sub-additive length. How much do you love
me? 14. (not necessarily wrong, but no scale
specified, cant answer whether good or not)
Chang on temperature.
What kind of representation should we give poverty? Exploitation?
How should we go about deciding what is a good representation?
o Good representations are use specific…ie pragmatic answer.
o Good representations match what the concept ‘really’ is…idealist answer.
o There is no good usage…relativist answer.
 Which is correct? How should we think about this part?
Values
Think about this for next time:
 how can the following measurements be value laden:
CPI, poverty, exploitation, income, GDP
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PH 221 Week 7: Measurement
Wittgenstein, from Philosophical Investigations.
65…I am saying that these phenomena have no one thing in common which makes
us use the same word for all,-but that they are related to one another in many
different ways. And it is because of this relationship, or these relationships, that we
call them all "language". I will try to explain this.
66. Consider for example the proceedings that we call "games". I mean board-games,
card-games, ball-games, Olympic games, and so on. What is common to them all? -Don't say: "There must be something common, or they would not be called 'games' "but look and see whether there is anything common to all. -- For if you look at them
you will not see something that is common to all, but similarities, relationships, and a
whole series of them at that. To repeat: don't think, but look! -- Look for example at
board-games, with their multifarious relationships. Now pass to card-games; here
you find many correspondences with the first group, but many common features
drop out, and others appear. When we pass next to ball-games, much that is common
is retained, but much is lost.-- Are they all 'amusing'? Compare chess with noughts
and crosses. Or is there always winning and losing, or competition between players?
Think of patience. In ball games there is winning and losing; but when a child throws
his ball at the wall and catches it again, this feature has disappeared. Look at the
parts played by skill and luck; and at the difference between skill in chess and skill in
tennis. Think now of games like ring-a-ring-a-roses; here is the element of
amusement, but how many other characteristic features have disappeared!
Sometimes similarities of detail. And we can go through the many, many other groups
of games in the same way; can see how similarities crop up and disappear. And the
result of this examination is: we see a complicated network of similarities
overlapping
and
cries-crossing:
sometimes
overall
similarities.
67. I can think of no better expression to characterize these similarities than "family
resemblances"; for the various resemblances between members of a family: build,
features, colour of eyes, gait, temperament, etc. etc. overlap and cries-cross in the
same way.-And I shall say: 'games' form a family.
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