fostering diversity (of thinking) in science

AMCTM 2014Copyrighted

St. Petersburg, September 1

Fostering Diversity (of thinking)in Measurement Science

Franco Pavese*, Paul De Bièvre**

* Former Research Director at theNational Research Council,Istituto di Metrologia “G.Colonnetti”(from 2006 INRIM)

IMEKO TC21, Chair

Torino, Italy

E-mail: [email protected]

** Independent Consultant on Metrology inChemistry (MiC)Former Unit Head, Stable IsotopeMeasurements IRMM,Founding Editor and Editor-in-Chief until2011 of the Journal “Accreditation andQuality Assurance”Kasterlee, BelgiumE-mail: [email protected]

This presentation is licensed under a Creative Commons Attribution 3.0 License



Prologue

In many fields of sciencewe observe increasing symptoms of a trend:the prevalence of single-path thinking, maybe

fostered by either the anxiety to take a decisionor

by the intention to attempt to ‘force’ a conclusion



Truth: the gnoseological* dilemma

“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 to each other.” [N. Abbagnano, Dictionary of Philosophy]

“Consistency is indifferent to truth. Once can be entirelyconsistent and still be entirely wrong” [Steven G. Vick]

* ”of the philosophy of knowledge and the human faculties for learning”



The history of thinking shows that, in the search for ‘truth’,general principles are typically subject to contrastingpositions, leading to irresolvable criticism.

Truth: the gnoseological dilemma

“Reason alone is incapable of resolving the variousphilosophical problems” [D. Hume]

Actually, it is impossible to demonstrate any position,including “relativism”—or similar categories

(“Relativism is the traditional epithet applied to pragmatismby realists” [R. Rorty])



Modern science, basically founded on empirism, asopposed to metaphysics, is usually considered exempt fromthe previous weakness.Considering doubt as a shortcoming, science reasoningaims at reaching, if not truth, at least certainties,and many scientists tend to believe that this goal canbe fulfilled in their field. However, let us listen to Fr Bacon:

Truth ⇒ CertaintyThe epistemological dilemma

“If we begin with certainties, we shall end in doubts; but ifwe begin with doubts, and are patient with them, we shall

end with certainties.” [Sir Francis Bacon 1605](…still an optimistic viewpoint …)



Truth ⇒ Certainty ⇒ ObjectivityThe illusion of objective knowledge

As alerted by philosophers, however, the previous beliefsimply arises from the illusion of science being able to attainobjectivity, as a consequence of being based on informationdrawn 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 ofsingle-path scientific reasoning.



Should these pillars stand firm, the theories developed forsystematically interlocking the empirical experience would,

similarly, consist of a single building block, with theoccasional addition of ancillary building blocks

accommodating specific new knowledge.(a static vision)

Truth ⇒ Certainty ⇒ ObjectivityThe illusion of objective knowledge

“Verification” [L. Wittgenstein] would become unnecessary… “Falsification” [K. Popper] a paradox …

the road toward the next “Scientific revolution” [T. Kuhn] impossible.



Confronted with the evidence available since long, andreconfirmed everyday, that the previous scenario does not apply,

the concept of ‘uncertainty’ came in.However, strictly speaking, it applies only if the object of theobservations (the ‘measurand’ in measurement science) is thesame. Hence the issue is not fully resolved, the problem is shiftedto another concept, :

the uniqueness of the measurand, a concept of non-random nature, leading to imprecision.

Truth ⇒ Certainty ⇒ ObjectivityRemedy 1: Uncertainty (& Imprecision)

“Concerning non-precise data, uncertainty is called imprecision …is not of stochastic nature … can be modelled by the so-callednon-precise numbers” [R. Viertl, EOLSS UNESCO Encyclopœdia]



Certainty ⇒ Uncertainty ⇒ ChanceRemedy 2: Decision

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 byestablishing a hierarchy in measurement results (e.g. based on thefrequency of occurrence), in order to take a ‘decision’ (i.e. forchoosing from various measurement results).Chance concept initiated the framework of ‘probability’, but expanded later intoseveral other streams, e.g., possibility, fuzzy, cause-effect, interval, non-parametric, … reasoning frames depending on the type of information availableor 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]



The illusions of chance –1Chance ⇒ (Prediction) ⇒ Decision

The ultimate common goal of any branch of science isto communicate measurement results and perform robustprediction.

In the probability frame, any decision strategy requires thechoice of an expected value as well of the limits of thedispersion interval of the observations.The choice of the expected value (‘expectation’: “a strong beliefthat something will happen or be the case” [from Oxford Dictionary])is not unequivocal, since several location parameters areoffered by probability theory—with a ‘true value’ still standingin the shade, deviations from which are called ‘errors’.



Chance ⇒ (Prediction) ⇒ DecisionThe illusions of chance –2

As to data dispersion, most theoretical frameworks tend to lackgeneral reasons for bounding a probability distribution, whose tailsthus 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 theintended use of the data.The terms used in this frame clearly indicate the difficulty andthe meaning that is applicable in this context:‘confidence level’ (confidence: “the feeling or belief that one can havefaith in or rely on someone or something” [from Oxford Dictionary]), or‘degree of belief’ (belief: “trust, faith, or confidence in (someone orsomething)” or “an acceptance that something exists or is true, especiallyone without proof” [ibidem])



Chance ⇒ (Prediction) ⇒ DecisionThe illusions of chance –3

As to data dispersion, alternatively, one can believe in usingtruncated (finite tail-width) distributions.However, reasons for truncation are generally supportedby uncertain information.In rare cases it may be justified by theory, e.g. a bound tozero –itself not normally reachable exactly (experimentallimit of detection)

Stating limits becomes itself again a decision, also in thiscase assumed to be fit for the intended use of the data.



Remedy 3: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, forsubsequent action),However, hypotheses cannot be proved, and inter-subjectiveagreements are strictly relative to a community and for agiven period of time.The loss of certainty resulted in the loss of uniqueness ofdecisions, and the concept of ‘risk’ emerged as a remedy.



Uncertainty ⇒ Chance ⇒ Decision ⇒ RiskThe illusions of risk –1

Any parameter chosen to represent a set of observationsbecomes ‘uncertain’,not because it must be expressed with a dispersion attributeassociated to an expected value, butbecause the choice of both parameters is the result ofdecisions, 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.



Uncertainty ⇒ Chance ⇒ Decision ⇒ RiskThe illusions of risk –2

In other words:

• The association of a ‘risk’ to a decision, a recentpopular issue, does not add any real benefit in respectto the fundamental issue.

• Risk is only zero for certainty, so zero risk isunreachable.

“The relations between probability and experience are also still inneed of clarification. In investigating this problem we shall discoverwhat will at first seem an almost insuperable objection to mymethodological views. For although probability statements play sucha vitally important role in empirical science, they turn out to be inprinciple impervious to strict falsification.” [K. Popper 1936]



The failure of remedies:deeper origin –1

Chance is a bright prescription for working on symptoms of thedisease, but is not a therapy for its deep origin, subjectivity.In fact, the very origin of the problem is related to ourknowledge interface—human being.

It is customary to make a distinction between the‘outside’ and the ‘inside’ of the observer, i.e. betweenthe ‘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 andreasonably stable reality outside us (objectivity of the “true value”).



The failure of remedies:deeper origin –2

This distinction is one of the reasons generating a dichotomy sinceat least a couple of centuries, between ‘exact sciences’ and otherbranches, often called ‘soft sciences’, like psychology, sociology,economy…For ‘soft’ science we are ready to admit that the objects ofobservations tend to be dissimilar, because every humanindividual is dissimilar from any other.In ‘exact’ science we are usually not readily admitting thatthe human interface between our ‘mind’ and the ‘realworld’ is a factor of influence affecting our knowledge.Mathematics stays in between, not being based on observations buton a ‘exact’ construction of concepts based on the thinkingmechanisms in our mind.



Consequences• All of the above should suggest scientists to be

humble about contending on methods for expressingexperimental knowledge— apart from grossmistakes (“blunders”).

• Different from the theoretical context, experience can beonly shared to a certain degree, leading, at best, to ashared decision. The association ofa ‘risk’ to a decision does not add any real benefit withrespect to the fundamental issue.

• One cannot expect a single decision to be valid in allcases, i.e. without exceptions. Risk isonly zero for certainty, so zero risk is unreachable.

• Similarly, no single frame of reasoning leading to aspecific type of decision can be expected to be valid inall cases.



Diversity: a resource• Also in science, ‘diversity’ is not always a synonym of

‘confusion’, a popular term used to contrast it, rather it is aninvaluable additional resource leading to betterunderstanding.

• Should this be the case, diversity rather becomes richness, bydeserving a higher degree of confidence in our pointing to thecorrect answers

(but, obviously, “nothing that has been or will be said makes it aprocess of evolution toward anything” [T. Kuhn]).

• This fact is already well understood in experimental science,where the main way to detect systematic effects is todiversify the experimental methods and procedures used.Why not accepting it also in reasoning?



The Guide for the Expression of Uncertainty in Measurement (GUM) in favour tochoose 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 tochoose 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 ofbase units;

The singled ‘official’ set of “recommended values” used for the numerical valuesof 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 andsystematic, with the concept of “correction” associated to the latter; …

Sparse examples of exclusive choicesin measurement science



General conclusions• At its origin, the indicated trend might be due to

a wrong assignment to a relevant Commission orTask Group, with the request of a single‘consensus’ outcome, instead of a rationally-compounded digest of the best availableinformation/knowledge.

• However, the consequence risks to bepolitics (needing decisions) leaking into science(seeking understanding),a trend carrying the danger of potentiallythreatening scientific integrity.

fostering diversity (of thinking) in science

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