Fostering Diversity (of thinking) in Science

Fostering Diversity (of thinking)
in Measurement Science
Franco Pavese*, Paul De Bièvre**
* Former Research Director at the
National Research Council,
Istituto di Metrologia “G.Colonnetti”
(from 2006 INRIM)
IMEKO TC21, Chair
Torino, Italy
E-mail: frpavese@gmail.com
This presentation is licensed under a Creative Commons Attribution 3.0 License
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** Independent Consultant on Metrology in
Chemistry (MiC)
Former Unit Head, Stable Isotope
Measurements IRMM,
Founding Editor and Editor-in-Chief until
2011 of the Journal “Accreditation and
Quality Assurance”
Kasterlee, Belgium
E-mail: paul.de.bievre@skynet.be
St. Petersburg, September 1

we observe increasing symptoms of a trend:
the prevalence of single-path thinking, maybe
fostered by either the anxiety to take a decision
by the intention to attempt to ‘force’ a conclusion
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Prologue
In many fields of science
or

Truth: the gnoseological* dilemma
* ”of the philosophy of knowledge and the human faculties for learning”
“Five fundamental aspects can be attributed to ‘truth’ …
 by correspondence
 by revelation (disclosure)
 by conformity to a rule
 by consistency (coherence)
 by benefit
They are not reciprocally alternative, are diverse and not-reducible
“Consistency is indifferent to truth. Once can be entirely
consistent and still be entirely wrong” [Steven G. Vick]
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to each other.” [N. Abbagnano, Dictionary of Philosophy]

Truth: the gnoseological dilemma
The history of thinking shows that, in the search for ‘truth’,
general principles are typically subject to contrasting
positions, leading to irresolvable criticism.
“Reason alone is incapable of resolving the various
philosophical problems” [D. Hume]
Actually, it is impossible to demonstrate any position,
(“Relativism is the traditional epithet applied to pragmatism
by realists” [R. Rorty])
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including “relativism”—or similar categories

Truth ⇒ Certainty
The epistemological dilemma
Modern science, basically founded on empirism, as
opposed to metaphysics, is usually considered exempt from
the previous weakness.
Considering doubt as a shortcoming, science reasoning
aims at reaching, if not truth, at least certainties,
and many scientists tend to believe that this goal can
be fulfilled in their field. However, let us listen to Fr Bacon:
“If we begin with certainties, we shall end in doubts; but if
we begin with doubts, and are patient with them, we shall
end with certainties.” [Sir Francis Bacon 1605]
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(…still an optimistic viewpoint …)

Truth ⇒ Certainty ⇒ Objectivity
The illusion of objective knowledge
As alerted by philosophers, however, the previous belief
simply arises from the illusion of science being able to attain
objectivity, as a consequence of being based on information
drawn from the observation of natural phenomena, taken as
‘facts’.
Fact:
“A thing that is known or proven to be true” [Oxford Dictionary]
“A piece of information presented as having objective reality”
[Merriam-Webster Dictionary]
Objectivity and cause-effect-cause chain are the pillars of
single-path scientific reasoning.
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The illusion of objective knowledge
Should these pillars stand firm, the theories developed for
systematically interlocking the empirical experience would,
similarly, consist of a single building block, with the
occasional addition of ancillary building blocks
accommodating specific new knowledge.
“Verification” [L. Wittgenstein] would become unnecessary…
the road toward the next “Scientific revolution” [T. Kuhn]
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(a static vision)
“Falsification” [K. Popper] a paradox …
impossible.

Remedy 1: Uncertainty (& Imprecision)
Confronted with the evidence available since long, and
reconfirmed everyday, that the previous scenario does not apply,
However, strictly speaking, it applies only if the object of the
observations (the ‘measurand’ in measurement science) is the
same. Hence the issue is not fully resolved, the problem is shifted
to another concept, :
the uniqueness of the measurand, a concept of non-random
“Concerning non-precise data, uncertainty is called imprecision …
is not of stochastic nature … can be modelled by the so-called
non-precise numbers” [R. Viertl, EOLSS UNESCO Encyclopoedia]
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the concept of ‘uncertainty’ came in.
nature, leading to imprecision.

Certainty ⇒ Uncertainty ⇒ Chance
Confronted with the evidence of diverse results of observations,
modern science’s way-out was to introduce the concept of
‘chance’—replacing ‘certainty’.
This was done with the illusion of reaching firmer conclusions by
establishing a hierarchy in measurement results (e.g. based on the
frequency of occurrence), in order to take a ‘decision’ (i.e. for
choosing from various measurement results).
Chance concept initiated the framework of ‘probability’, but expanded later into
several other streams, e.g., possibility, fuzzy, cause-effect, interval, non-parametric,
… reasoning frames depending on the type of information available
or on the approach to it.
“With the idol of certainty (including that of degrees of imperfect
certainty or probability) there falls one of the defences of
obscurantism which bar the way of scientific advance.” [K. Popper]
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Remedy 2: Decision

The illusions of chance –1
Chance ⇒ (Prediction) ⇒ Decision
The ultimate common goal of any branch of science is
to communicate measurement results and perform robust
prediction.
In the probability frame, any decision strategy requires the
choice of an expected value as well of the limits of the
dispersion interval of the observations.
The choice of the expected value (‘expectation’: “a strong belief
that something will happen or be the case” [from Oxford Dictionary])
is not unequivocal, since several location parameters are
offered by probability theory—with a ‘true value’ still standing
in the shade, deviations from which are called ‘errors’.
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As to data dispersion, most theoretical frameworks tend to lack
general reasons for bounding a probability distribution, whose tails
thus extend without limits to infinitum.
However, without a limit, no decision is possible; and,
the wider the limit, the less meaningful a decision is.
Stating a limit becomes itself a decision, assumed to fit the
intended use of the data.
The terms used in this frame clearly indicate the difficulty and
the meaning that is applicable in this context:
‘confidence level’ (confidence: “the feeling or belief that one can have
faith in or rely on someone or something” [from Oxford Dictionary]), or
‘degree of belief’ (belief: “trust, faith, or confidence in (someone or
something)” or “an acceptance that something exists or is true, especially
one without proof” [ibidem])
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As to data dispersion, alternatively, one can believe in using
truncated (finite tail-width) distributions.
However, reasons for truncation are generally supported
by uncertain information.
In rare cases it may be justified by theory, e.g. a bound to
zero –itself not normally reachable exactly (experimental
limit of detection)
Stating limits becomes itself again a decision, also in this
case assumed to be fit for the intended use of the data.
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Uncertainty ⇒ Chance ⇒ Decision ⇒ Risk
But … what about ‘decision’?
When (objective) reasoning is replaced by choice,
a decision can only be based on
• a priori assumptions (for hypotheses), or
• inter-subjectively accepted conventions (predictive, for
subsequent action),
However, hypotheses cannot be proved, and inter-subjective
agreements are strictly relative to a community and for a
given period of time.
The loss of certainty resulted in the loss of uniqueness of
decisions, and the concept of ‘risk’ emerged as a remedy.
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Remedy 3:

Any parameter chosen to represent a set of observations
becomes ‘uncertain’,
not because it must be expressed with a dispersion attribute
associated to an expected value, but
because the choice of both parameters is the result of
decisions, and a decision cannot be ‘exact’ (unequivocal).
Any decision is fuzzy.
The use of risk does not alleviate the issue:
if a decision cannot be exact, the risk cannot be null.
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The illusions of risk –1

In other words:
• The association of a ‘risk’ to a decision, a recent
popular issue, does not add any real benefit in respect
to the fundamental issue.
• Risk is only zero for certainty, so zero risk is
unreachable.
“The relations between probability and experience are also still in
need of clarification. In investigating this problem we shall discover
what will at first seem an almost insuperable objection to my
methodological views. For although probability statements play such
a vitally important role in empirical science, they turn out to be in
principle impervious to strict falsification.” [K. Popper 1936]
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The illusions of risk –2

Chance is a bright prescription for working on symptoms of the
disease, but is not a therapy for its deep origin, subjectivity.
In fact, the very origin of the problem is related to our
knowledge interface—human being.
It is customary to make a distinction between the
‘outside’ and the ‘inside’ of the observer, i.e. between
the ‘real world’ and the ‘mind’.
Note: we are not fostering here a vision of the world as a ‘dream’.
There are solid arguments for conceiving a structured and
reasonably stable reality outside us (objectivity of the “true value”).
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The failure of remedies:
deeper origin –1

This distinction is one of the reasons generating a dichotomy since
at least a couple of centuries, between ‘exact sciences’ and other
branches, often called ‘soft sciences’, like psychology, sociology,
economy…
For ‘soft’ science we are ready to admit that the objects of
observations tend to be dissimilar, because every human
individual is dissimilar from any other.
In ‘exact’ science we are usually not readily admitting that
the human interface between our ‘mind’ and the ‘real
world’ is a factor of influence affecting our knowledge.
Mathematics stays in between, not being based on observations but
on a ‘exact’ construction of concepts based on the thinking
mechanisms in our mind.
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The failure of remedies:
deeper origin –2

• All of the above should suggest scientists to be
humble about contending on methods for expressing
experimental knowledge— apart from gross
mistakes (“blunders”).
• Different from the theoretical context, experience can be
only shared to a certain degree, leading, at best, to a
shared decision. The association of
a ‘risk’ to a decision does not add any real benefit with
respect to the fundamental issue.
• One cannot expect a single decision to be valid in all
cases, i.e. without exceptions. Risk is
only zero for certainty, so zero risk is unreachable.
• Similarly, no single frame of reasoning leading to a
specific type of decision can be expected to be valid in
all cases.
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Consequences

• Also in science, ‘diversity’ is not always a synonym of
‘confusion’, a popular term used to contrast it, rather it is an
invaluable additional resource leading to better
understanding.
• Should this be the case, diversity rather becomes richness, by
deserving a higher degree of confidence in our pointing to the
correct answers
(but, obviously, “nothing that has been or will be said makes it a
process of evolution toward anything” [T. Kuhn]).
• This fact is already well understood in experimental science,
where the main way to detect systematic effects is to
diversify the experimental methods and procedures used.
Why not accepting it also in reasoning?
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Diversity: a resource

Sparse examples of exclusive choices
in measurement science
 The Guide for the Expression of Uncertainty in Measurement (GUM) in favour to
choose a single framework, with the ‘error approach’ discontinued in favour of an
‘uncertainty approach’;
 The Guide for the Expression of Uncertainty in Measurement (GUM) in favour to
choose for its future edition the single approach—‘Bayesian’— replacing
‘frequentist’ parts;
 The International System of Measurement Units (SI) proposed to change, with
“fundamental constants” replacing ‘physical states or conditions’ in definitions of
base units;
 The singled ‘official’ set of “recommended values” used for the numerical values
of quantities (fundamental constants, atomic masses, differences in scales, …);
 The pretended permanent validity of numerical value stipulations;
 The traditional exclusive classification of the errors/effects in random and
systematic, with the concept of “correction” associated to the latter; …
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• At its origin, the indicated trend might be due to
a wrong assignment to a relevant Commission or
Task Group, with the request of a single
‘consensus’ outcome, instead of a rationally-compounded
information/knowledge.
• However, the consequence risks to be
politics (needing decisions) leaking into science
(seeking understanding),
a trend carrying the danger of potentially
threatening scientific integrity.
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General conclusions
digest of the best available

Fostering Diversity (of thinking) in Science

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