Newton on Islandworld: - Am MIT spezialisierte KI-Forschung

Newton on Islandworld:
Ontic-Driven Explanations
of Scientific Method

Adrian Currie
CSER, University of Cambridge

Kirsten Walsh
Philosophy, University of Nottingham

Philosophers and scientists often cite ontic factors when explaining the methods and
success of scientific inquiry. Das ist, the adoption of a method or approach (and its
subsequent success or otherwise) is explained in reference to the kind of system in
which the scientist is interested: these are explanations of why scientists do what
they do, that appeal to properties of their target systems. We present a framework
for understanding such “ontic-driven” explanations, and illustrate it using a toy-
Fall, the biogeography of “Islandworld.” We then put our view to historical work,
comparing Isaac Newton’s Opticks to his Principia. Newton’s optical work is
largely experiment-driven, while the Principia is primarily mathematical, Also
usually, each work is taken to exemplify a different kind of science. Jedoch,
Newton himself often presented them in terms of a largely consistent method.
We use our framework to articulate an original and plausible position: Das
the differences between the Opticks and the Principia are due to the kinds of
systems targeted. Das ist, we provide an ontic-driven explanation of methodolog-
ical differences. We suspect that ontic factors should have a more prominent role in
historical explanations of scientific method and development.

This paper has had a long development. Adrian presented the germ of the idea at the Phi-
losophy Seminar Series at the University of Sydney in May 2014, where Maureen O’Malley,
John Matthewson and Mark Colyvan provided crucial input. Im November 2014 Kirsten and
Adrian presented the complete idea to the HPS working group at Penn State, thanks in
particular to Michael Weisberg. We also received useful feedback on drafts from Daniel
Nolan and two anonymous referees from Perspectives in Science. Both of us have also had various
useful conversations over the years with too many people to fairly remember. Part of the
research for this publication was made possible through the support of a Fellowship at the
Institute for Research in the Humanities, University of Bucharest, and a grant from Templeton
World Charity Foundation. The opinions expressed in this publication are those of the author(S)
and do not necessarily reﬂect the views of Templeton World Charity Foundation.

Perspektiven auf die Wissenschaft 2018, Bd. 26, NEIN. 1
© 2018 vom Massachusetts Institute of Technology

doi:10.1162/POSC_a_00270

119

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Newton on Islandworld

Einführung

1.
As philosophers, we are often in the business of explaining scientiﬁc
method. Das ist, we ask why such-and-such investigation was carried
out as it was, what worked and what didn’t, and why. Hier, we introduce
a framework for understanding “ontic-driven” responses to these kinds of
Fragen. Explanations of method are ontic-driven when they appeal to
properties of the systems under investigation. We shall use our frame-
work to develop a fruitful and (at least prima facie) plausible hypothesis:
that several methodological differences between Isaac Newton’s two major
contributions to natural philosophy, his work on mechanics and optics, Sind
due to ontic differences. We’ll start by providing some examples of ontic-
driven explanations and characterizing them abstractly.

Ontic-driven explanations are common in scientists’ own methodolog-
ical reﬂection—whenever they chalk up a method’s effectiveness or other-
wise to the nature of the system targeted. Consider Diamond and
Robinson: “…the cruel reality is that manipulative experiments are impos-
sible in many ﬁelds widely admitted to be sciences. That impossibility
holds for any science concerned with the past…one cannot manipulate
the past” (Diamond and Robinson 2010, P. 1). Diamond and Robinson
point to a paradigmatic scientiﬁc capacity—controlled manipulative
experiments—and argue that for some targets (historical ones) that capacity
is unavailable, and unavailable because of the nature of the target system:
past events are not suitable experimental targets.1 They go on: “One there-
fore has to devise other methods of “doing science”: das ist, of observing,
describing and explaining the real world, and of setting the individual ex-
planations within a larger framework” (Diamond and Robinson 2010, P. 1).
Das ist, because some scientists target systems which are not amenable to
experimental approaches, different methods are required. Another example
of ontic-driven discussion is Jacob Weiner’s concerns about ecology:

Frustration with the apparent lack of progress [in ecology] has led
numerous ecologists to question the way scientiﬁc research in ecology
is done… Many ecologists attribute the lack of progress in ecological
science to the nature of the ‘beasts,’ not to methodological issues…
but many researchers think that the way ecology is done could be
part of the problem. (Wiener Würstchen 1995, P. 153)

What explains ecology’s (apparent) lack of progress? Perhaps ecologists are
doing the best they can—what they should—given the systems they
investigate. Or perhaps they are making some kind of methodological
mistake. The former answer is ontic-driven; the latter is not.

1. Obwohl, for a different view, see Jeffares 2008.

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Philosophers, zu, highlight ontic features when discussing scientiﬁc
method and epistemology. Zum Beispiel, according to both difference-
making and mechanistic accounts, scientiﬁc explanation proceeds by
identifying special properties of systems. Both views take the properties
in question to be variables playing privileged causal roles. The former,
“difference makers,” are those which inﬂuence the target variables under
certain counterfactual perturbations ( Waters 2007; Woodward 2003,
2010); the latter are concerned with mechanistic components and their
organization, required in combination for the production of some phenom-
enon or behavior (Erheben 2013, Craver 2007, Machamer and Darden 2000).
On both views, features of systems—ontic features—play a central role in
how explanation proceeds. Another contemporary concern is modelling
and idealization. Scientiﬁc representation often involves omission and dis-
tortion. Philosophers have argued that these distortions are necessitated by
the complexity of the systems scientists investigate ( Weisberg 2007,
Winsberg 2010, Cartwright 1999, Mitchell 2002). On such views, scien-
tists construct indirect, idealized representations, Modelle, which allow
them to navigate the complex systems they seek to understand. Also, philos-
ophers often identify a scientiﬁc strategy—an explanatory structure, pat-
tern of reasoning, or theoretical construct—and then justify that strategy
in light of properties of the relevant target systems.

The second half of this paper will present an ontic-driven explanation of
differences in Isaac Newton’s methodology. And indeed, philosophers and
historians studying Newton occasionally highlight ontic features in
accounting for the differential success of his methodological strategies.
Zum Beispiel, Steffen Ducheyne argues that Newton’s optical phenomena
are simply not amenable to the kind of rigorous causal explanations avail-
able to celestial phenomena (Ducheyne 2012, P. 219–22). And, George
Smith argues that, despite Newton’s best efforts in investigating ﬂuid
mechanics, “the empirical world did not cooperate” (Schmied 2001, P. 249).
Our account of ontic explanation, and the framework we use to understand
Es, allows such ontic-driven explanations to be more explicit, better situated,
and better supported.

An ontic-driven explanation, Dann, accounts for an investigative strategy
by pointing to properties of the system targeted. We can get somewhat
clearer on this. Explanation is fruitfully understood in contrastive terms
(Lipton 1990; van Fraassen 1980). Das ist, when we desire an explanation,
we seek features in virtue of which the explanandum diverges from relevant
(actual or counterfactual) contrasts. Zum Beispiel, Weiner is after the factors
which distinguish ecology from more (scheinbar) progressive sciences (In
his case, molecular biology). Is the relevant difference between ecology and
molecular biology a methodological deﬁciency on ecology’s part, or does it

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Newton on Islandworld

come down to ontic features—the “nature of the beasts”? Mit anderen Worten,
are ecological systems simply different from molecular systems in a way
which necessitates differing epistemic strategies? Wenn ja, we have an ontic-
driven explanation.

Und so, an explanation of scientiﬁc method is ontic-driven when the
explanatory target and the relevant contrasts diverge in virtue of properties
of the systems investigated. Natürlich, ontic features are not all that mat-
ters. Investigative approaches are also explained by appeal to technological
and theoretical circumstances, to scientiﬁc aims, to sociological and insti-
tutional factors, or even to the psychologies of individual researchers.2 His-
torians and sociologists of science, especially, often emphasize intellectual
and cultural context. It is sometimes argued that we cannot understand
how science works divorced from the traditions, beliefs, and inﬂuences
of the time. Pitt, zum Beispiel, argues that analyses of “observation” can
only be made in reference to speciﬁc time periods (Pitt 2001). Jim Lennox
claims that the best approach to understanding contemporary (and pre-
sumably past) scientiﬁc theoretical confusion is by studying “…the histor-
ical origins and development of those problems” (Lennox 2001, P. 657).
As he says, “the foundations of a particular scientiﬁc ﬁeld are shaped by its
Geschichte, and to a much greater degree than many of the practitioners of a
science realize” (Lennox 2001, P. 657). Burian recommends grouping scien-
tiﬁc practice either in terms of the evolution of a particular scientiﬁc prob-
lem, or in terms of contexts: “…such studies need to take account of the
multiple settings within which scientiﬁc work takes place—theoretical,
technical, instrumental, institutional, politisch, finanziell, national…”
(Burian 2001, P. 387). On such views, why scientists do what they do
is necessarily tied to the rich details of a particular time and place.

Ontic-driven explanations differ from, but potentially complement,
those preferred by some sociologists of science—particularly those associ-
ated with the Edinburgh Strong Programme (Barnes and Bloor 1982,
Shapin and Schaffer 2011) and empirical relativism (Collins 1975). Hier,
“rational” or “internal” explanations favored by philosophers of science are
deemphasized in favor of explanations which appeal to the role of social
factors: the political, the personal, and the highly contingent. Generally
Apropos, in explaining scientiﬁc change, and why scientists take the
approaches that they do, we need not choose between an abstract analysis

2. Zum Beispiel, Hacking’s work emphasises the role of technology and background
theory in driving scientiﬁc method (Hacking 1983); explanatory pluralists such as Sterelny
(z.B., 1996) and Jackson and Pettit (1992) appeal to the explanatory program (the aims) von
Wissenschaftler; Kuhnian (z.B., 1996) approaches to scientiﬁc change tend to be institutional, oder
at least pedagogical; Nersessian (1999) appeals to psychologies (“mental models”) in ex-
plaining conceptual change in science.

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of the logic of science and the social and political context involved in the
construction of knowledge.3 Science is complex, and explaining its features
involves a multitude of factors, from the abstract to the social, Und, Wir
vorschlagen, the ontic. How scientiﬁc disciplines develop depends both on
how scientists reason, their social context, and the kinds of systems they
are trying to understand. Oft, good explanations will involve a diverse
buffet, not a homogenous, single-course meal.

Zusamenfassend, our framework isn’t in conﬂict with these other explanatory
resources. It captures the aspects of scientiﬁc methodology which are de-
termined ontically, but fuller explanations will often draw on non-ontic
factors. Having said this, we do suspect that important ontic details
are sometimes obscured by over emphasizing social/historical factors.
Newton’s differing approaches to optics and mechanics may, in large
Teil, be explained by the nature of optical and mechanical systems,
and this has potentially been obscured.

Note that we focus on just one aspect of scientiﬁc investigation: un-
covering regularities, generalizations, and laws. Das ist, recurrent features
of the world which ground scientiﬁc explanation and prediction. As we
shall see, Newton explained planetary motions by appeal to his theory
of universal gravitation, and explained optical phenomena by appeal to
the composition of white light. We are interested in how such regularities
are established. This doesn’t require taking a stance on the status of such
regularities (whether they be “ceteris paribus” or “law-like,” and so forth),
we are only interested in how scientists come to know about them. Nor
do we take a stance on the nature of conﬁrmation: sufﬁce to say, the kinds
of tests we discuss will do epistemic work on any plausible view.

We begin with a toy case, the biogeography of “Islandworld.” The
“laws” of Islandworld bear a superﬁcial resemblance to actual biogeograph-
ical theory, but we use it as a tool for concretizing the ideas in our frame-
arbeiten, rather than as a serious analysis of ecology or biogeography. We then
articulate our framework via discussion of macroevolutionary theory. Mit
this in place, we apply it to Newton’s work in the Opticks and the Principia.
Our examples, Dann, are varied: from ecology, to paleontology, to me-
chanics and optics. This is a feature, not a bug: we argue that reﬂections
on scientiﬁc method frequently employ a general kind of explanation—
ontic-driven explanation—and that our framework grants traction on the

3. Helen Longino has argued convincingly that such positions rely upon a problematic
dichotomy between “internal” and “external” explanations of science. Against this dichot-
omy, she argues that scientiﬁc rationality plays out in and through the social environment
that scientists ﬁnd themselves in (Longino 2002, Kerl. 2).

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Newton on Islandworld

nature of such explanation. Given the generality of our purpose, wide-
ranging examples are appropriate.

Islandworld

2.
Islandworld is a globe, its geography consisting of a single continent (Die
mainland), and many islands of varying sizes and positions relative to both
the equator and the mainland. Islandworld is similar to Earth in that the bio-
geography of each island—here understood in terms of species number—is
related to that island’s spatial properties. Islandworld species-richness is
determined by three “laws.”4

L1: Larger islands are more species-rich than smaller islands;
L2:

Islands closer to the equator are more species-rich than islands fur-
ther from the equator; Und
Islands closer to the mainland are more species-rich than islands
further from the mainland.

L3:

For our purposes, the precise mathematical relationship between island-
property and species-richness is irrelevant: they could be linear or logarithmic,
deterministic or probabilistic. Islandworld, Dann, lacks both the complexity of
the real world, and the subtlety of actual biogeographical theory (see foot-
Notiz 8). The point of doing this is two-fold. Erste, the simple nature of
Islandworld allows us to articulate our framework: the model is a pedagog-
ical tool. Zweite, Islandworld is similar enough to real ecological theory to
provide a partial defense of our framework’s scope. Potentially, it could be
developed to understand the nature of method in ecology. But that is not
our purpose. What matters here is the advice we have for the biogeogra-
phers of Islandworld: how might they go about establishing biogeograph-
ical theory, and what would determine the success of that method?

The most obvious way of establishing a law is by holding the effects of
other inﬂuences ﬁxed. Das ist, we should seek islands which differ in only
one relevant property. In establishing, sagen, L1, ensure you only examine
islands which are equidistant from the equator and the mainland. If it
turns out that species richness tracks island size on equidistant islands,

4. Islandworld differs from Earth by the sheer simplicity of its biogeography. The “laws”
of Islandworld have sophisticated cousins on Earth. Earthling species richness on islands
(and similar locales) is taken to be broadly determined by two factors: the distance effect
(how far the island is from sources of colonists affects how likely it is that new species will
turn up on the island L3); and the size effect (the species-area curve connects species rich-
ness to island size, typically logarithmically L1). In addition to this, many other factors are
taken to inﬂuence species richness on Earth’s islands. These include the climate: hotter,
wetter climates tend to encourage species richness (hence L2). The founding document
of modern island biogeography is taken to be MacArthur and Wilson 1967.

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then L1 is (to some extent, mindestens) established. Call this method “isola-
tion.”5 According to isolation, to establish a regularity, we should seek
tests which differ only in terms governed by that regularity.

Jedoch, it may be that the scientists of Islandworld are unable to test
via isolation: there may not be enough (or any!) equidistant islands, Und
the Islandworlders may lack the technology and theory to fabricate them.
Wenn ja, isolated tests are impossible as each law’s inﬂuence cannot be exam-
ined in isolation from the others. Call the inﬂuence of laws on one another
“interference.” In such cases, there are no objects with the relevant sets of
properties required for isolated testing.

Isolation does not exhaust the means by which we can establish laws.
The Islandworlders can instead test their theories in combination. Do L1,
L2 and L3 in tandem determine species richness? Wenn ja, the laws are con-
ﬁrmed. If sufﬁcient islands of differing sizes and distances from the equator
and mainland are available, the laws can be established.

Und so, we have two methods for establishing Islandworld theories of
biogeography. By the ﬁrst, we isolate the factor we are interested in by
holding ﬁxed other relevant factors across test cases. By the second, Wir
use the laws in combination. What determines the appropriate method?
The amount of interference. We ask, is there, or can we fabricate, a situ-
ation where one law alone determines the property of interest?

Interference is ontic, it is a property of the system under investigation,
and so appealing to it provides an ontic-driven explanation of Island-
worlder methodology. Whether they establish their biogeographical laws
via isolation or via combination depends on Islandworld’s geographical
layout. Assuming that the technological and theoretical capacities are held
ﬁxed, the relative position and sizes of islands makes the difference.

Let’s complicate things. Islandworld is occasionally shaken by under-
water earthquakes. These spawn tsunamis which in turn sink parts of
islands. Let’s imagine the earthquakes and their effects are stochastic
and independent of L1, L2, and L3. The result is that some islands decrease
in size without corresponding decreases in biodiversity. Das ist, earth-
quakes undermine L1. Let’s call this kind of affect “noise.”6 The law still
holds, let us imagine, but only ceteris paribus—when not effected by earth-
quakes. How do earthquakes effect Islandworld biogeographical theory?

5. Isolation is most clearly carried out in experimental contexts. Hier, our capacity to
actively manipulate systems allows us to bring about test cases of causal regularities. Sehen
Okasha 2011.

6. Our use of the term “noise” is somewhat idiosyncratic, as it picks out exogenous
factors affecting a system’s behavior, as opposed to the more usual epistemic sense of noise,
which contrasts it with “signal.”

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Newton on Islandworld

If earthquakes are frequent on Islandworld, it doesn’t follow that scien-
tists will be unable to establish laws by isolation or combination. Jedoch,
there will be two consequences. zuerst, epistemic conﬁdence could be under-
mined by non-systematic exceptions. Zweitens, and more interestingly, Die
applicability of Islandworld biogeographical theory will be restricted, as the
laws together are not the ﬁnal word on species richness. Even in the right
circumstances for isolated tests—an abundance of islands of the right size
and distance from equator and mainland—because the target system is noisy,
the applicability of subsequent theories is limited. Islandworld laws will not
predict species number reliably outside of their tests. And so Islandworlders in
noisy circumstances will be less successful than those in quiet circumstances.
Wieder, this difference in success requires an ontic-driven explanation. Der
nature of Islandworld, the frequency of earthquakes, makes a difference to
the biogeographers’ success.7

Und so, Islandworlder method and success depends ﬁrst, on the amount
of interference between the biogeographical laws and second, on the
amount of noise from earthquakes. High interference undermines the
Islandworlders’ capacity to conduct isolated tests, while high noise lowers
both the efﬁciency of tests and the applicability of resulting theory. Im
next section, we will characterize these dimensions in more detail and pres-
ent our framework.

Interference and Noise

3.
The amount of interference and noise in a system partly governs the appro-
priate scientiﬁc method for its investigation, and this generates ontic-driven
explanations. We will illustrate this claim in section 4. Before getting there,
Jedoch, we shall explain the central distinction of the framework, Und
present it schematically.

3.1. The Distinction
The difference between interference and noise depends on a distinction be-
tween inter- and intra-system factors. Das ist, with respect to some system,
some factors are endogenous, d.h., “part” of the system, while others are exog-
enous, d.h., “outside” of the system. In Islandworld, this was stipulated: island

7. Our discussion of Islandworld might strike ecologists as odd, given that changes to
Islandworld—the sinking of islands, for instance—would ultimately affect the species com-
position of other islands as well. The dynamical nature of ecological systems, and ecologists’
focus on those dynamics, are not well-captured by our discussion of Islandworld. But again,
the point of the example is not directly to understand the work of ecologists or the nature of
ecological systems, eher, it is to provide an illustration of our framework. Interference and
noise, we think, are useful conceptual tools for understanding ecology’s ontic difﬁculties in
üben, but we leave that task for later work.

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size and position were a proper part of Islandworld biogeography, while
earthquakes were not. But on what basis might we draw such a distinction?
We shan’t provide an analysis here; In der Tat, we are skeptical that this can
getan werden. One reason for skepticism is that, whether or not a variable falls
within some domain—and in particular why it does—is an empirical ques-
tion. Scientiﬁc investigation, rather than a priori analysis, determines what
counts as interference or noise for some domain. Darüber hinaus, as we shall see,
interference and noise are generated by a variety of sources, undermining
generic characterization. dennoch, we can point to related distinctions
and provide illustrations. Darüber hinaus, that scientists themselves often rely on
such distinctions partly vindicates our using them.

Marc Lange’s account of laws relies on a distinction akin to ours. Für
him, a law is part of a stable set. Das ist, it is logically consistent with
the possibilities set by the other laws in that relevant domain. If L1 is a
law on Lange’s view, then it will remain true across the range of possibil-
ities described by L2 and L3. But how do we determine each domain’s
laws? Hier, (following Mill) Lange distinguishes between greater causes
and “…petty, local, idiosyncratic inﬂuences that must be ascertained on
a case-by-case basis” (Lange 2005, P. 398). By Lange’s account, a necessary
condition of being a law vis-à-vis some domain is capturing a greater cause
relevant to that domain.8 In Islandworld, zum Beispiel, island size is a greater
cause of species richness. Im Gegensatz, although earthquakes can affect species
richness, they are not greater causes. What makes something a greater cause
is in part whether we can say something systematic about that factor’s effect
in the relevant domain. On Islandworld, island size has a speciﬁc and sys-
tematic effect on species richness. Darüber hinaus, the effect can be captured using
relatively simple dynamics. Earthquakes are not like this: their effect on
species richness depends on local, idiosyncratic factors—where the earth-
quake struck, its magnitude, und so weiter. Debate in macroevolution provides
an illustration of greater and lesser causes, which we’ll connect to interfer-
ence and noise.

Macro-evolutionary theory targets large-scale patterns in morphological
evolution, explaining the “shape of life” in terms of radiation, speciation,
mass-extinction, und so weiter. Reductionists hold that evolution via natural
Auswahl, which explains the evolution of particular traits on the “micro-
scale,” is sufﬁcient to explain patterns of the “macro-scale”: macro-evolution
is micro-evolution scaled up. Anti-reductionists, in contrast, believe that
micro-evolutionary forces alone are insufﬁcient to explain important
macro-evolutionary features. They often point to the contingent “histo-
ricity” (Beatty 2006; Beatty and Carrera 2012) of macro-evolutionary

8. This is merely an aspect of Lange’s account.

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Newton on Islandworld

processes such as speciation (Gould and Eldredge 1977) and extinction
(Gould 1989) to argue that, zum Beispiel, natural selection is not the only
“force” bearing on macro-evolution.9

One anti-reductionist argument highlights mass extinctions (sehen
McConwell and Currie 2017, Zum Beispiel). At least sometimes, mass
extinctions are caused by “external” disruptions, most dramatically by
extra-terrestrial impacts, but also changes wrought by continental drift
and atmospheric shift. It is thought that these factors are not within the
purview of evolution by natural selection—organisms are not “designed”
by natural selection to survive mass extinctions—and so a different theory
is required to understand macro-evolution. In essence, the debate is about the
role or otherwise of both drift, non-selective, often stochastic, forces which
inﬂuence genotypic and phenotypic evolution, and macro-evolutionary
analogues such as species-sorting (Turner 2011). We are not interested here
in entering the debate about the nature of drift and natural selection,10
eher, we think it nicely illustrates the intra/inter-domain distinction
we are after.

One might understand anti-reductionism about macro-evolution as the
view that, on a macro-evolutionary scale, natural selection is not the only
major cause, or fails to even count as a major cause. Let’s imagine that mass
extinctions are sometimes caused by extra-terrestrial impacts, and that mass
extinctions make a real difference to macro-evolutionary patterns. Darüber hinaus,
let’s say that such events have the features of major causes: they are relatively
systematic and can be understood with relatively simple theory. Wenn ja, natürlich
selection is likely not the only major cause of macro-evolution. If the role of
chance and outside disruptions are such that natural selection does not have
a systematic effect on macro-evolutionary patterns, then it is not even a
major cause. Beachten Sie, dass (usually at least) anti-reductionists in no way deny
that natural selection is important on the micro-scale—they are not anti-
Darwinian. Eher, vis-à-vis macro-evolution, natural selection is either in-
sufﬁcient (only one of the major causes), or irrelevant (a lesser cause).

Let’s connect the distinction between interference and noise to greater
and lesser causes. Recall the two anti-reductionist views about macro-
evolution. The weaker view includes other greater causes: to accommo-
date macro-evolutionary patterns, extra theoretical machinery covering
drift, species sorting, und so weiter, must be added to our arsenal. Hier,

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9. See Sterelny 2003 for a general comparison of the two views through an analysis of

Gould’s work, and Dennett 1995 for a classic reductionist rejoinder.

10. Philosophers of biology differ on whether ‘drift’ constitutes an actual process or
force, or whether it should be considered statistical ‘error’ (see Plutynski 2007 for a general
overview).

Perspektiven auf die Wissenschaft

129

natural selection is a greater cause, but interferes with drift, and is itself
interfered with. The stronger anti-reductionist denies that natural selec-
tion is a greater cause; if anything, it is noise from a macro-evolutionary
Perspektive. Im Gegensatz, the reductionist considers drift to be a lesser
cause, merely generating noise. Und so, interference is the relationship
between greater causes, while noise is from lesser causes. The distinction
between greater and lesser causes, and the kinds of distinctions those in
the debate about macroevolution draw, turn crucially on the idea that
vis-à-vis some system, some causal factors are endogenous and others are
exogenous.

To reiterate, this is no analysis of the difference between interference and
noise, but rather an elucidation. The following three points are important.
zuerst, the difference between interference and noise depends upon the
properties of systems. Das ist, the difference is ontic. Daher, disagreement
between reductionists and anti-reductionists about macro-evolution centers
on the nature of macro-evolutionary systems and processes. Zweitens, what
counts as interference or noise is system-relative. If anti-reductionists are
right about macroevolution, then drift interferes with natural selection on
the macro-scale. Yet they may happily concur that it is a greater cause on
the micro-scale. Thirdly, and relatedly, whether something is a source of
noise or interference vis-à-vis some system is decided by scientiﬁc investiga-
tion: we doubt there is an a priori analysis available.

This third point deserves further discussion, in service of which we’ll
look at the sources of noise and interference. These are multiply realizable
and scale-dependent. Any worldly factor which makes isolation testing
troublesome could be seen as a source of interference. On Islandworld,
zum Beispiel, island position is a source of interference: if no equidistant
islands are available, Islandworlders lack the appropriate objects to estab-
lish L1 via isolation. John Matthewson (2011) and Alkistis Elliott Graves’
(2016) distinction between “complexity” and “heterogeneity” is a useful
way of thinking about sources of noise and interference. We can under-
stand a system’s “complexity” in terms of the number of components,
and their interaction. An electric sewing machine is a fairly complex sys-
tem. Its operation relies on sensitive interaction between needles, motor,
foot pedal, und so weiter. Isolated tests on any particular part of the machine
become difﬁcult. A system’s complexity can generate interference: modu-
larity begins to break down, intervening on and tracing causal relation-
ships becomes more difﬁcult, und so weiter. Although sewing machines
are complex, they are often not heterogeneous. “Heterogeneity” relates
to the different types of components within and between systems. Sewing
machines, particularly those of the same make and model, tend to operate
in the same way, using the same components. This homogeneity means

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130

Newton on Islandworld

that knowledge of one sewing machine will be easily generalized across
viele. If Tolstoy is right, unhappy families are heterogeneous, as each gen-
erates unhappiness in a different way. Due to this, understanding the
dynamics of unhappiness in one family will not tell us much about un-
happiness in another family. Heterogeneity, Dann, generates noise. As there
are many ways of being complex and being heterogeneous, there are many
sources of interference and noise.

The enormous range of sources of interference and noise prevents a pre-
cise analysis of these concepts. Jedoch, as we see in macro-evolutionary
debate, scientists do distinguish between endogenous and exogenous fac-
tors pertaining to some system. That the distinction plays a central role in
empirical disputes justiﬁes our taking it seriously despite imprecision.

Two more points are required. Erste, although the framework is primar-
ily ontic, it is necessarily indexed to theoretical and technological capaci-
Krawatten (hence our term “ontic-driven”). To see this, consider various ways in
which interference could occur. Some interference might be unsolvable in
principle—two processes might be necessarily entangled, zum Beispiel.
Let’s add a fourth law to Islandworld: any island that is both equidistant
from the equator and the mainland is barren. In this scenario, it is nomo-
logically impossible to test L1 in isolation. This seems extraordinarily un-
likely for biogeography, but analogues might occur in, sagen, particle
Physik. More realistically, most cases of high interference are not so due
to nomological or logical restrictions, but due to (sometimes extremely
challenging) technological or practical ones. Zum Beispiel, if Islandworlders
are not lucky enough to ﬁnd equidistant islands, the technology required
to construct them, and the time required for the requisite species to turn
up or evolve, would most likely make isolation tests prohibitive. As we’ll
see in Newton’s case, in such circumstances scientists often do conduct
isolated studies, but these employ proxies to supplement combination
testing.

Endlich, you might worry that our distinction is held hostage to the de-
cisions scientists make about whether or not something counts as a sys-
tem,11 or that it requires a strong view about the relationship between
sozial, pragmatic, and epistemic context on one hand, and ontic factors
andererseits. Such worries are misplaced. All that is required for
our account to gain purchase is for ontic factors to play some role in de-
termining which systems scientists investigate, how they conceive of them,
and whether such investigations succeed. The distinction between inter-
ference and noise can be accommodated by strong views which place strin-
gent restrictions on what the valid systems are, but can ﬁt just as happily

11. We’re grateful to an anonymous referee for highlighting this issue.

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131

with more relaxed—even “promiscuous” (Dupré 1993)—views which
allow scientists bountiful wiggle-room vis-à-vis the systems they target
and how they divide them. Only views claiming that ontic features place
no restrictions on scientists’ capacities to identify, delineate, and investi-
gate systems will make trouble for the ontic status of the distinction be-
tween noise and interference. And such views are implausible.

With the basic distinction in hand, we can now turn to the framework.

3.2. The Framework
Recall our aim: to understand ontic-driven explanations of scientiﬁc
method. Our thought is that how scientists go about establishing regular-
ities will depend on the nature of the system they target; speciﬁcally, An
the amount of noise and interference within that system. We can envision
noise and interference using a two-dimensional space (siehe Abbildung 1, below).
Where systems fall within that space determines the kind of access scien-
tists have, and thus the appropriate methodology (das ist, whether isola-
tion or combination tests are available, and their effectiveness). Weiter,
recall that we understand ontic-driven explanation in contrastive terms.
Systems don’t have tout court “amounts” of interference or noise, eher,
the measure is relative. Zum Beispiel, when we come to compare Newton’s
Principia to his Opticks, we shall argue that optical systems have less inter-
ference than astronomical ones, but that astronomical systems are less
noisy. The relativity of the measure allows our account to apply across a

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Figur 1. The framework

132

Newton on Islandworld

vast range of systems despite the differences between them. With the
understanding that our claims are system-relative, let’s identify some loca-
tions and indicate some possible examples.

Let’s begin with systems of low interference and low noise: “tame sys-
tems.” These can be tested via isolation, and behavior beyond tests is to a
large extent determined by the relevant greater causes. If Islandworld bio-
geography is tame, then scientists are able to establish their theories both
via isolation and in combination. Darüber hinaus, in virtue of the lack of noise
from earthquakes, their theories will be projectable. Das ist, they will be a
reliable guide to species richness throughout Islandworld. Possible candi-
dates for tame systems might be physical or chemical systems. Für in-
Haltung, not only can chemical interactions be isolated and studied in the
lab, but those interactions often occur similarly in “the wild” (although see
Cartwright 1983, 1999 for skepticism about physics, and Havstad 2017
for chemistry).

As we increase a system’s interference, we reach circumstances where
isolated tests are difﬁcult or impossible, but behavior is still regular. Diese
are “quiet systems.”12 Although isolatable tests are unavailable, combina-
tory tests are—and the established theories will be happily projectable.
Islandworlders in this situation would not be able to hold ﬁxed L2 and
L3 in order to test L1, but they would ﬁnd that, by combining the three
laws, reliable and accurate predictions about species number are achievable.
Plausible examples of such cases might be ﬂuid mechanics and astrophysics.
Although isolating planetary systems is infeasible, relatively trustworthy
predictions can be made by applying physical laws in combination.

Holding interference low, and increasing noise, we ﬁnd noisy systems.
These are amenable to isolated tests, if we control for noise. Jedoch, Die
adequacy of subsequent theory will be limited. If Islandworld biogeogra-
phy is noisy, then although equidistant islands are available to test L1 (oder
the Islandworlders have the technology and patience required to fabricate
tests), the common occurrence of earthquakes renders the laws a poor guide
to actual species richness. Some plausible systems of this nature are biolog-
ical and behavioral systems. Obwohl, zum Beispiel, animal behavior can
be isolated and examined in the lab, wild and laboratory circumstances
diverge, making it difﬁcult to export results.

Endlich, turning both interference and noise to full, we ﬁnd “wild sys-
tems.” These are both unamenable to isolated tests and are riddled with
exceptions. Scientists facing such systems might ﬁnd themselves ques-
tioning whether their targets are really “systems” at all. Some tentative

12. These are what Nancy Cartwright has called “natural nomological machines”

(Cartwright 1999).

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133

examples might be evolutionary, ecological, and economical systems.
Although such systems are sometimes taken to be amenable to experi-
mental study or something analogous,13 typically, such systems are con-
sidered to be extremely difﬁcult to investigate in isolation, und das
results of such studies only apply across limited cases.

This framework, we argue, can be used to generate and understand
ontic-driven explanations of scientiﬁc methodology. Das ist, when asking
why some scientiﬁc investigation proceeds as it does, we should attend to
the target system’s interference and noise relative to the explanatory con-
Bünde. We do not pretend that this is always the best explanation. Eher,
when an ontic-driven explanation is called for, this framework has the
goods. Our aim for the remainder is to harness the framework in a real-
world case.

4. An Ontic-Driven Explanation of Newton’s Methodology
The methodological differences between Isaac Newton’s two great works of
natural philosophy, the Opticks and the Principia, are often thought to
reﬂect developments in Newton’s methodology, varying aims of investiga-
tion, differences in tradition, or differences in technology or theory. But we
shall argue that a case can be made for taking the primary difference to be
the subjects of the investigations. Newton’s two great works target differ-
ent kinds of systems, which require different methodological approaches.
We argue that this aspect of Newton’s methodology is amenable to an
ontic-driven explanation. This discussion of Newton serves two purposes.
Einerseits, his work illustrates our framework and demonstrates its
Potenzial. And on the other hand, we use our framework to generate a
novel, prima facie plausible and likely fruitful hypothesis about why Newton
claims to have a consistent methodological approach, but employs different
methods in different situations.

Our treatment is somewhat simpliﬁed: given our purpose, a discussion
which did justice to the rich, sophisticated state of contemporary Newton
scholarship would be prohibitive. Having said this, we take our claims
about Newton seriously; and consider the picture we paint broadly accu-
rate. Newton is a startling and inﬂuential example of scientiﬁc success and
as such getting the details right is important, but it would be a shame if
the demand for detail was such that Newton’s example couldn’t inform
more general projects such as the one at hand.

13. Zum Beispiel, sometimes convergent evolution is taken to be a “natural experiment”
which tests evolutionary theories (Currie 2013), and ecological theories are sometimes studied
using model organisms in so-called “bottle-experiments” (Odenbaugh 2006).

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Newton on Islandworld

Here’s an odd feature of Newton’s career. He is taken to have spawned
two important, but different, Wissenschaften: an experimental science exempliﬁed
in the Opticks, and the mathematical science exempliﬁed in the Principia.
Und doch, his methodological reﬂections remained remarkably consistent
throughout his life. Consider this representative quote from Cohen and
Schmied: “There is, vielleicht, no greater tribute to the genius of Isaac Newton
than that he could thus engender two related but rather different traditions
of doing science” (Cohen and Smith 2002, P. 31). On this view Newton is
the father of two scientiﬁc traditions. Erste, the austere, formal mathema-
tism of his celestial mechanics. And second, the complex and sophisticated
experimentalism of his optics. When considering the motions of bodies
and the forces that produce them, Newton was a mathematician; Wann
considering the properties of light and colors, Newton was an experimen-
talist. Although he draws the distinction very differently from Cohen and
Schmied, Thomas Kuhn also argued that Newton’s two major contributions
represent two profoundly different traditions. For him, the Principia was a
“classical” science, uniﬁed with other mathematical inquiries such as
astronomy and harmonics. Im Gegensatz, the Opticks was a “Baconian”
Wissenschaft, to be lumped with studies of magnetism, Elektrizität, and heat.14
The large divergence between Kuhn and Cohen and Smith notwithstand-
ing, the Opticks and the Principia are often taken to exemplify very different
methodologies.

Jedoch, Newton’s own writing about the methodology of the Opticks
and the Principia suggests a different story. Consider the following, a passage
from Newton’s “anonymous” report from the Royal Society’s 1715 exami-
nation of the calculus dispute with Leibniz: “The Philosophy which
Herr. Newton in his Principles and Optiques has pursued is Experimental; Und
it is not the Business of Experimental Philosophy to teach the Causes of
things any further than they can be proved by Experiments” (Newton
1715, P. 222). Hier, Newton uniﬁed his two works under the label “exper-
imental philosophy,” suggesting that, in stark (and undeniably snarky) con-
trast to Leibniz, both works are grounded in observation and experiment,
rather than speculative hypotheses. And so apparently Newton took himself
to have a distinct methodology, exhibited in both of his great works.

Commentators have often interpreted this and other such statements as
purely rhetorical: in his dispute with Leibniz, Newton made a political
decision to align himself with the Royal Society and, by extension, to iden-
tify his methodology with experimental philosophy. Jedoch, while we
lack the space to make a satisfactory case for it here, we think this professed

14. More recently, Kuhn’s inﬂuential account has been called into question by, für

Beispiel, Anstey 2014 and Domski 2013.

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unity is not a mere rhetorical ﬂourish on Newton’s part, but a serious phil-
osophical claim.15 For instance, we think Newton’s experimentalism can
be seen in the reasoning in book 3 of the Principia, which is based on the
“phenomena” of observed planetary motions, and in the scholia in books 1
Und 2 of the Principia, which are littered with suggestions for future exper-
imental programs. Darüber hinaus, in both works, Newton makes his stance on
hypotheses very clear. In the Principia, Er (In)famously declares Hypotheses
non ﬁngo (“I do not feign hypotheses” (Newton 1999, P. 943)). And in the
Opticks, he begins, “My Design in this Book is not to explain the Properties
of Light by Hypotheses, but to propose and prove them by Reason and
Experiments” (Newton 1952, P. 1).16 But the unity runs deeper than this.
Niccolò Guicciardini suggests that the two works are uniﬁed by their use
of the method of analysis. He writes: “In the Principia analysis is a deduc-
tion of forces from motions; in the Opticks it is a deduction from compo-
sitions to ingredients… In both cases one has a deduction of causes from
effects” (Guicciardini 2011, S. 316–17). He continues:

Weiter, the procedure of deduction from experiments (in the Opticks) Und
from phenomena or observations (in the Principia) has the tentative,
heuristic, and complex structure of the analytical heuristic method of
the mathematicians. Newton could draw a comparison between the
experimental method adopted in natural philosophy and the method of
analysis of the mathematicians because he placed experimentation within
a deductive mathematical procedure… (Guicciardini 2011, P. 317)

Zusamenfassend, the unity of Newton’s methodology, that endures over time and
across his scientiﬁc work, is grounded in the use of mathematical reasoning
to derive theoretical propositions from experiments and phenomena—
deducing causes from effects. Below, we’ll sketch this as his “mathematico-
experimental” method.

The following passage from Newton’s ﬁrst published paper (1672) is an

early statement of this methodology:

A naturalist would scearce expect to see the science of [colors]
become mathematicall, & yet I dare afﬁrm that there is as much

15. For an inﬂuential account of this position, see Shapiro 2004. And for replies see

Walsh 2012a, 2012B.

16. The distinction between theories and hypotheses is central to Newton’s methodol-
Ogy. For Newton, theories are on epistemically surer footing than hypotheses because they
are grounded on phenomena, whereas the latter are grounded in speculations ( Walsh
2017A). For a discussion of the distinction between theories and hypotheses in early modern
philosophy more generally, see Ducheyne 2013.

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certainty in it as in any other part of Opticks. For what I shall tell
concerning them is not a hypothesis but most rigid consequence,
not conjectured by barely inferring ’tis thus because not otherwise or
because it satisﬁes all Phænomena (the Philosophers universall
Topick,) but evinced by the mediation of experiments concluding
directly & without any suspicion of doubt. (Newton 1959–1977,
Bd. 1, S. 96–7)

Hier, Newton claimed that his science of optics is experimental, in that it is
grounded in observation and experiment, and mathematical, in that theoretical
propositions are deduced from experiment, in the style of mathematicians,
without recourse to speculative hypotheses. These two aspects constitute the
methodology which remained consistent throughout his life.17

Now consider another representative passage. This one’s from book 1 von

the Principia (1687):

Mathematics requires an investigation of those quantities of forces
and their proportions that follow from any conditions that may be
supposed. Dann, coming down to physics, these proportions must
be compared with the phenomena, so that it may be found out
which conditions [or laws] of forces apply to each kind of attracting
bodies. Und dann, ﬁnally, it will be possible to argue more securely
concerning the physical species, physical causes, and physical
proportions of these forces. (Newton 1999, S. 588–89—brackets
indicate translators’ comment)

Hier, Newton claimed that mathematical reasoning can carry us from
causes to effects—or from forces to the motions they produce. But to do
“physics,” that is, to harness the power of mathematics to explain actual
physical systems, we must reason in the other direction—from motions to
their forces.18 This passage is best understood contextually: it leads us into

17. Commentators generally view the quoted passage as extreme, and there is some
disagreement vis-à-vis the extent to which it is representative of Newton’s epistemological
commitments. Shapiro and Guicciardini, Zum Beispiel, have argued that Newton quickly
retracted his extreme claims of certainty and instead expressed a more moderate epistemic
attitude towards his theory of light (Guicciardini 2011, P. 20; Shapiro 1989, P. 225, 1993,
P. 14) (against this position, see Walsh 2017b). Hier, Jedoch, we introduce this passage to
demonstrate that, well before his difﬁculties with Leibniz, Newton was presenting his op-
tical work as mathematico-experimental. We can make this point without taking a position
on the debate about Newton’s notion of certainty.

18. In the above passage, Newton might have been appealing to the well-known distinction
between “pure mathematics” (d.h., arithmetic and geometry) and “mixed mathematics” (d.h., astron-
omy, optics, harmonics, usw.). Traditionell, pure mathematics was said to deal with mathematics as
it applied to intelligible things, das ist, those things that can be apprehended by the intellect or

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Abschnitte 12 Und 13 of book 1, where the focus is on centripetal forces di-
rected toward individual particles of matter. Immediately following this
passage is a sequence of mathematically derived conditional propositions
relating centripetal forces directed toward whole bodies and centripetal
forces directed toward their individual parts composing those forces. Nur
as the above quotation says, these mathematical propositions investigate
“those quantities of forces and their proportions that follow from [a subset
von ] any conditions that may be supposed.” Newton ﬁnally arrives at Prop-
osition 92 (Newton 1999, P. 618), which describes an experimental pro-
gram to (1) establish whether the forces toward whole bodies are composed
of forces toward the parts of those bodies and (2) to measure how the latter
forces vary with distance. Zusamenfassend, what we ﬁnd is an experimental pro-
gram akin to the one investigating optical phenomena. Jedoch, Newton
evidently realized how weak gravitational forces toward everyday bodies
Sind, and saw no way to carry out this program at the time.

Und so, Newton’s methodology has two aspects: the mathematical and
the experimental. Let’s make these more explicit. Mathematical: Nach
to Newton, just as mathematical inferences could be performed without
epistemic loss, so could philosophical inferences (i.e. inferences about phys-
ics). Das ist, it is possible (with the help of mathematical tools such as
geometry and calculus) to deduce new physical propositions from princi-
ples and laws. And these new propositions will have the same epistemic
status as the original principles and laws. Experimental: According to
Newton, theories must be inferred from experimentally-established prin-
ciples: i.e. principles deduced from phenomena, acquired via observation
and experiment. Außerdem, Newton seems to have been rather inﬂa-
tionary about what such empirical enquiry—even a single “experimentum
crucis”—could achieve. In his more extreme statements, claiming they
could yield truth “without any suspicion of doubt.”19

Vorstellung. Im Gegensatz, mixed mathematics was concerned with the application of mathematics
to natural phenomena. So it was said to deal with mathematics as it applied to sensible things, Das
Ist, those things that can be apprehended by the senses. See Dunlop 2012, P. 77 for a discussion of
this distinction.

19. This notion can be characterised as “compelled assent”: the evidence compelled
Newton undeniably to his conclusion, and he expected others to draw the same conclusion
in the same context (see Walsh 2017b). Zum Beispiel, in his correspondence with Lucas
(August 1676), Newton wrote: „[Let Lucas examine the experiments given.] For if any
of those be demonstrative, they will need no assistants nor leave room for further disputing
about what they demonstrate. The main thing he goes about to examin is the different re-
frangibility of light. And this I demonstrated by the Experimentum Crucis. Now if this dem-
onstration be good, there needs no further examination of the thing; if not good the fault of
it is to be shewn, for the only way to examin a demonstrated proposition is to examin the
demonstration” (Newton 1959–1977, Bd. 2, S. 79–80).

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Newton on Islandworld

These features in combination make sense of Newton’s claims about a
“mathematical science.” From principles or laws, one may deduce pro-
positions or theorems without epistemic loss. The challenge, Dann, is to
establish those principles. Newton thought that this was best achieved exper-
imentally. And so Newton’s methodology was “mathematico-experimental.”
To drive the point home, consider this passage from book 2 part II of the
Opticks, written later in Newton’s career: “Now as all these things follow from
the properties of Light by a mathematical way of reasoning, so the truth of
them may be manifested by Experiments” (Newton 1952, P. 240). In arguing
that Newton’s methodology is much more uniﬁed and consistent than usually
recognised, we are not suggesting that it was static and unvarying. In der Tat,
over the course of his working life, Newton was deeply engaged with
methodological questions, working to improve, develop, and nuance his
investigative and theorising skills. Darüber hinaus, different contexts and re-
search programs presented Newton with different methodological chal-
lenges to overcome. Also, Newton’s methodology was dynamic and
progressive. We think it is plausible, Jedoch, that the mathematico-
experimental procedure sketched above was an enduring methodological
commitment. Development and variation took place within the parameters
of this fundamental feature of Newton’s methodology. The analysis we offer
in the following sections highlights one aspect of this variation: the ontic
features of different target systems.

In sum, Newton apparently spawned two very different sciences, Die
experimental optics and the mathematical mechanics, and yet his method-
ological reﬂection betrays a unity, his mathematico-experimental method.
Newton’s methodological reﬂections describe two works uniﬁed by one
methodological approach; but the two works seem to exemplify different
ways of investigating natural systems. Und so, Hier, we think an ontic-
driven explanation will be illuminating. Our ﬁrst task, Dann, is to ask what
was different about Newton’s targets which necessitated these differences.
Our second (and brief ) task is to inquire into their differing success: Die
mechanical project is taken to have outperformed the optical one. We will
present ontic-driven answers to both questions. In a nutshell, on our view,
Newton’s optical system exhibited less interference than his celestial sys-
tem, and thus, where the former was amenable to (experimental) Isolierung
tests, the latter was not. This goes some way towards explaining the differ-
ence in how Newton approached these systems. Jedoch, we argue, optical
systems are much noisier than celestial ones, and so the regularities which
Newton established were much more widely applicable in the case of me-
chanics than optics—which explains the differing success of those projects.
Before we examine the two sciences in more depth, we should say some-
thing about how our ontic-driven explanation ﬁts with other explanations

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of Newton’s methodology. As implied in the introduction, we are ecumen-
icists about explanation. Das ist, we do not think there is one single privi-
leged way of explaining an historical episode. Explanations are contrastive:
they serve to explain why one thing happened rather than another. Mit
respect to a given historical episode, there might be multiple sets of con-
trasts that interest us, leading to multiple legitimate explanations of a
single historical episode. Newton’s methodology is a case in point. Depending
on our primary concerns, explanations of Newton’s methodology could
appeal to multiple factors: zum Beispiel, Newton’s position in the Royal
Society (Feingold 2001), his education at Cambridge (Dunlop 2012), sein
primary interest in alchemy (Newman 2016), und so weiter, could each form
the basis of an explanation of his method. Although these explanations are
not equivalent, they are also not necessarily in competition. Eher, each high-
lights a different aspect of Newton’s methodology. And we think this is valu-
able. Different kinds of contrastive explanations allow us to bring different
features of Newton’s work into focus, and explore different hypotheses. Eins
feature of Newton’s methodology which, we think, has been largely over-
looked is its relationship to the system being investigated. And we think
our ontic-driven explanation sheds important light on this feature.

4.1. How to Establish Principles
Let’s compare Newton’s ‘experimental’ approach to optics with his
‘mathematical’ approach to mechanics. As we shall see, both are examples
of his mathematico-experimental method: propositions are deduced from
principles, which are established by experiment. Warum, Dann, does the method
look so different in the two cases? Drawing on our account of ontic-driven
explanations, we’ll tentatively suggest that the two works differ in the
method by which principles are established. The Opticks contains paradigm
instances of isolation-testing. We attribute this approach to the low inter-
ference in such systems. The Principia, by contrast, relies on combination-
testing. This is because, as we’ll see, the target system has high interference.
We argue, Dann, that an ontic-driven explanation of this methodological dif-
ference is available. Establishing such a thesis requires more work, but for our
purpose of illustrating our framework and establishing its utility, availability
and plausibility are sufﬁcient.

4.1.1. Isolation-Testing in the Opticks Newton’s Opticks follows the quasi-
geometrical style of the Principia: it opens with a set of deﬁnitions and
axioms, before the theory is developed in a series of propositions (labelled
as either theorems or problems). Newton establishes each proposition exper-
imentally, calling the procedure “proof by experiments.” He begins by stat-
ing the proposition, then discussing a sequence of experiments which are

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supposed to establish the proposition beyond doubt. A discussion follows
explaining how the experiments support the proposition.20

Here we shall focus on the ﬁrst proposition of Book 1 part I.21 Proposition 1
theorem 1 states that “Lights which differ in Colour, differ also in Degrees of Refran-
gibility22” (Newton 1952, P. 20). This proposition is an important ﬁrst step in
establishing one of Newton’s key claims about light: that there is a one-to-one
correspondence between refrangibility and spectral color.23 Establishing this
correspondence enabled Newton to make use of geometrical properties of light
(rectilinear propagation, regular refraction and reﬂection, und so weiter) to make
inferences about the color-producing properties of light.24 The inference
might be reconstructed as follows:25

P1. There is a one-to-one correspondence between refrangibility and

spectral color.

20. These discussions also contain detailed instructions and illustrations, which suggests
that the reader was supposed to work through the experiments, perhaps even attempting to
replicate them, in order to grasp the truth behind the demonstrations.

21. Natürlich, by focusing on a single proposition, we do not do justice to the sophis-
ticated design of Newton’s experimental program, in which combinations of experiments
accumulate to establish a sequence of theoretical propositions. In diesem Papier, Jedoch, Wir
are interested in Newton’s Opticks insofar as it offers paradigm cases of isolation-testing. Der
experiments supporting proposition 1 provide a particularly clear and accessible example.
22. “Refrangibility” refers to the disposition of light to refract when passing from one
medium into another, or a “predisposition, which every particular Ray hath to suffer a par-
ticular degree of Refraction” (Newton 1959–1977, Bd. 1, P. 96).

23. The proposition which gets him the rest of the way to the one-to-one correspondence is in
Book 1 part II: proposition 2 theorem 2, “All homogeneal Light has its proper Colour answering to its Degree
of Refrangibility, and that Colour cannot be changed by Reﬂexions and Refractions” (Newton 1952, P. 122).
24. It is signiﬁcant that, in both the Opticks and the early paper on which it is based
(Newton 1672), Newton establishes geometrical properties of white light before consider-
ing color. (Certainly this fact has been lost on many of Newton’s critics, both then and
now.) There are at least two good reasons for this. zuerst, a technological limitation: Es
was one thing to isolate and manipulate small rays of light, but it was much more difﬁcult
to isolate and manipulate a single color, which required extraordinary precision and very
good eyesight. Zweitens, as we’ve already seen, Newton’s aim was to develop a rigorous
mathematical science of optics: angles, sizes, shapes, and positions were things that he
could talk about mathematically; hue, saturation and brightness were not.

25. This inference can be seen more explicitly in a letter to Huygens (23 Juni 1673).
Hier, Newton sets out his account in ﬁve deﬁnitions and ten propositions. Proposition 1
corresponds to my P2, propositions 2 Und 3 together correspond to my P1, and propositions
4 Und 5 together correspond to my C (Newton 1959–1977, Bd. 1, P. 293). (Propositions
6–10 offer an account of colored bodies.) Newton claims that proposition 4 is derived from
deﬁnitions 1 Und 3 and proposition 1, and that proposition 5 is derived from deﬁnitions 1
Und 3 propositions 2 Und 3. It is a remarkable feature of Newton’s theorising strategy that
he frequently provided two lines of support for his propositions: (1) demonstration via de-
duction from established propositions and (2) demonstration via experiment.

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P2. White light is composed of rays of many refrangibilities.
C. White light is composed of rays of many spectral colors.

Newton provides two experiments in support of proposition 1. In experi-
ment 1 Newton draws a line down the centre of a piece of black card, Und
paints one half red and the other half blue. Then he uses sunlight to illu-
minate the card, and peers at the card through a prism, which he holds
close to his eyes (siehe Abbildung 2 below). When he tilts the prism upwards,
the card appears to move upwards, the blue half (dg) appearing higher than
the red half ( fe). When he tilts the prism downwards, the card appears to
move downwards, the blue half (δν) appearing lower than the red half
(φε). From this experiment, Newton concludes that the blue light refracts
to a greater degree than the red light, and hence the blue light is more re-
frangible than the red light:

Wherefore in both Cases the Light which comes from the blue
half of the Paper through the Prism to the Eye, does in like
Circumstances suffer a greater Refraction than the Light which
comes from the red half, and by consequences is more refrangible.
(Newton 1952, P. 21)

In experiment 2, Newton takes the same piece of card and winds
“a slender Thred of very black Silk” (Newton 1952, P. 23) around it, Also
that several horizontal black lines pass across the colors. He stands the card
upright against a wall, so that the colors stand vertically, side-by-side, Und

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Figur 2. The Opticks, Book 1 part I, ﬁgure 11 (Newton 1952, P. 22)

142

Newton on Islandworld

illuminates it with a candle. He places a glass lens at a distance of six feet
from the card, and uses it to project the light coming from the illuminated
card onto a piece of white paper which is at the same distance from the lens
on the other side (siehe Abbildung 3 below). He moves the piece of white paper
to and fro, taking precise note of where and when the red and blue parts of
the image are most distinct (the purpose of the black thread is to indicate
distinctness: the image is most distinct when the lines created by the
thread are sharpest). He ﬁnds that when the red part of the image appears
most distinct, the blue part is faint and blurred; and when the blue part of
the image is most distinct, the red part is faint and blurred. And that, In
order to obtain a distinct red image, the paper has to be held 1½ inches
further away than it is to obtain a distinct blue image. He concludes:

In like Incidences therefore of the blue and red upon the Lens, Die
blue was refracted more by the Lens than the red, so as to converge
sooner by an Inch and a half, and therefore is more refrangible.
(Newton 1952, P. 25)

Newton takes these experiments to establish proposition 1: that rays of
different colors are differently refrangible. He does this by isolating red
and blue light, and then projecting the light through glass to observe its
geometrical properties. In the first experiment, zum Beispiel, the colored
card serves to isolate the colored light and the prism projects the light,
causing it to bend.

The one-to-one correspondence between refrangibility and spectral color was
important for at least two reasons. zuerst, it established that refrangibility
and color are connected. Newton didn’t think that one was the cause of
the other—that, sagen, refrangibility caused the ray to be a certain color, or vice
versa. Eher, he thought both refrangibility and color were original proper-
Krawatten, primary properties, of light. Somit, when white light is projected

Figur 3. The Opticks, Book 1 part I, ﬁgure 12 (Newton 1952, 27)

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through a prism, the rays separate (via refraction) to reveal their individual
colors. Zweitens, it established that there is no interference between the two
properties. Mit anderen Worten, Newton could neither change the original color of
a ray of light by refraction, nor change the refrangibility of a ray of light by
changing its color (e.g. by mixing it with another color). Refrangibility and
spectral color were, according to Newton, ﬁxed and immutable properties of
light.

Although this case is a particularly clear example of Newton’s reasoning
from experiment to proposition, the discussion thus far is insufﬁcient to
argue that the method of Newton’s Opticks (or even just the method of
Book 1) followed the mathematico-experimentalist approach we discussed
über. If space was no concern and our primary purpose was establishing
such a claim, we might be tempted to work through all the experiments
that contribute to establishing P1. But here we’re interested in showing
that a plausible, ontic-driven, explanation of the differences between
Newton’s approaches to different systems is available—thus highlighting
the utility of our account of ontic-driven explanations, and its suitability to
historical contexts. We take these experiments to be paradigm cases of
isolation-testing, analogous to Islandworlders examining equidistant
islands to establish L1, and examining islands of equal size to establish
L2 and L3. The successful use of isolation-testing suggests a system of
low interference.

4.1.2. Combination-Testing in the Principia Newton’s Principia deals with
the motions of bodies and the forces that produce them—books 1 Und 2, mit
the motions of bodies qua abstract mathematical objects; Buch 3, mit dem
motions of celestial bodies as revealed via observation. In book 3, Newton
puts forward his theory of universal gravitation, which states that any two
bodies in the universe attract each other with a force that is directly pro-
portional to the product of their masses and inversely proportional to the
square of the distance between them. On Islandworld, we sought to estab-
lish each law separately—in establishing L1, we went hunting for islands
which were equidistant from the mainland and the equator. In the case of
universal gravitation, such isolation testing is impossible. Warum? Weil, als
we shall see, bodies interfere with one another. Und so, Newton’s strategy in
the Principia departed from that of the Opticks: using his three laws of
Bewegung, he employed a creative mixture of combination-testing and a kind
of proxy isolation-testing to establish his laws. Let’s examine this in more
detail.

Newton established his theory of universal gravitation in two stages.
Erste (in books 1 Und 2), he modelled the laws. He started with a one-body
System, in which a single body orbited a central point. In a one-body sys-
tem, and in the absence of external forces, the body would remain either at

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rest or in uniform rectilinear motion—in accordance with law 1 (the law of
inertia). So Newton conceived of circular motion as a combination of two
Dinge: uniform rectilinear motion and a centrally directed force that draws
the body away from its rectilinear motion. These together cause the body
to orbit the central point. From law 2 (the net force law), and its corollar-
ies, Newton was able to calculate the motions produced by various forces,
und umgekehrt. Newton found that, if the centrally-directed force dimin-
ishes with the square of the distance between the body and the central
Punkt (i.e. an inverse-square centripetal force), then the body would display
Keplerian motion.26

Having demonstrated the results of laws 1 Und 2 in a one-body system,
Newton added a complexity. In the one-body system, the body orbited a
central point; Jetzt, he made that central point a body. In a two-body sys-
tem, law 3 comes into play. In this case, law 3 amounted to mutual attrac-
tion: the central body acted on the orbiting body and vice versa. The result
was that both bodies were now in motion, orbiting their combined center
of gravity. Newton demonstrated that, with a small correction to the har-
monic law, both bodies would display Keplerian motion, both with respect
to one another and with respect to their common center of gravity.

Newton then proceeded to add further complexity in a step-by-step
Mode. So far, he had treated the bodies as mass points; now he considered
them as objects with shape and dimension. He added a third body orbit-
ing the original one (as the moon orbits the Earth which orbits the Sun27),
und so weiter. He considered orbits of different shapes, forces of different
strengths, and even complex situations involving the motions of multiple
bodies on different planes. This modelling stage was akin to a series of
isolation tests on a mathematical system. By carefully adding complexity,
one step at a time, Newton was able to establish the consequences of his
laws and to learn how they interact in complex systems. We submit that
this can be illuminatively understood as a series of proxy isolation tests,
with Newton’s mathematical system acting in place of real celestial ob-
Projekte. (As mentioned in the introduction, the complexity of target systems
is sometimes appealed to in explaining modelling practices in science—
considering such work as “proxy isolation testing” strikes us as a promising
thought, which we leave for later development).

26. Keplerian motion can be deﬁned by three rules now known as “Kepler’s laws”: (1)
the orbit of a planet is an ellipse, with the sun at one of the two foci; (2) a line segment
joining a planet and the Sun sweeps out equal areas in equal times; Und (3) the square of the
orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Sehen
Wilson 2000 for an account of how these propositions came to be regarded as “laws.”

27. Obwohl, he did not draw this explicit connection until book 3.

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In the second stage (Buch 3), Newton established the resemblance be-
tween his models and his target system: the motions of celestial bodies. Er
started by treating each of the ﬁve primary planets as a one-body system;
noting that, generalized and idealized, the ﬁve primary planets approxi-
mate Keplerian motion with respect to the Sun. He also noted that the
moons of Jupiter and the moons of Saturn, orbiting their respective
planets, approximate Keplerian motion, and that the Moon approximates
Keplerian motion with respect to the Earth. Jetzt, Newton had already
established that, in a one-body system, a body displays Keplerian motion
if and only if it is maintained by an inverse square centripetal force. Also
idealized, the planets and moons also display Keplerian motion. Somit,
Newton was able to infer that the planets and moons maintain their
motions by an inverse square centripetal force. He concluded that this
force was gravity—i.e., the force that causes an apple to fall to the ground.
Dann, in a series of de-idealizations, Newton established that, as the Sun
exerts a gravitational pull on each of the planets, so the planets exert a grav-
itational pull on the Sun. Ähnlich, the moons exert a gravitational pull on
their planets. And ﬁnally, the planets and moons exert gravitational pull
on each other. Zusamenfassend, he conceived of the solar system as a complex series
of pair-wise interactions. Newton argued ﬁrstly, that each pair (d.h., jede
planet-moon, sun-planet and sun-moon system) in isolation would dis-
play Keplerian motion (both with respect to one another and with respect
to their common center of gravity). And secondly, that every deviation
from Keplerian motion could, grundsätzlich, be accounted for by identify-
ing every pair-wise interaction. To demonstrate this, he used observational
data to show that Jupiter and Saturn sensibly perturb one another to pre-
cisely the degree predicted by the law.28 And so Newton was able to ex-
plain why the planets and moons only approximate Keplerian motion:
every body attracts every other body with a force that is proportional to
its mass and diminishes with the square of the distance between them.

In sum, in the Principia, Newton sought to establish his theory of universal
gravitation. The challenge he faced was to establish and measure centripetal
forces acting on orbiting celestial bodies. He was unable to measure these
forces directly, because it was not possible to observe celestial bodies in iso-
lated one- and two-body systems. Jedoch, by modelling the laws of motion
in increasingly complex systems, Newton was able to learn how bodies be-
have, when acted upon by inverse-square forces from multiple sources. Nur

28. George Smith refers to this process as detection of second-order phenomena. For his
discussion of the role of perturbation-detection in Newtonian mechanics see Smith 2014.
And for a detailed discussion of Newton’s reasoning to universal gravitation (Book 3 prop-
osition 7 and its corollaries) (see Harper 2011, S. 291–99).

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in the abstract world of Newton’s mathematics could bodies be studied as
isolated one- and two-body systems. In the real world, each body—each planet,
moon, sun, and comet—mutually attracts every other body. Also, in examining his
mathematical system, Newton engaged in a kind of proxy isolation testing; In
establishing universal gravitation, he relied on combination testing. It was only
by taking into account each pair-wise interaction that he was able to produce
highly accurate explanations of celestial motion. By analogy, Islandworlders
without access to isolation-testing could establish laws 1–3 by showing how
they each together predicted species richness across Islandworld’s islands.

4.2. Comparing the Opticks and the Principia
We have characterized Newton’s methodology as “mathematico-experimental.”
Newton’s propositions were deduced from experimentally established prin-
ciples. We have examined the strategies by which Newton established his
principles in the Opticks and the Principia. In the former case, he proceeded
via isolation; in the latter, via combination. In light of our framework for
ontic-driven explanations of scientiﬁc method, we submit that this differ-
ence in method can be explained by the nature of the systems he investi-
gated. Newton’s optical system was amenable to isolation-testing: he could
gather together rays of a single color and manipulate them as a single beam
to establish geometrical properties. An analogous test in the Principia would
involve isolating a single planet to observe its motion around an empty
center. But even if Newton could do this, the experiment would not yield
results, because gravity is a relational property: there is no gravity in a one-
body system, because there is nothing to attract the body. And if Newton
could isolate a two-body system, he would have to deal with perturbations
caused by mutual attraction. Mit anderen Worten, in Newton’s celestial system,
the pair-wise interactions of bodies are not independent of one another. In
response to these ontic challenges, we saw Newton adopt two complemen-
tary epistemic strategies. zuerst, he represented the bodies abstractly—via a
mathematical model—and carried out something like an isolation test
on that proxy. Zweitens, he tested via combination: a complex series of
pair-wise interactions that could produce the approximate Keplerian
motion he was after to support his theory of universal gravitation.

Let’s return to our question: how can we reconcile Newton’s uniﬁed
methodological statements with his disparate approaches to optical and
celestial systems? One promising answer, we submit, is ontic-driven.
Newton’s celestial target exhibits much higher interference than his optical
target. The source of the interference in mechanical systems is the universality
of gravity—as each body effects the motion of every other body, physical
isolation cannot be achieved. On Islandworld, the various islands do not
interact with one another in ways which generate interference—and nor

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does the refrangibility and spectral color of sunlight in the Opticks. Und so
Newton took different routes to establishing the principles of his celestial
and optical systems: the former via combination (and proxy-isolation), Die
latter via isolation. With the principles established, the mathematical arm
of Newton’s method came into play. The central difference in method, Dann,
is the approach to the experimental arm. Faced with two systems exhibiting
different amounts of interference, Newton needed to employ different strat-
egies for experimentally establishing the principles. Daher, an ontic-driven
explanation of the difference not only ﬁts, but also brings certain features
of Newton’s investigations into sharper focus: nämlich, the parallel roles
played by isolation- and combination-testing. This ontic focus, we think,
complements the focus on traditions, biography and social factors of many
of Newton’s commentators.

But what can we say about the varying success of the two projects? As we
mentioned earlier, Newton’s theory of universal gravitation was undoubtedly
an enormous success—consequently, the Principia is usually considered to be
the crowning achievement of seventeenth-century natural philosophy. And
yet, his attempts to mathematize and explain optical phenomena were ulti-
mately considered, no more so than by himself, a failure—and a failure spe-
ciﬁcally of his method.29 Space forbids detailed discussion, but we submit that
the answer, wieder, may be ontic-driven. Where we emphasized interference
to explain the difference in method, we suspect that noise has something to
tell us about success. Noise, you will recall, undermines the applicability of
theory. Exogenous factors muck up our system’s tidy, regular behavior.

Newton’s theory of universal gravitation applied both to terrestrial ob-
jects and celestial ones—including comets. And so it had enormous power
to unify, explain and predict.30 His optical theory, Jedoch, did not fare so
well once it left the conﬁnes of the experimental system of book 1. zuerst,

29. Ducheyne follows Cohen in arguing that the Opticks is an “incomplete treatise," In
that Newton fails to offer a completed account of diffraction phenomena (what Newton
calls “inﬂexion”) Und, stattdessen, concludes the treatise with a series of queries (Ducheyne
2012, S. 181–84; Cohen 2001, S. 18–23). Ducheyne moreover points out that “Optical
phenomena did not easily lend themselves to a Principia-style physico-mathematical treat-
ment” (Ducheyne 2012, P. 219). He attributes this difﬁculty to problems of epistemic
Zugang: in mechanics Newton had a good understanding of the entities that constitute
the explananda, but in optics, he did not. In der Tat, any ideas he had regarding the nature
of light were hypotheses, and therefore, best avoided by his own methodological decree.
Daher, Ducheyne’s explanation is ontic-driven in part. We take ourselves to be offering a
more nuanced ontic-driven explanation; one which engages with particular features of the
interaction between methodology and the target system at hand.

30. Tatsächlich, on Earth, noise entered the system in the form of air resistance. In the scho-
lium to the laws, Newton described some experiments which allowed him to deal with this
(Newton 1999, P. 424).

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despite his best efforts in book 3,31 Newton failed to construct a mathe-
matical model of diffraction. The properties of this system interfered with,
d.h., caused exceptions to, his putative “laws” of optics—in particular, sein
assumption of the rectilinear propagation of light. The principles Newton
employed in book 1 were no match for the complexities of such phenom-
ena, and he never came close to matching the scope and rigor of his model
of universal gravitation. Und so, he was unable to draw from his observations
any conclusions that he was willing to assert as propositions. Zweitens, In
contrast to the clear and forceful statement of achievements and conclusions
that we ﬁnd in the Principia, Newton concluded his Opticks with a list of
increasingly speculative questions.32 Thus, admitting openly that this
conclusion could only pose questions, and not answers.33

Based on this discussion, we can contrast Newton’s two systems in
terms of the dimensions we presented in Figure 1. Newton’s celestial
mechanics targets a relatively quiet system: there is high interference,
but low noise. Newton’s optical systems are comparably noisy: interference
is low, but noise is high. This ontic contrast accounts for both the differing
methodologies and the differing successes of the two projects.

4.3. A Wild System: Book 2 of the Principia
We would be remiss if our discussion of Newton’s successes (and failures)
did not (at least brieﬂy34) consider book 2 of the Principia, which studies
the forces of resistance to motion in various types of ﬂuids—and is widely
considered to be a failure.35 We’ll highlight two relevant aspects: (1) Die

31. These are well-documented by Shapiro (2001).
32. Even Newton’s theory of ﬁts in Book 2 War, at best, a mixed success. While he
eventually succeeded in producing a mathematical account of the colors of thin plates, Es
was poorly received, and the properties of ﬁts (i.e. the action occurred in the direction of
Bewegung) were incompatible with diffraction (which needed a cause that could act transverse
to that direction) (Shapiro 2001). Und doch, despite these failures, Book 2 was extremely
important and inﬂuential. Zum Beispiel, Newton’s experiments on thin plates in book 2
offered tools for investigating matter at extremely small dimensions (on the order of
1/100,000 of an inch) and extremely great distances (z.B., the planets and even distant stars)
(Sepper 1994, S. 128–29).

33. While Newton’s queries are usually taken to represent a failure of the Newtonian
method, we cannot ignore the historical fact that they were extremely inﬂuential, forming
the basis of the experimental science of electricity (Cohen 1956).

34. For the details of Newton’s work on ﬂuid resistance, see Smith 2001, 2005.
35. At least partly for this reason, Buch 2 has been largely ignored by scholars. In der Tat,
Clifford Truesdell remarked that this book is, to all intents and purposes, “the part of the
Principia that historians and philosophers, scheinbar, tear out of their personal copies”
(Truesdell 1970). Notwithstanding its failures, Buch 2 has been important and inﬂuential
to the development of a science of ﬂuid resistance (this is discussed by Smith in the intro-
duction to Newton 1999, S. 188–94).

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mixture of combination-testing and proxy isolation that was so successful
for celestial mechanics fails in the case of ﬂuid resistance; (2) Das, Wir
submit, is due to the system under investigation being a relatively wild
System.

The aim of book 2 was to understand the forces operating on bodies in
ﬂuids. Newton understood total resistance as a function of several kinds of
resistance and properties of the ﬂuid (such density and viscosity), repre-
sented by the following equation:

Rtotal ¼ a þ bv þ cv2

Where a, B, and c are coefﬁcients that demanded empirical determination.
Newton applied the same methodology here as he did in his study of uni-
versal gravitation, aiming (1) to ﬁnd a mathematical solution for the prob-
lem and (2) to isolate the physical mechanisms in order to understand their
separate contributions to the motion. And so the goal of Newton’s work on
ﬂuid resistance was to disaggregate the coefﬁcients and determine their
individual magnitudes.

Newton carried out two experimental programs concerned with ﬂuid re-
sistance. The ﬁrst is a program of pendulum experiments, in which a pen-
dulum bob moved through air, Wasser, and mercury. Newton inferred
resistance forces from the rate of decay of the pendulum motion in these
different ﬂuids. The second is a program of vertical fall experiments. Diese
involved dropping spheres of different sizes and different materials in various
ﬂuids—some of these experiments were conducted inside the newly—or
almost—completed St Paul’s Cathedral in London. Newton inferred resis-
tance forces from the time it took the bodies to fall a certain distance.

We have already argued that the success of the theory of universal
gravitation can be attributed to two factors. Erste, the phenomena were
such that the contributions of individual bodies could be disaggregated.
Newton conceived of the inverse-square centripetal force as the primary
cause of celestial motion. Deviations from Keplerian motion could then
be treated as second-order phenomena: evidence of additional sources of
attraction. Zweite, the system was relatively free from noise. In the con-
text of celestial motion, gravitational forces swamp all other forces, Und
so the observational data was very regular and predictable. We now sug-
gest that Newton’s study of ﬂuid resistance failed because the system in
question was problematic with respect to both factors: it was wild, exhib-
iting both comparatively high noise and interference.

zuerst, Newton was unable to disaggregate the contributions of differ-
ent kinds of resistance. There were both theoretical and experimental rea-
sons for this. The problem was that the data contained too much variation

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to serve as the basis for investigating secondary factors, d.h., ﬂuid friction
and tenacity. This suggested that he hadn’t properly isolated the inertial
contribution. In his vertical fall experiments, he treats inertial resistance as
a greater cause, assuming that it swamps the other resistance forces. Somit,
he treats the other components as lesser causes, d.h., as noise. This led him
to attempt to control for those features, das ist, not include them in his
theoretical understanding of the system in question. It is now understood,
Jedoch, that these components are better thought of as interference: Sie
affect inertia in ways that cannot be disaggregated. Mit anderen Worten, inertia
can neither be theoretically nor physically isolated from other contribu-
tionen. Zum Beispiel, forces arising directly from viscosity are often negligi-
ble, but even then, indirect effects of viscosity govern the forces arising
from ﬂuid inertia. (In the ﬁrst instance, Newton tried to treat viscosity
as noise, but it was really interference.)

Zweitens, Newton was unable to anticipate the sources of noise in his
System, such as surface ﬁnish, local small irregularities and even rotation
(and other irregular motions of the bodies). Tatsächlich, the shape of the body
was much more crucial than he realized. Newton knew that his results
didn’t hold for shapes other than spheres (z.B., disks). But the small pro-
tuberance at the top of a spherical pendulum bob, where it attaches to the
string, had a much larger effect than he realized.36

It is notable that we are still unable to calculate the forces of resistance
acting on spheres, not to mention any other shapes, from theory alone.
Testing in wind tunnels and so on is required. Interference is so high that
it is difﬁcult even to establish what’s part of the system and what isn’t.
The source of the interference is the complexity of ﬂuid resistance. An
Matthewson’s account (discussed in section 3.1), complexity is the result
of a large number of components interacting in a complicated way. (Recall
that complexity does not entail heterogeneity across systems—the same
components may still be involved in every case). In ﬂuid resistance, fric-
tion, tenacity, and other features such as surface ﬁnish interact in such
complex ways that they forbid disaggregation. As we noted earlier, manche-
times interference is unsolvable in principle: two components are necessar-
ily entangled. This is such a case.

Newton tried to use the same methodology to understand ﬂuid resis-
tance as he had to understand celestial mechanics. But the system wasn’t
amenable. We submit that it is the ontic aspects which draw apart the

36. Tatsächlich, faced with this (at the time) unknown source of resistance, and in the ab-
sence of any other likely explanation, Newton suggested that the additional resistance was
an artefact of the experiment: the to-and-fro motion of the pendulum created a current in
the ﬂuid, which was, in effect, another source of resistance.

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success of Newton’s celestial mechanics, and the failure of his ﬂuid dynam-
ics.37 In the face of such a wild system, it’s not clear what he could have
done differently.

5. Abschluss
Our discussion of Newton had two purposes. The ﬁrst was to illustrate and
apply the machinery we developed in sections 2 Und 3. We have argued
that contrasting “interference” and “noise” offers a framework for under-
standing the ontic-driven explanations of scientiﬁc method that scientists
and philosophers of science often provide. The second was to articulate a
novel claim about Newton’s methodology. The difference between his “ex-
perimental” and “mathematical” work, we suspect, was not that one was
experimental and the other, mathematical. Eher, he established his prin-
ciples using different—but both ultimately experimental—methods. Wir
think it is illuminating and fruitful to explain this in terms of ontic dif-
ferences between the systems Newton examined. One was quiet; the other,
noisy. Just as the epistemic strategies and successes of Islandworld bio-
geography can be understood in the ontic-driven terms we have presented,
Also (at least potentially) can Newton’s actual scientiﬁc achievements.

As we discussed in the introduction, philosophers, Historiker, Und
sociologists of science often emphasize socio-historical factors. And rightly
so—we often cannot understand Newton (or ecological debate, or macro-
evolution) in vacuo. We must take into account the inﬂuences, intellectual
climate, and traditions of the time, as well as technological and theoretical
Kapazität. Jedoch, in all this rich detail, an important aspect which can be
missed—or at least left underemphasized—is the nature of the system under
investigation. In Newton’s case, we saw that an ontic-driven explanation
potentially defuses the tension between his apparently uniﬁed methodolog-
ical statements and his apparently disuniﬁed approach to actual science.
There is a place—even in history—for ontic-driven explanation.

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37. Smith draws a similar conclusion in Smith 2001.

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