Table Of ContentHistory of Mechanism and Machine Science 39
Danilo Capecchi
Epistemology
and Natural
Philosophy in the
18th Century
The Roots of Modern Physics
History of Mechanism and Machine Science
Volume 39
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Danilo Capecchi
Epistemology and Natural
Philosophy in the 18th
Century
The Roots of Modern Physics
123
DaniloCapecchi
IngegneriaStrutturale eGeotecnica
Sapienza Universitàdi Roma
Roma, Italy
ISSN 1875-3442 ISSN 1875-3426 (electronic)
History of Mechanism andMachineScience
ISBN978-3-030-52851-5 ISBN978-3-030-52852-2 (eBook)
https://doi.org/10.1007/978-3-030-52852-2
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To my wife
Preface
At the beginning of the modern era, what is now called science was spread out
among various disciplines: theology, handcrafts, magic, alchemy, astrology, med-
icine, natural philosophy, and mixed mathematics (that is optics, astronomy,
mechanics,music,etc).Inthe18thcentury,thesedisciplineshadalreadybrokenup
and became recomposed into an organization of science of the natural world that
was similar to the modern one. The most important transformation was that
affectingnaturalphilosophy,whichwasconsidered,atleastintheacademicworld,
themostnobleandbyfarthemostimportantformofknowledge.Itceasedtobea
philosophy in the canonical sense, merging with other forms of knowledge and
givingraisetodisciplinessuchasphysics,naturalhistory,chemistry,medicine,and
engineering, names which, while not initially fully shared, were established in the
19th century and are still used today. The new philosophers of nature were no
longer canonical philosophers, although they continued to think about philosophy.
They were rather mathematicians in the broad sense, namely, scholars who were
interestedinmorethanjustpuremathematics.Insomecases,thisisparticularlytrue
for the new branches of physics such as electricity and magnetism, and they were
also simply educated gentlemen, gifted with intelligence and curiosity.
Thepresentbookaimstodocumentthisprocessoftransformation,concentrating
onthe18thcentury,acenturythatinthepasthadbeenconsidereduninterestingfor
the history of science. It would represent the transition from the age of genius and
the birth of modern science, in the 17th century, to the age of prodigious devel-
opment,inthe19thcentury.Thisviewdoesnotstanduptothoroughanalysis.The
18th century, the century of Enlightenment and reason, as will be clear from the
present book, was rather a century of great ferment and novelty.
Tomake thenarrativepracticable forasingleindividual,nogreat emphasishas
beenplaced ontheprecisegenesisofthevariousconceptsand methods developed
inscientificenterprises,exceptwhenthiswasnecessarytomakethemclear.Ihave
beencontenttotakesnapshotsofsituationsbytakingalookatdiscreteintervalsof
time. In several situations, reference ismade to the authors who are famous today,
such asNewton,the Bernoullis, Euler, d’Alembert, Lagrange, Lambert, Volta, etc.
Not so much because they were the most creative and original minds, but mainly
vii
viii Preface
because their writings represent a synthesis of contemporary and previous studies.
The above names should, therefore, be considered more labels of a period than
references to real historical characters. The history of science was not made up of
isolatedheroes,butbyanentirecommunityanditslegacy,byteachers,anonymous
collaborators of celebrities, playing this role often only as a result of their social
status. It is true that in the 18th century scientific research was carried out by a
handfulofscholars;thoughsmall,itwasstillanarmy,however,whosegeneralsare
onlyrepresentativeofthevictoriescarriedoutbythesoldiers.Referringonlytothe
great characters of science has in any case an advantage that there is no need
entering the merits of their acquisitions because well documented by historians,
thus leaving room for other aspects.
This book intends to answer these three fundamental questions:
1. Wasthetransformationofancientnaturalphilosophyinto(modern)sciencedue
to an internal evolution or an external appropriation?
2. What was the role of mechanical and experimental philosophies in this
transformation?
3. What was the role of the newly born infinitesimal mathematics (Calculus)?
The answers come as follows:
1. It was a conquest from the outside by mathematicians (broader sense). They
were able to extend the approach of mixed mathematics to the study of most
phenomena.
2. Mechanical philosophy was crucial. It aroused interest in natural philosophy in
many not canonical philosophers—including mathematicians—because its
argumentationsweremuch simplerthanthose offered bycanonicalphilosophy,
imbued with metaphysics. A similar argument holds good for experimental
philosophy.
3. The role of Calculus was twofold. On the one hand, its great fecundity made it
possibletosolveverycomplexproblems,thusgivingmathematicsmoreappeal
intheapproachofphilosophyofnature.Asregardstoapplications,ontheother
hand,theneedtorefertoregularfunctionsdefinedoncontinuameantthatnature
was seen through glasses with thick lenses, which influenced its interpretation.
Beforegoingfurther,anomenclatureshouldbeestablishedbecausemanyofthe
termsinuseinthepastandstillinusetodayhavechangedtheirmeaning,andthusa
stipulation is necessary:
(cid:129) Canonical natural philosophy. Study of nature under the concepts of matter,
cosmos, and causation. Examples of canonical natural philosophies are the
Aristotelean,thePlatonic,themechanicistic;butnotNewton’sandtheapproach
to nature after him, even though the term natural philosophy is retained also in
such cases.
(cid:129) Mixed mathematics. Mathematics related to physical problems—that somehow
joinsqualitytoquantity—astheywereestablishedintheearlymodernera,such
as astronomy (physical or positional), surveying, fortification, ballistic,
Preface ix
mechanics, hydrodynamics, pneumatics, and so on. A category quite distinct
from that of subalternate sciences of Aristotelian mould that sometimes are
considered as the canon of mixed mathematics.
(cid:129) Canonical philosophers (or simply philosophers). Scholars that besides natural
philosophy considered also and in a systematic way metaphysics and either
logic, or ethic, or theology.
(cid:129) Mathematical practitioners (or mathematicians broad meaning or more simply
mathematicians). People with a more or less important training in theoretical
mathematicswhowerealsoinvolvedinpracticalactivities(notethattheideaof
pure mathematicians is quite modern; until at least the end of the 18th century
more or less all mathematicians were involved in practical activity or at least
wroteaboutpracticaluseofmathematics).ThetermMathematicalpractitioners
was introduces as a historical category in 1954 by the English geographer and
historianofscienceEvaGermaineRimingtonTaylor(1879–1966),butitisused
here quite freely.
Of course one can envision a spectrum between canonical philosophers and
mathematical practitioners. The columns of the following table show the possible
main combinations, ranging from canonical philosophers with a very limited
interest in mathematics (first column) to skilled artisans who knew little of phi-
losophy and mathematics (last columns). H means high involvement and L means
low or medium involvement.
Philosophy H H L L
Mathematics L H H L
16thCentury.ThebirthofGreekrationalityrepresentedafundamentalstepfor
the change in the form of the western knowledge of the natural world. But in the
16th century the change was possibly more radical when mathematicians began to
widen the fields of classical mixed mathematics—which had flourished in
Hellenistic Greece and remained vital in the Middle Ages—certainly pressed by
demandsoftechnologyfromarapidlyexpandingsociety,byappropriatingofparts
of the canonical natural philosophy.
17thCentury.Theprocessofappropriationbecamemoreevidentasthecentury
progressed. Traditional mixed mathematics, optics, astronomy, music, mechanics,
flanked by many other disciplines that in previous centuries had been studied only
in natural philosophy, such as acoustics, meteorology, and hydrodynamics, were
given a new and fundamental acquisition: dynamics (term introduced by Leibniz).
Successobtainedinthisfieldbythemathematical(andexperimental)approachdue
to the contribution of many scholars, including Galileo, Torricelli, Cavalieri,
Huygens, Mariotte, Roberval, Descartes, Borelli, Leibniz, and eventually Newton,
hadafundamentalroleintheprocessoferosionoftheoldphilosophyofnatureby
(mixed) mathematicians. Because of this success, with the greater interest in
experimentationtoclarifyanddiscovernew“facts”,andtheinterestinapplications,
naturalphilosophy wasseendifferently than inthepast. Lessattentionwas paidto
traditional issues concerning nature, essence, and properties appropriate to all
x Preface
bodies—the so-called physica generalis—and more attention was paid to the
examination and discussion of the particular bodies—the so-called physica par-
ticularis. Traditional explanations, both Aristotelian and Cartesian, appeared in
some way sterile. Indeed the theories put forward did not have any element of
objectivity;thesamephenomenoncouldbeexplainedinonewaybyonescholar,in
another way by another, without an agreement being reached. New approaches to
the study of nature became so appealing because, despite providing answers in a
morerestricted range,they hadsomekindofobjectivityandwereable tolead toa
consensus of opinion. Furthermore, together with the explanations, the new
approaches also provided for the prediction of phenomena, which had great utili-
tarian value, leading to technological applications.
Skepticismtowardcanonicalnaturalphilosophyledtothebirthofexperimental
philosophy.ItdevelopedindifferentwaysontheContinentandinEngland,sothat
itisstipulatedbysomehistoriansthatthelabelexperimentalphilosophybeapplied
to English experimentations only, sponsored by the Royal society. The way of
relatingtoexperimentationisattributedbythesehistorianstotheconceptionofthe
roleofthedemiurgeandmagicintheCreationand,therefore,inwhatiscalledthe
ordinary course of nature. In England, more freedom would have been granted to
the demiurge than on the Continent, and this would have given greater freedom to
theEnglish,whowerenotobligedtosubsumeexperimentsundergeneralnecessary
laws. As a result, English scholars would have developed a science that favored
phenomenological aspects while continental academics would have paid more
attention to causation.
18th Century. The appropriation of natural philosophy by mathematicians
became substantially complete. This process was aided by the spreading of
Calculus, which made it possible to address many of yet unsolved problems. The
receivedviewpointconsidersthechangeintheapproachtophilosophyofnatureto
be largely a consequence of the technical results Newton achieved in the
Philosophiae naturalis principia mathematica and Opticks and his empirical view.
Since the 19th century, Newton has generally been seen as the founder of modern
science,inparticularofclassical mechanics,intheformithastoday. Thispointof
view was also prevalent among modern science historians, at least until the
mid-20th century. The assessment of Newton by contemporaries was more bal-
anced. He was recognized as a great mathematician; his results in astronomy were
consideredextraordinary,butfewsawhimasabringerofrevolutionaryresults,not
even in the fundaments of mechanics. In fact, he was considered just one of the
many. Before him, Huygens, Wallis, and Hooke had obtained results of no less
importance than his. Modern historiography introduces great variations in the
received point of view, giving to Newton only what is Newton’s.
In mechanics, the old mixed mathematics of Hellenistic origin, together with
statics and Galilean dynamics, changed into a theory that had the same ambitions
ofthecanonicalnaturalphilosophy,namely,togiveaglobalresponsetothenature
of motion based, however, only on a mathematical approach. The Bernoullis,
Varignon, Euler, and a few others, explicitly introduced algebra and differential
calculus, operating a non-trivial transformation that invested the very role of
