some remarks on a heuristic point of view about the role of experiment in the physical sciences

7/30/2019 Some Remarks on a Heuristic Point of View about the Role of Experiment in the Physical Sciences

http://slidepdf.com/reader/full/some-remarks-on-a-heuristic-point-of-view-about-the-role-of-experiment-in-the 1/17

SILFSNew Essays in Logic and

Philosophy of Science

Editors

Marcello D’Agostino

Giulio Giorello

Federico Laudisa

Telmo Pievani

Corrado Sinigaglia

The papers collected in this volume are based on

the best contributions to the conference of the

Italian Society for Logic and Philosophy of Science

(SILFS) that took place in Milan on 8-10 October

2007. The aim of the Society, since its foundation

in 1952, has always been that of bringing together

scholars — working in the broad areas of Logic,

Philosophy of Science and History of Science — who

share an open-minded approach to their disciplines

and regard them as essentially requiring continuous

confrontation and bridge-building to avoid the

danger of over-specialism. In this perspective,

logiciansand philosophers of science should not

indulge in inventing and cherishing their own “internal

problems” — although these may occasionally be

an opportunity for conceptual clarification — but

should primarily look at the challenging conceptualand methodological questions that arise in any

genuine attempt to extend our objective knowledge.

As Ludovico Geymonat used to put it: “[good]

philosophy should be sought in the folds of science

itself”.

Contributions are distributed into six sections, five

of which — “Logic and Computing”, “Physics and

Mathematics”, “Life Sciences”, “Economics and

Social Sciences”, “Neuroscience and Philosophy of

Mind” — are devoted to the discussion of cutting-

edge problems that arise from current-day scientific

research, while the remaining section on “General

Philosophy of Science” is focused on foundational

and methodological questions that are common

to all areas.

11 S

I LF S

SI LF S

N ewE s s a y si nL o gi c an d

Phi l o s o ph y of S ci e

n c e

E di t or s

M ar c el l oD’ A g o s t i n

Gi ul i o Gi or el l o

F e d eri c oL a u di s a

T el m oPi ev ani

C orr a d o Si ni g a gl i a

SILFS

1848900035_cover.indd 1 28/10/2010 21:07



Table of contents

Editors’ preface ix

List of contributors xi

PART I LOGIC AND COMPUTING 1

Umberto Rivieccio

A bilattice for contextual reasoning 3Francesca Poggiolesi

Reflecting the semantic features of S5 at the syntactic level 13

Gisele Fischer Servi

Non monotonic conditionals and the concept I believe only A 27

Carlo Penco, Daniele Porello

Sense and Proof 37

Andrea Pedeferri

Some reflections on plurals and second order logic 47

G. Casini, H. Hosni

Default-assumption consequence relations in a preferentialsetting: reasoning about normality 53

Bianca Boretti, Sara Negri

On the finitization of Priorean linear time 67

Riccardo Bruni

Proof-theoretic aspects of quasi-inductive definitions 81

Giacomo Calamai

Remarks on a proof-theoretic characterization of polynomialspace functions 95

PART II PHYSICS AND MATHEMATICS 115

Vincenzo Fano, Giovanni Macchia

How contemporary cosmology bypasses Kantian prohibition

against a science of the universe 117Giulia Giannini

Poincare and the electromagnetic world picture. For arevaluation of his conventionalism 131

Marco Toscano

“Besides quantity”: the epistemological meaning of Poincare’squalitative analysis 141



vi

Laura FellineStructural explanation from special relativity to quantummechanics 153

Miriam Cometto

When the structure is not a limit. On continuity throughtheory-change 163

Gianluca Introzzi

Approaches to wave/particle duality: historical analysis andcritical remarks 173

Marco Pedicini, Mario Piazza

An application of von Neumann algebras to computationalcomplexity 183

Miriam FranchellaPhenomenology and intuitionism: the pros and cons of aresearch program 195

Luca Bellotti

A note on the circularity of set-theoretic semantics for set theory 207

Valeria Giardino

The use of figures and diagrams in mathematics 217

Paola Cantu

The role of epistemological models in Veronese’s and Bettazzi’stheory of magnitudes 229

PART III LIFE SCIENCES 243

Pietro Omodeo

Evolution by increasing complexity in the framework of Darwin’stheory 245

Stefano Giaimo, Giuseppe Testa

Gene: an entity in search of concepts 257

Elena Casetta

Categories, taxa, and chimeras 265

Flavio D’Abramo

Final, efficient and complex causes in biology 279

Ludovica Lorusso

The concept of race and its justification in biology 289

PART IV ECONOMICS AND SOCIAL SCIENCES 301

Marco Novarese, Alessandro Lanteri, Cesare

Tibaldeschi

Learning, generalization, and the perception of information: anexperimental study 303

Andrea Pozzali

Tacit knowledge and economics: recent findings and perspectivesof research 319



vii

Viviana Di GiovinazzoFrom individual well-being to economic welfare. Tibor Scitovskyexplains why (consumers’) dissatisfaction leads to a joylesseconomy 327

Federica Russo

Explaining causal modelling. Or, what a causal model ought toexplain 347

Enzo Di Nuoscio

The epistemological statute of the rationality principle.Comparing Mises and Popper 363

Albertina Oliverio

Evolution, cooperation and rationality: some remarks 377

Francesco Di IorioSelf-organization of the mind and methodological individualismin Hayek’s thought 389

Simona Morini

Can ethics be naturalized? 403

Stefano Vaselli

Searle’s collective intentionality and the “invisible hand”explanations 409

Sergio Levi

The naturalness of religion and the action representation system 423

Andrea Zhok

On value judgement and the ethical nature of economicoptimality 433

Dario Antiseri

Carl Menger, Ludwig von Mises, Friedrich A. von Hayek andKarl Popper: four Viennese in defense of methodologicalindividualism 447

PART V NEUROSCIENCE AND PHILOSOPHY OF

MIND 463

Fabio Bacchini

Jaegwon Kim and the threat of epiphenomenalism of mentalstates 465

Wolfgang HuemerPhilosophy of mind between reduction, elimination andenrichment 481

Laura Sparaci

Discourse and action: analyzing the possibility of a structuralsimilarity 493

Alessandro Dell’Anna

Visuomotor representations: Jacob and Jeannerod betweenenaction and the two visual systems hypothesis 505



viii

Daniela TagliaficoMirror neurons and the “radical view” on simulation 515

Vincenzo G. Fiore

Multiple realizations of the mental states: hunting for plausiblechimeras 529

Arturo Carsetti

The embodied meaning and the “unfolding” of the mind’s eyes 539

Katja Crone

Consciousness and the problem of different viewpoints 547

Giulia Piredda

The whys and hows of extended mind 559

Carmela Morabito

Movement in the philosophy of mind: traces of the motor modelof mind in the history of science 571

Jean-Luc Petit

The brain, the person and the world 585

PART VI GENERAL PHILOSOPHY OF SCIENCE 601

Gustavo Cevolani, Vincenzo Crupi, Roberto Festa

The whole truth about Linda: probability, verisimilitude, and aparadox of conjunction 603

Antonino Freno

Probabilistic Graphical Models and logic of scientific discovery 617

Massimiliano Carrara, Davide FassioPerfected science and the knowability paradox 629

Luca Tambolo

Two problems for normative naturalism 637

Silvano Zipoli Caiani

Explaining the scientific success. A critique of an abductivedefence of scientific realism 649

Mario Alai

Van Fraassen, observability and belief 663

Marco Giunti

Reduction in dynamical systems: a representational view 677

Alexander Afriat

Duhem, Quine and the other dogma 695

Edoardo Datteri

Bionic simulation of biological systems: a methodologicalanalysis 711

Luca Guzzardi

Some remarks on a heuristic point of view about the role of experiment in the physical sciences 725



Some remarks on a heuristic point of view about the role of experiment in thephysical sciences

Luca Guzzardi

1 IntroductionOne major contribution of the 20th century epistemology is the focus on anon-naıve concept of experiment. We have learnt experiment does not provideeither a “verification” or an immediate “falsification” of a theory; physicalobservations are theory-laden and the experimental praxis follows the theoryand is at the expenses of a silent, long and slow theoretical work. Otherwisethe experimental praxis wouldn’t simply exist, and the work of experimentersis by far and in the first place a theoretical one. We can trace this attitude backto Pierre Duhem’s Theorie physique (1906) and Karl R. Popper’s Logik der

Forschung (1934; Logic of Scientific Discovery , 1959). Associated with thispoint of view, which seems in itself very difficult to question, one can often findthe unexpressed assumption that experiments are control means of theory, so

they have no other purpose than to test and control the correctness of a systemof empirical statements. According to this, any other role experimentationcould play has so little importance in the eyes of epistemologists that it isat best a collection of interesting peculiarities (and a waste of time in theworst case). This point of view is appropriately summarized in the incipit of Popper’s Logic of Scientific Discovery :

A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the field of the empirical sciences, moreparticularly, he constructs hypotheses, or systems of theories, and tests them againstexperience by observation and experiment [15, p. 3], [16, p. 27]. 1

In this paper I will try to show how this view, that emphasizes the prominenceand prevalence of theory against experiment, leads to overlook a major use

of experiments, provided with strong historical evidence and supported byepistemological arguments. In the picture I will try to give, experiments donot play the main role of “empirical control” of theory, though they can beused with that function. But I shall argue that their main role is a differentone.

1Note that the words “whether theorist or experimenter” were added in the Englishedition 1958–1959 (and were not reported in the German edition 1966), as if Popper felta need of specification or emphasis: the “experimenter” must do the same work, followthe same procedure and — more importantly — apply the same methods as the “theorist”colleague



726 Luca Guzzardi

A cautionary argument is to be made in advance: I do not claim my sug-gestions will apply to any field of empirical sciences, though I think this wouldbecame arguable, provided that appropriate changes in my picture are intro-duced. However, I don’t try here to embark on this enterprise. This is also thereason why historical examples in this paper are only taken from the historyof physics and my suggestions are restricted to the physical sciences.

2 Proof: a legal concept and its epistemological

pendant

In which sense does an experiment become an experimental test ? How didthis idea that a certain experience is actually a proof against or in favour of a certain belief, conviction or system of hypotheses acquired relevance till to

the point it has become obvious? An answer to this could be find in a brief account of the history of the concept of proof .

The term “proof” traces most probably back to legal jargon. Generallyspeaking, to describe something as a proof means to establish a criterion fordeciding about something: proof is what provides the basis of our decisionand justify it. So, for instance, the verdict of “not proven”, typical of theScots Law, means an acquittal for insufficient proof, because evidence is soinadequate and defective that a judge would have no reason to convict a de-fendant. This legal background, which transpires from the humean (and thankantian) image of a “court of justice” for the reason,2 involves sometimes purescientific work as well: this is the case of William Thomson’s (Lord Kelvin)assessment of a particular and very sofisticated theory of aether he himself contributed to developed some years before: “I am thus driven to admit, inconclusion, that the most favourable verdict I can ask for the propagation of laminar waves through a turbulently moving inviscid liquid [i.e. the ether]is the Scottish verdict of not proven ”[19, p. 352]. According to Kelvin, theproblem with this theory was not the refined mathematics developed by himand others, but merely the experience, which didn’t suffice to support thetheory.

The legal imprint of the term proof still sticks on this concept even if wemove away from legal jargon.3 In an arithmetical textbook dated around 1430

2See [11, p. 3], [12, A11, eng. tr. p. 101]. Not to mention what Kant argues aboutthe legal sense of the concept of (transcendental) deduction in §13 of the Critique of PureReason. A goo d understanding of the concept of proof, its development and backgroundalso in legal terms is provided by [6] (see more in particular about Kant and Hume [6, pp.

15–23 it. tr.]; about proof and the legal tradition [6, pp. 35–43 it. tr.]).3Very interestingly the concept of proof seems originally have been affected by religioustradition too. One of the first occurrences of the term “proof” (intertwined with its “legal”meaning) you can find in English is contained in a Middle-age text known as Ancren Riwle or Ancrene Wisse , a Regula for Anchoresses written around 1200 by an anonymous Englishchurchman for the instruction of a small community of three women about to becomereligious recluses. In this book we can find one of the first occurrences of the word inEnglish. What in the eyes of the anonymous author justifies rules (therefore providingproofs) are mostly stories from the Bible. So in a couple of passage the speaker who givesthe rule to the three young ladies argues: “That this is true [...] here is the proof [preoue ]”[1, pp. 52, 53] and further: “Because I said that we find this both in the Old Testamentand also in the New, I will, out of both, show an example and proof” [1, pp. 154, 155]. Theterm “proof” is used here in the sense of what makes good — that is proves — a statement:



Role of experiment in the physical sciences 727

and called The art of nombryng (a translation of a Latin textbook De arte numerandi , written in the 13th century and attributed to John of Holywood),proof [prouffe ] takes explicitely the meaning of a test or a trial to check thecorrectness of an arithmetical calculation: “The subtraccioun is none otherbut a prouffe of the addicioun, and the contrarye in like wise”[2, p. 6]. Infact, this sentence, despite the triviality by which it is only seemingly affected,brings to bear what I called the legal origin of the concept of proof. Inverseoperations in Mathematics are treated as proofs because they allow to decide— to judge — about the correctness of calculi, providing a justification of them. Nevertheless, by this way the arithmetical proof achieves somehow anew feature, namely the feature of a trial — a term involving an obviouslegal background. Like in a lawsuit, the fact to have overcome a trial (thesubtraction proof for the addiction, for example) puts de iure the calculationinto the realm of what is legitimate, so to speak, beyond reasonable doubt.

As in Hume’s and Kant’s metaphor of the court of justice for human reason,on this theoretical level “proof” can indicate both the individual evidencesused to convince the mind and the entire process of convincing someone — aprocess sometimes called demonstration , that is the ability to deducing some-thing from certain, definite assumptions produced before the attentive andwatchful eye of understanding. The relationship between proof and demon-stration was developed by John Locke (in Book IV of his Essay Concerning

Human Understanding , 1690). He put emphasis on the first one, with animportant reference to the process of vision:

Those intervening Ideas, which serve to shew the Agreement of any two others, arecalled Proofs; and where the Agreement or Disagreement is by this means plainly and

clearly perceived, it is called Demonstration , it being shewn to the Understanding,and the Mind made see that it is so [13, Book IV/ii, 3, p. 532].

A proof builds up a demonstration in so far as it brings to evidence what, asbeeing seen , takes its own place within positive and true knowledge. Some-thing that has achieved this status of a demonstrated and established truthcan never be moved away from that place by any kind of contrary judgement.Indeed, the understanding see it and “the Mind made see that it is so”.

But Locke points out all this has no relation with experience, both crudeor controlled in the form of experiment. According to him, the way of findingthruths by proofs and demonstrations applies only to ideas and even what hecalls “the Art of finding Proofs” is one major breakthrough of an argumenta-tion style which “is to be learned in the Schools of Mathematicians, who from

very plain and easy beginnings, by gentle degrees, and a continued Chain of Reasonings, proceed to the discovery and demonstration of Truths” [13, BookIV/xii, 7, p. 643]. On the contrary, experiments would absolutely be notable to yield established knowledge. Though they have a different and veryimportant role:

A Man accustomed to rational and regular Experiments shall be able to see fartherinto the Nature of Bodies, and guess righter at their yet unknown Properties, thenone, that is a stranger to them: But Yet, as I have said, this is but Judgement andOpinion, not Knowledge and Certainty [13, Book IV/xii, §10, p. 645; italics mine].

an evidence that is sufficient or contributes to establish anything; for instance, a rule forliving.



728 Luca Guzzardi

3 A patient experimental cultureLocke remarkably reduced the significance of experiment in the sense of aproof: because of the weakness of achieving knowledge by means of experience,every “test” we undertake even to falsify (not to say to verify) our theoriesis not but “judgement and opinion”. Above all, what is important in Locke’sidea about experimenting nature is not that experiments are means to proveor test our knowledge, but that they are a substantial part of a heuristics, sothey can lead and ultimately help grow our knowledge. Of course, we needto examine step by step any individual case of a phenomenon to be sure that“our principle will carry us quite through, and not be as inconsistent withone Phoenomenon of Nature”[13, Book IV/xii, §13, p. 648]. However, thisis nothing but a side effect of a preliminary “be accustomed to rational and

regular Experiments”, that lead our opinion and compel us to some guesses.Therefore, experimentation is the source of the whole process of guessing. Thisaspect reaches far beyond Locke’s empiricist perspective because it doesn’tinvolve merely the logic of scientific discovery; it rather deals with both thepraxis and the practice of science: such a specific praxis as we can by andlarge outline it.

As well known, Locke had close relationship with the environment of theRoyal Society.4 According to its Statute “frequent” meetings of the fellows —if possible once a week — should be hold. “The business of their weekly Meet-ings shall be, to order, take account, consider, and discourse of PhilosophicalExperiments, and Observation” [18, p. 145]5 — where the expression “philo-sophical experiments” means nothing but experiments in natural philosophy,i.e. scientific experiments as we are used to call them.

Remarkably, to make experiments — an activity that Bishop Thomas Sprat(who was himself a fellow and one of the first historians of the Royal Society)regarded as the substantial part of the meetings — was not the business of any Fellow. The Constitution of the Society stated that a person shouldbe selected for this purpose and his exclusive duty had to be providing forexperiments. The name of such “employee” was the Curator of experiments .While the Fellows came from the most different occupations and cultivatednatural philosophy as their personal interest and passion, however seriousthese might be, curators were professional experimenters and they got bythe Society — i.e. by the Fellows themselves — a salary for their work (theStatute established a maximum of two hundred pounds per year, but the firstcurator, Robert Hooke, got only thirty pounds in addition to an apartment

in the buildings of the Royal Society).4Locke was elected a fellow of the Royal Society in November 1668 (six years later its

foundation). It is known he was quickly appointed to a committee for experiments andtwice served on the council, but apparently he has little contributed to the work of theSociety. Nevertheless, he dedicated the Essay, first published in 1690, to his friend ThomasHerbert, then President of the Society; throughout his life, either in England or in exile,Locke followed with interest the Society’s activities. About the relations between Lockeand the Royal Society with regard to the purposes of present paper see [3, vol. 1, pp.245–249], [17, pp. 73–74], [21, pp. 52–58], [23, pp. 36–38], and [22, pp. 17–23]. AboutLocke’s “experimental Knowledge” see [4, 204–209].

5Sprat’s quoted text follows the edition London 1667.




The office of a curator must have been a delicate one, as the complicatedappointment procedure points to: to begin with, unless an eminent personwas known to the Fellows for his competence and worth, usually curators hadto be examined very carefully by the Society before “election”. They werefirst recruited for a trial period, which normally didn’t take a full year, at theend of which “they shall be either elected for perpetuity, or for a longer timeof probation, or wholly rejected” [18, p.147]. Specifically, their business wasto

take care of the managing of all Experiments, and Observations appointed by theSociety, or Council, and report the same, and perform such other tasks, as the Society,or Council shall appoint: such as the examining of Sciences, Arts, and Inventions nowin use, and the bringing in Histories of Natural and Artificial things, & c.[18, p.147].

The Statute provided also a brief sketch of a typical curator: his backgroundand competence had to be appropriate to the office, he had to be “skilledin Philosophical, and Mathematical Learning, well versed in Observations,Inquiries, and Experiment of Nature and Art” [18, p.147]. In other words,curators were essentially technicians, who had of course to know the elementsof natural philosophy and mathematics and, so to speak, feeling at home inapplying them. However, this knowledge was first of all intended for their job,i.e. managing experiments before an audience consisting of the Fellows of theRoyal Society.

According to Locke, the most valuable gift of a good philosopher trainedat the School of Mathematicians, who proceed by proofs and demonstrations(and maybe refutations) of their own ideas is perhaps “sagacity”, that is

the ability to find out quickly and without delay a basis for the argumentshe want to use, providing them with an indubitable certainty. The mostimportant quality of a curator of experiments must have been, instead, theinfinite patience he needed to vary every time his experiments and carefullyexamine a profusion of individual cases. After all, any experimenter knowsthat everything is nothing but an individual, unique case... “Natur ist nur

einmal da ”, as Ernst Mach put it in The Science of Mechanics : nature is butonce there.

But after all varying experimental conditions of a phenomenon means toshow, ad excludendum , what does not change in variation and how thingsgenerally are, so that one can illustrate through experiments the typical be-haviour of things. Therefore, curators were required to have a great deal of imagination, both for observing nature in so many aspects as possible and for

illustrative, teaching purposes. The aim of experiments in public demonstra-tions (at the Royal Society, for example) was not only to show nature, butalso to illustrate theories in so many ways as possible.

Like in Locke’s account, for learning science is needed to see and discussexperiments mainly through the ability of a good experimenter. Rememberthat according to Locke experiments had a very important role in teaching:people “accustomed to rational and regular Experiments shall be able to seefarther into the Nature of Bodies, and guess”, and so on. Experiments actedsomehow as a propaedeutics to research, for young and less young naturalphilosophers (like the Fellow of the Royal Society) could learn the “art” of



730 Luca Guzzardi

“seeing farther into the Nature of Bodies” and make guesses about their prop-erties. But no illusions about that: in Locke’s eyes experiments provide veryrestricted control, in most cases they say nor “yes” neither “no” and there isno assurance of an unquestionable verdict from them.

So experiments would play their major role in giving so to speak a sensibleillustration of theories and training scientists about them. Often during 17thand 18th century experimenters were called demonstrators in scientific fields,meaning with that laboratory professionals who gave “public demonstrations”of an experiment for teaching purposes before a more or less large audience.Their aim was not the same of the theorists (or something like that the the-orists could expect by experimenters), i.e. to test a set of hypotheses. Theyrather aimed to provide what I called “a sensible illustration” of a theory, sothat people could learn and discuss that theory. In order to perform this, theexperimenter-demonstrator, an institutional version of which is embodied bythe curator of experiments at the Royal Society, did not have to take criticalattitude against theories he was “demonstrating”. He had to be a loyal sup-porter and a strenuous defender of these; he had to be convinced of these inorder to convince his audience. In this regard, by no means an experimentaldemonstration, either in Popper’s or in Locke’s sense, would provide a proof for or against a theory. But a demonstration illustrates a theory6 and in themeantime it can also give an apology , so the experimenter properly plays therole of an apologist .

One may think, I actually am trying here to make an apology of somethingnamely of the inductive method, that is inferring theories from experiments.But to state an apology through experiments in the sense I have just described

does not involve an application of inductivism. Experimenters as I have de-scribed them — scientists of a well recognizable kind in the history of science— don’t bother stating a (new) general theory starting from empirical data.Scientists as Robert Hooke, Francis Hauksbee or Jean-Theophile Desaguliers— all of them Curators of experiments at the Royal Society — and manyothers, when they act as apologists (and uniquely in this case), only take careof defending theory against possible assaults by enemies and “infidels” andpreventing potential “heretics” from proselytizing.7

To state an apology is also very different from performing an experimentaltest of a theory: in last case, even if we are expecting a positive result infavour of a certain theory, in principle an error could occur — that is thefallibilistic point of view. But apology does imply that there is no doubt that

theory is fundamentally correct (though some details could vary).

8

There-fore, there is no need of any control at all. And this applies in principle : thepossibility something might be wrong in the very fundament of the theory atissue is not even taken into account. Apology implies two actions are basi-

6This sense of scientific demonstration was probably relevant for Kant himself. On thisissue see [14, pp. 95–97].

7Sometimes they are “driven” in doing this job by theorists or eminent scientists, as ithappened in the case of Newton and “his” curator Francis Hauksbee. See [10, pp. 229–234].

8I don’t need to point out that often experiments can be designed in order to extend agiven theory. As well known, this feature has been emphasized by Bas van Fraassen, whosepoint of view I discuss in the third section of present paper.




cally needed: defending and convincing . A theory will not be confirmed nor“corroborated” in Popper’s sense, which implies a reference to a (fallibilistic)degree of confidence that doesn’t occur here. A theory will rather be literally“confirmata ” in Latin meaning of the word: experiments confirm a theory inthe sense that they make it firmer, more solid against possible assaults thanit would be without them.

No matter of “corroboration degree”; no matter of psychology or convic-tions. This is something objective. As historians of science have recognizedsince some decades, the rapid success of Newtonianism and his general ac-ceptance as the standard view during 18th century throughout the Continentwas also due to an efficient apologetics. Amongst its ma jor advocates are tobe mentioned Dutch authors as Willem Jacob ’sGravesande and Pieter vanMusschenbroek. Following Hauksbee’s and Desaguliers’ experimental tradi-tion, ’sGravesande wrote in 1721 a physics textbook addressed to studentsthat very quickly became (with its third edition, 1724) one of the mostimportant and influent treatises of his age. Its Latin title remarkably wasPhysices Elementa Mathematica, experimentis confirmata sive Introductio ad

philosophiam Newtonianam — i.e. The Mathematical Elements of Physics

Confirmed by Experiments . What is really impressive about this book is theprofusion of experiments compared with the small number of pages devotedto mathematical scholii. It’s also not surprisingly that the first English trans-lation of this textbook (1725) was made by a curator of the Royal Society,namely Jean-Theophile Desaguliers.9

4 Two cultures of experiment and a heuristic point of

view on its roleI have contrasted the usual concept of experiment as a control, which I de-scribed using analogies from a legal background (but note how many andpowerful analogies with originally legal concepts Popper uses in Chapter 5 of The Logic of Scientific Discovery , namely “The Problem of the Empirical Ba-sis”),10 with a broader concept, where experiments have at least a threefoldrole: first, they are illustrations of a theory and by this way can provide a gooddeal of examples for (in second place) teaching and (in third place) defending

the theory itself. These different nuances about the role of experiment are of course related and interacting issues. They share at least one thing: up tothis point experiments tightly remain in the hands of theorists, who need toillustrate and defend their creatures and perhaps to find and teach followers.

And of course the theorist (not the experimentalist, pace Popper) feels the9For further details see [8]. More in particular about ’sGravesande’s and J.-T. Desag-

uliers’ role in defending and “confirming” Newtonianism, see [7, pp. 96–97].10So for example: “The verdict of the jury (vere dictum = spoken truly), like that of the

experimenter, is an answer to a question of fact (quid facti ?) wich must be put to the juryin the sharpest, the most definite form”. Than, Popper makes clear that “what questionis asked, and how it is put, will depend very largely on the legal situation, i.e. on theprevailing system of criminal law (corresponding to a system of theories)”. And again: “Incontrast to the verdict of the jury, the judgement of the judge is ‘reasoned’; it needs, andcontains, a justification. The judge tries to justify it by, or deduce it logically from, otherstetements: the statements of the legal system, combined with the verdict that plays therole of initial conditions” [16, pp. 109–110].



732 Luca Guzzardi

need to test his theory and exploits the ability of skilled experimenters forthis purpose.

In addition to this, following Locke I have argued that experiments canprovide what we could properly call a heuristics. Though this last featuremight be related with the three nuances I have mentioned above, I want tosuggest that providing a heuristics means something very different. I will tryto explain what the difference is.

At the origin of modern physics there might be a distinction both influentand elusive between two different kinds of experimental culture, which alsoshaped different research styles and different ways to consider science and sci-entific methods. One culture thinks of experimentation as if it would only bedepending on theories and points out that it provides a control for theories.Following a suggestion by Ian Hacking, I shall call this the theoretical approach

to the experiment .11 Supporters of this culture mostly ignore other features of experimentation, which on the contrary are as crucial as the only one aspectthey emphasize, though maybe less elevated (such as the illustrative-teaching-defending role of experiment). Therefore, they can regard an experiment asa proof in favour of or against a theory. Maybe this first approach to exper-iments, with the concept of proof as its legal pendant, arose in courtrooms,thanks to the job of brilliant orators, lawyers and judges; then it settled fromthe dusty reading stands of the universities on the aseptic writing desks of natural philosophers and finally reached the chairs of the fellows of titledinstitutions like The Royal Society.

Roughly in the meantime another culture of experiments, which I shall callthe experimental tradition , was growing both in craftsman laboratories and

in the first machine shops, amid dusty workbenches, scraps of unsuccessfulexperiments and instruments without any apparent utility, unawarely devel-oped by scarcely educated people who have no fear to dirty their own hands.Of course we can find this tradition in the same rooms of the Royal Society;but their representatives did not sit in that educated and mixed audience.The experimental tradition rather passed through the skilled hands of cleverprofessionals like the Curators of experiments: people with technical-practicalbackground who had to perform experiments before that audience. For themexperiment was synonymous with uncertainty and doubt, because we onlyfaced with individual cases, and no proofs can be made from experiments.But in their hands experiments, if treated with care, could provide a usefulheuristics, so that the experimenters could make (and let make to their au-

dience) some guesses about the nature of bodies, to put it again in Locke’sterms. An attentive intervention by a skilled and patient experimenter couldand did open new ways to research, driving his guesses and those of his audi-ence.

To do this one needs a very peculiar kind of knowledge. I argue that thedesign and implementation of an experiment requires more craftsmanship thanpure, theoretical and objective knowledge: it involves an actual manipulation

11Hacking refers to “experimental and rational faculties” complaining “Popper andLakatos”, amongst others, because they “emphasize only the rational faculty” (that isthe style I term here “the theoretical approach to the experiment”) [9, pp. 260–261].




of the world, based not only on knowing something, but most of all on knowinghow things are to be made and, last but not least, on personal experience.In other words experiments are a pragmatic matter, indeed matter of praxis

and practice . In The Aim and Structure of Physical Theory Pierre Duhemgave a colourful and vivid idea of this sort of “knowledge”, when he claimedwhat a researcher has to know to enter a laboratory. Duhem’s suggestion is,maybe consistently with the author’s will, often read as an example of theory-ladeness of observation or experiment. But the theory of which experimentswould be “laden” with is of this very peculiar kind: it is, so to speak, atheory-intended-for-the-experiment . The theoretical work of an experimenter,if there is something like that, does not simply deal with abstract notions.This kind of knowledge is meaningful only in the context of an actual makingexperiments. It is a practical, applied knowledge of how instruments are tobe used, how devices are to be manufactured, how they as experimenters haveto dirty their own hands.

This pragmatic knowledge — this knowledge of a theory-intended-for-the-experiment — plays an extremely important role in the actual implementationof experiments. I have emphasized that one of the most important qualitiesof an experimenter is patience in varying experimental conditions to showwhat does not change and what is to be considered the typical behaviourof things, that is the way things generally are. That was for exemple thecase of Francis Hauksbee, the curator of experiments of the Royal Societywhose appointment in 1703 was heavily supported by Newton himself as thePresident of the Society: his ability in varying experimental conditions becamelegendary. In particular, it was this ability that led him to his remarkable

results in examining some subtle electrical phenomena as the luminosity of phosphorus in a Torricelli vacuum.12

From this point of view making experiments is very different from simplytesting (controlling) a theory, although experiments can be used for such apurpose. And yet, this doesn’t suffice to claim for a heuristic role of experi-ments. According to a well-known witty remark a la Clausewitz, dued to Basvan Fraassen, experimentation is nothing but continuation of “theory con-struction” by other means. However, van Fraassen is not willing to admitthat “experiments are [...] designed to test theories, to see if they shouldbe admitted to the office of truth-bearers” [20, p. 73].13 Experiments, hepoints out, rather aims to “fill in the blanks in a developing theory”, so awhole “theory construction” can make advance. In fact, as Ian Hacking has

observed, this filling in the blanks becomes the major issue of experimen-tation in van Fraassen’s account of the “scientific image”: indeed, “fillingin the blanks [means] guiding the continuation of the construction, or thecompletion, of the thoery”. On the other hand, the theories formulate thequestions worth being answered and embody “a guiding factor in the designof the experiments to answer those questions” [20, p. 74].14 Experiments arealways theory-dependent and theories come first. By no means an experi-

12About Hauksbee’s experiments see the quoted work by [10, p. 230].13About his famous Clausewitz-styled statement see [20, p. 77].14For a criticism see also [9, pp. 238–240].



734 Luca Guzzardi

menter could suggest to a theorist a new insight through his own work: invan Fraassen’s account, even if experiments are not only tests “for empiricaladequacy of the theory as developed so far”, nevertheless they cannot be any-thing but useful “blank-fillers” for a theory could make progress. Accordingto van Fraassen, this “being-for-a-theory” of any experiment (as opposed tothe “theory-intended-for-the-experiment” outlined above) should entirely ful-fil and exhaust the role of the experiment. Though experiments could help toconstruct or complete a theory, it’s up to the theory to provide a heuristics.

However, this seems not to be consistent with historical evidences. Notonly the case studies van Fraassen refers to are prone to a quite differentinterpretation, as shown by Hacking. In addition, his view can neither explainthe relevance of professional experimenters as the Curators and the functionthe Statute of the Royal Society stated for them, nor account for the threefoldrole of experiment (illustrating-teaching-defending theories) I discussed above.Finally, van Fraassen’s perspective doesn’t take into adequate account thatsometimes experimentation can be the guiding factor which come first in thedesign of a specific theory.

The double-slit experiment provides a good exemple of that. In XIX cen-tury this was supposed to be (in fact, it was) a crucial experiment betweencorpuscular and wave theory of light; but in XX century the double-slit ex-periment became a major issue for quantum mechanics; and here his roleas a test is evanescent against his role as a heuristic tool. Look at the useRichard Feynman makes of it in his presentation of quantum mechanics: it isa heuristic one — a heuristics which indicates the most important features of quantum theory.

Note that it doesn’t matter here if this experiment is actually a Gedanken-experiment , but only the role it plays. As Feynman states: “We are doinga “thought experiment”, which we have chosen because it is easy to thinkabout. We know the results that have been done, in which the scale and theproperties have been chosen to show the effcts we shall describe” [5, vol. 3,pp. 1–6]. Just in the same way a skilled experimenter as Francis Hauksbeechose, so to speak, “the scale and the properties” of phenomena “to show theeffcts” he aimed to describe: in other words he chose a heuristics. This isnot filling in the blanks of a guiding theory behind the experiment; this issimply a good example of a “theory-intended-for-the-experiment” (or of an“experimental faculty”, to put it in Hacking’s terms).

According to Feynman, the double-slit experiment “has in it the heart of

quantum mechanics. In reality, it contains the only mystery. We cannotmake the mystery go away by “explaining” how it works. We will just tell

you how it works. In telling you how it works we will have told you aboutthe basic peculiarities of all quantum mechanics”[5, vol. 3, pp. 1–13]. So theexperiment is a little bit more than a blank-filler in the theory constuction of quantum mechanics: in reality, it embraces the whole theory. Feynman evenrefuses any theoretical explanation behind the phenomenon: “One might stilllike to ask: “How does it work? What is the machinery behind the law?” Noone has found any machinery behind the law. No one can “explain” any morethan we have just “explained”. No one will give you any deeper representation




of the situation. We have no ideas about a more basic mechanism from whichthese results can be deduced” [5, vol. 3, pp. 1–13]. Explanation here simplyratifies in the unchangeable statement of the law that typical , paradigmaticbehaviour of things the experiment has found, shown and demonstrated. Toput it in Locke’s terms, the double-slit experiment helps “guess righter at [...]yet unknown properties” of nature and Feynman still uses it to shape his pathintegrals formulation of quantum mechanics.

So, shall we maybe reverse van Fraassen’s claim? Is really experimentationthe continuation of theory construction by other means? Or shouldn’t weadmit, without burding this with any inductivist nuance, that theory is often

the prosecution of experiments with other means (and experiments sometimesprovide a first glimpse of a theory)? Maybe Popper is right to argue, quotingNovalis, one has to cast nets to catch fish — and hypotheses are our nets.We need audacious, open-minded hypotheses, “marvellously imaginative andbold conjectures”, to put it in Popper’s terms. I would like to suggest that oneway to make such “marvellously imaginative and bold conjectures” is indeedto make experiments .

BIBLIOGRAPHY[1] The Ancren Riwle. A Treatise on the Rules and Duties of Monastic Life . Edited and

translated from a semi-saxon manuscript of the 13th century by J. Morton, printed forthe Camden Society, London 1853.

[2] The art of Nombryng . A translation of John Holywood’s De arte numerandi. In The Earliest Arithmetics in English . Published for the Early English Text Society (ExtraSerie, n. 118), Oxford University Press, Oxford 1922.

[3] H.R.F. Bourne. The Life of John Locke . Scientia Verlag, Aalen 1969 (Reprint of theEdition London 1876).

[4] J. Colman. Lockes Theorie der empirischen Erkenntnis. In John Locke, Essay ¨ uber den menschlichen Verstand . Herausgegeben von U. Thiel, pages 197–221. Akademie Verlag,Berlin 1997.

[5] The Feynman Lectures on Physics. Addison-Wesley, Reading 1964.[6] F. Gil. Provas. INCM, Lisboa 1986. It. tr. Prove. Attraverso la nozione di pro-

va/dimostrazione . Jaca Book, Milano 1990.[7] G. Gori. La fondazione dell’esperienza in ’sGravesande . La Nuova Italia, Firenze 1972.[8] W.J. ’sGravesande. Physices Elementa Mathematica, experimentis confirmata sive In-

troductio ad philosophiam Newtonianam . Leidae 1720–1721.[9] I. Hacking. Representing and Intervening. Introductory Topics in the Philosophy of

Natural Science . Cambridge University Press, Cambridge 1983.[10] J.L. Heilbron. Electricity in the 17th and 18th Centuries. A Study of Early Modern

Physics. University of California Press, Berkeley 1979.[11] D. Hume. A Treatise of Human Nature . Edited by D. Fate Norton and M.J. Norton.

Oxford University Press, Oxford/New York 2000.[12] I. Kant. Kritik der reinen Vernunft [1st edition]. In Kant’s Gesammelte Schriften , her-

ausgegeben von der Koniglich Preussischen Akademie der Wissenschaften, erste Abt.,Bd. IV. Reimer, Berlin 1911. Eng. tr. Critique of Pure Reason [The Cambridge Editionof the Works of Immanuel Kant]. Cambridge University Press, Cambridge 1998.

[13] J. Locke. An Essay Concerning Human Understanding . Edited with an introduction,critical apparatus and glossary by P.H. Nidditch. Clarendon Press, Oxford 1975.

[14] F. Moiso. Morfologia e filosofia. In Annuario Filosofico. Mursia, Milano 1992.[15] K.R. Popper. Die Logik der Forschung . J.C.B. Mohr (Paul Siebeck), Tubingen 1934,

1966.[16] K.R. Popper. The Logic of Scientific Discovery . Hutchinson & Co., London et a. 1959,

1968.[17] M. Purver. The Royal Society: Concept and Creation . Routledge and Kegan Paul, Lon-

don 1967.



736 Luca Guzzardi

[18] T. Sprat, The History of Royal Society of London For the Improving of Natural Knowl-dege , edited with critical apparatus by J.I. Cope and H.W. Jones, Routledge and KeganPaul, London 1959.

[19] W. Thomson. On the propagation of laminar motion through a turbulently movinginviscid liquid. In The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , 24, 1887.

[20] B. van Fraassen. The Scientific Image . Clarendon Press, Oxford 1980.[21] J.W. Yolton. Locke and the Compass of Human Understanding. A Selective Commen-

tary on the “Essay”. Cambridge University Press, Cambridge 1970.[22] P. Walmsley. Locke’s Essay and the Rethoric of Science . Bucknell University Press,

Lewisburg and Associated University Presses, London 2003.[23] R.S. Woolhouse. Locke . The Harvester Press, Brighton 1983.

some remarks on a heuristic point of view about the role of experiment in the physical sciences

Documents