## 1. Hume's Evaluation of Newton



This section analyzes Hume's relationship to the public Newton
and other early interpreters of Newton as available to Hume. The
analysis reveals that Hume is more critical of and less indebted to
core elements of Newton's philosophy than commonly thought. A
benefit of this analysis is that many interpretive debates over how to
understand Hume's philosophy can be reformulated clearly and
with fewer anachronisms.



Hume's explicit reflections on Newton's writings and
character reveal a more ambivalent picture than commonly thought: Hume
shows respect, even admiration for Newton's achievements, but he
also expresses reservations. Behind this ambivalence one can find
serious philosophic objections to Newton's life and project.
This section looks, first, at Hume's brief discussions of
Newton's life and achievements and, then, analyzes the aims
behind Hume's "science of man".



Hume does not doubt the longevity of Newton's intellectual
achievement: 



> 
> 
> The severest scrutiny, which NEWTON'S theory has undergone,
> proceeded not from his own countrymen, but from foreigners; and if it
> can overcome the obstacles, which it meets with at present in all
> parts of Europe, it will probably go down triumphant to the latest
> posterity. ("Of the Rise and Progress of the Arts and
> Sciences", EMPL 121) 
> 
> 
> 



But elsewhere, when Hume comments more directly on Newton, there are
signs of ambivalence: 



> 
> 
> Were we to distinguish the Ranks of Men by the Genius and Capacity
> more than by their Virtue and Usefulness to the Public, great
> Philosophers would certainly challenge the first Rank, and must be
> plac'd at the Top of human Kind. So rare is this Character,
> that, perhaps, there has not, as yet, been above two in the World, who
> can lay a just Claim to it. At least, Galileo and Newton seem to me so
> far to excel all the rest. ("Of the Middle Station of
> Life", EMPL 550) 
> 
> 
> 



According to Hume, Newton has unusual philosophic talent. Yet, the
backhanded nature of Hume's compliment is unmistakable.
Newton's work is not characterized by its virtue; the
achievements of Newton's philosophy are not very useful to the
rest of mankind. For Hume there is a moral point of view from which
Newton's achievements may seem less than entirely
praiseworthy.



This ambivalence about Newton is not an isolated incident in
Hume's writings. In the last volume of *The History of
England*, Hume writes:



> 
> 
> In Newton this island may boast of having produced the greatest and
> rarest genius that ever arose for the ornament and instruction of the
> species. From modesty, ignorant of his superiority above the rest of
> mankind; and thence, less careful to accommodate his reasonings to
> common apprehensions: More anxious to merit than to acquire fame: He
> was, from these causes, long unknown to the world; but his reputation
> at last broke out with a lustre, which scarcely any writer, during his
> own life-time, had ever before attained. (HE VI, 542)
> 
> 
> 



In this passage, Hume singles out Newton as the "greatest
genius" (no mention of Galileo this time). Hume is following
Fontenelle's interpretation of Newton as a modest genius not
concerned with acquiring fame (Fontenelle 1728--see
 Other Internet Resources
 below). But again, Hume's praise is not entirely
straightforward. It turns out that part of Newton's achievement
is due to his failure to possess two kinds of self-knowledge: Newton
did not understand how much smarter he was than others and Newton did
not understand how far removed from ordinary people's concerns
his theories were. Hume implies that if Newton had been more
self-aware and more attuned to the environment in which he was
writing, he would have been more likely to adjust his mode of
reasoning to public prejudice. On Hume's account Newton did not
properly understand his relationship to his readership and,
paradoxically, this partly accounts for Newton's success. It
seems not to have occurred to Hume that Newton's mode of
presentation in the *Principia* was a deliberate one to avoid
controversy with those who could not follow its intricate geometric
arguments--an intention Newton makes explicit in the introduction
to Book 3 of the *Principia*.



Moreover, Hume thinks that in certain other respects, Newton shares in
the superstitious prejudices of his time. This shows another sense in
which Hume's admiration for Newton's genius is limited.
While defending the stylistic abilities of King James I, Hume
comments: 



> 
> 
> [King James I] has composed a commentary on the Revelations, and
> proved the pope to be Antichrist; may not a similar reproach be
> extended to the famous writer Napier; and even to Newton, at a time
> when learning was much more advanced than during the reign of James?
> From the grossness of its superstitions, we may infer the ignorance of
> an age; but never should pronounce concerning the folly of an
> individual, from his admitting popular errors, consecrated by the
> appearance of religion. (HE V, 155) 
> 
> 
> 



However, Hume did not doubt Newton's religious sincerity: 



> 
> 
> It is for the same reason, I maintain, that Newton, Locke, Clarke,
> etc. being Arians or Socinians, were very sincere in the creed they
> profest: And I always oppose this argument to some libertines, who
> will needs have it, that it was impossible, but that these
> philosophers must have been hypocrites. (NHR 12.23n78)
> 
> 
> 



Thus, Hume has no doubts about the intellectual quality of
Newton's achievements. His reservations are moral even
theological in nature. One can distinguish these along a private and a
public dimension. Hume thinks that Newton's life reveals a man
with genuine limitations in understanding (let alone transcending)
himself and his times. Hume calls into question the moral quality of
Newton's works because they do not serve the public interest and
they, and the Newtonians that follow him, are infected with
superstitious beliefs (this line of argument is pursued more fully in
Russell 2008). While Hume's criticism of Newton as a man are
revealing of Hume's understanding of what it is to be a
philosopher, Hume's criticism of the purpose behind
Newton's project ties directly to the anti-Newtonian aims of
Hume's "science of man". This project is viewed by
many contemporary scholars, who emphasize Hume's
"naturalism", as Hume's equivalent of what one today
would call "cognitive science" (Garrett 1997).



While Hume admits that Newton was the "greatest genius"
that "ever arose for the ornament and instruction of the
species", he is unwilling to acknowledge Newton's
"Virtue" or "Usefulness to the Public".
Moreover, Newton's project lends cover for gross
"superstition". Instead, in the "Introduction"
to the *Treatise*, Hume offers an ambitious alternative
project: his "science of man". (In EHU 1.12 he calls it a
"true metaphysics", which battles "abstruse
philosophy and metaphysical jargon...mixed up with popular
superstition". Given Hume's criticism of Newton, he may
have Newton in mind here.) Hume emphasizes the foundational nature of
this project:



> 
> 
> There is no question of importance, whose decision is not comprised in
> the science of man; and there is none, which can be decided with any
> certainty, before we become acquainted with that science. In
> pretending, therefore, to explain the principles of human nature, we
> in effect propose a compleat system of the sciences, built on a
> foundation almost entirely new, and the only one upon which they can
> stand with any security. (THN "Introduction", see Boehm
> 2016)
> 
> 
> 



The success of Hume's systematic "science of man"
has a positive and a negative component. On the positive side, 



> 
> 
> In these four sciences of Logic, Morals, Criticism, and Politics
> [i.e., political economy], is comprehended almost everything, which it
> can any way import us to be acquainted with, or which can tend either
> to the improvement or ornament of the human mind. 
> 
> 
> 



Hume makes it absolutely clear where his priorities are: 



> 
> 
> Nor ought we to think, that this latter improvement in the science of
> man will do less honour to our native country than the former in
> natural philosophy, but ought rather to esteem it a greater glory,
> upon account of the greater importance of that science, as well as the
> necessity it lay under of such a reformation. 
> 
> 
> 



In short, according to Hume his "science of man" is far
more valuable than Newton's natural philosophy. This is why Hume
ends the "Introduction" to the *Treatise* with the
claim that 



> 
> 
> we may hope to establish...a science [of man], which will not be
> inferior in certainty, and will be much superior in utility to any
> other of human comprehension.
> 
> 
> 



Moreover, the content of the "science of man" reveals that
even the very Newtonian sciences of 



> 
> 
> Mathematics, Natural Philosophy, and Natural Religion, are in some
> measure dependent on the science of MAN; since they lie under the
> cognizance of men, and are judged of by their powers and faculties.
> (THN "Introduction") 
> 
> 
> 



For Hume the "science of man" is the
"foundational" science because it is presupposed to some
degree by all the other sciences (see also Hazony 2014; Hazony &
Schliesser 2016; Boehm 2016, 2019).



The details of Hume's "science of man" show the
weakness of our ordinary cognitive capacity; at the same time it
offers an argument for staying within confines of (potential) ordinary
experience. Hume's cognitive science has a normative consequence
in that knowledge of it is supposed to reduce the inclination toward
intellectual overreaching. For, the practitioners of "mitigated
scepticism" (cf. the "modest scepticism" of
"Appendix" to the *Treatise*) will not 



> 
> 
> be tempted to go beyond common life, so long as they consider the
> imperfection of those faculties which they employ, their narrow reach,
> and their inaccurate operations. (EHU 12.3.25) 
> 
> 
> 



Hume's "science of man" constrains the extent of our
theorizing. In subsequent sections it will be illustrated how Hume
reinterprets the limits and content of Newtonian natural philosophy in
light of his "science of man" or "true
metaphysics".


## 2. Hume's Scientific Education



There is surprisingly little direct evidence of Hume's knowledge
of Newton's texts. Most of it is circumstantial. Recent archival
and careful hermeneutic research by Michael Barfoot (1990) has
increased our knowledge of the kind of education in different elements
of natural philosophy Hume would have received as a student at
Edinburgh (see also Emerson 2009; Stewart 2005; Wright 1990). This
usefully supplements what can be gleaned from Hume's writings
and letters. While new material may show up one day, four important
conclusions follow from his study.



First, it is very likely that Hume was exposed to many works in the
new natural philosophy, medicine, and mathematics in Europe and
Britain. Second, while Hume was a student, Boyle's writings and
methodology were emphasized at The University of Edinburgh. It appears
that Boyle was favored as the pre-eminent exemplar of modern natural
philosophy because of the theological uses of this form of knowledge
in eighteenth century natural religion. Given the tenor of the
education at Edinburgh and evidence derived from Hume's oeuvre,
it is very likely that Hume had a working knowledge of Boyle's
hydrostatics. Besides, if Hume's project aims at an account of
hidden processes underlying observed regularities (as Landy 2017
suggests), as opposed to inductively establishing those regularities,
then Hume's project is consonant with much of Boyle's (see
Sargent 1995).



Second, while at the Jesuit College at La Fleche
(1735-37) Hume was certainly exposed to Cartesian and
Malebranchian ideas (Perinetti 2018), and some of his most influential
arguments, concerning, e.g., causation and natural theology had their
origins in this intellectual environment. Some commentators (e.g.,
Wright 2009: 51ff) have argued that the proper interpretation of
Hume's methodological aspirations and his account of the mind
should spring primarily from this Cartesian and Malebranchian
context.



Third, Hume would have been reasonably familiar with Newton's
*Opticks*, especially his writings on colors. It is less clear
how thorough his working knowledge of it was (see Schliesser 2004 for
some concerns). However, it is less likely that he was exposed to most
of the technically challenging parts of *Principia*. As the
catalogue at La Fleche testifies, there was four entries
directly related to Newton, of which only one, a 1720 French edition
of Newton's *Opticks* (but no edition of
*Principia*), refers to an edition that could have been there
during Hume's stay (Perinetti 2018: 51). Moreover, if Hume never
read the third edition of the *Principia*, then this could help
explain his lack of interest in Newton's fourth rule of
reasoning which was added to the third edition (see
 section 4.5,
 Rules of Reasoning).



Fourth, it remains unclear how proficient Hume became in mathematics.
There is manuscript evidence that he attended George Campbell's
extramural lectures on
 fluxions.[2]
 These notes require careful study, but Barfoot reports that these
manuscripts show "little evidence of the application of fluxions
to natural philosophy as such" (1990: 190 fn76). Barfoot is
correct to suggest that Hume's treatment of mathematics shows
debts to Berkeley's criticism of Newton. There is less evidence
for Barfoot's claim that Hume would have had working knowledge
of the most technical parts of the *Principia*.



It is likely that Hume did get to know the relevant editions of
*Opticks* already during his years spent at the University of
Edinburgh, and may well have been exposed to lectures on it as well,
but it is uncertain how reliable his working knowledge of it was
(Barfoot 1990, esp. 158 and 152). Although in general he was
dissatisfied with university education, at least he found some
satisfaction in his natural philosophy class taught by Robert Steuart
(Stewart 2005: 21-25). A probably more important introduction to
the outlook that has spread due to the influence of the
*Opticks* came from Hume's medical readings in relation
to his mental breakdown at the age of 18. The most important document
of this struggle is his 1734 "Letter to a Physician"
(*Letters* 1:14-18.), in which the medical description of
his condition, as M.A. Stewart (2005: 24n48) puts it, "seems to
be consciously modelled on George Cheyne's *The English
Malady*", published in 1733. A similarly likely source is
Mandeville's *Treatise of the Hypochondriack and Hysterick
Diseases* (1st ed. 1711, 2nd ed. 1730, see
Wright 2009: 8-9). In his latter life he probably benefitted
from discussions with philosophical friends and colleagues, most
notably with William Cullen and Joseph Black, these discussions,
however, came only after the publication of Hume's chief
philosophical works. These friendships were indeed philosophical in
the sense that they were founded, at least partly, on sympathies for
Hume's philosophical project (see, e.g., Hume's letter to
Cullen in *Letters* 1:163)



It should be emphasized, however, that archival evidence may radically
change our picture of Hume's formal education and continuing
interest in Newton's natural philosophy. In addition to the
manuscript mentioned above, known marginal notes in Hume's hand
in a copy of the *Edinburgh Review*, where works in Newtonian
natural philosophy were reviewed, may reveal further evidence about
the nature and quality of his response to issues in Newtonian natural
 philosophy.[3]


## 3. Hume's Berkeley-ian View of Newton's Achievements



In *The History of England*, Hume writes about Newton's
research methodology as follows: 



> 
> 
> there flourished during this period a Boyle and a Newton: men who trod
> with cautious, and therefore the more secure steps, the only road
> which leads to true philosophy...[Newton is] cautious in
> admitting no principles but such as were founded on experiment; but
> resolute to adopt every such principle, however new or unusual. (HE
> VI, 542) 
> 
> 
> 



While this is rather terse, Hume calls attention to three important
elements in Newton's natural philosophy: (a) Newton's
commitment to an experimental method; (b) the cautious nature of
Newton's methodology; (c) Newton's boldness once
experiments have established a "principle". In eighteenth
century terminology, a "principle" is akin to what we
would call a "law" or a "fundamental/causal
explanation". In order to avoid misunderstanding, Hume equates
Newton's methodology with Boyle's only on points (a) and
(b), not point (c). Moreover, Hume is aware (as will be shown in
 section 4.1)
 that Newton rightly rejected Boyle's conception of mechanism.
So, Hume admires Newton's methodology, and sees it as a source
of progress.



So, for Hume, Newton uses experiment to arrive at explanations. Thus,
he seems to echo and accept Newton's claim about
"*hypotheses non fingo*" (see the relevant section
in the
 entry on Newton).
 Once such "principles" or explanations have been arrived
at experimentally, Hume sees Newton as adopting them boldly, even if
they are unusual or surprising. Hume appears to have assimilated the
importance of Newton's third rule of reasoning (see
 section 4.5
 below). Moreover, Hume is discerning the (broad) outlines of
Newton's commitment to the method of analysis and synthesis
(Newton's *Opticks*, Query 31; for discussion, see
 section 4.7).
 But in Hume's account there is no mention of the importance of
mathematics in Newton's methodology (see
 section 4.6).
 Hume lack of interest in this aspect of Newton's methodology
may be a consequence of his education (see
 section 2).



Nevertheless, Hume's interpretation of the status of
"principles" makes him deviate from Newton's
methodology in a fundamental fashion. In the *Treatise*, he
uses the "science of man" to claim it is "beyond the
reach of human understanding" to "penetrate into the
nature of bodies, or explain the secret causes of their
operations". He cannot "approve" of the ambition to
go beyond knowing bodies by their external properties (THN 1.2.5.25).
This contradicts the final paragraph of the "General
Scholium" of the *Principia*, where Newton promises a
program of research, perhaps inspired by the success of Francis
Hauksbee's electrical experiments, to penetrate into the nature
of matter. Although this program was by no means finished by the time
of Newton's death, Newton's optical research had revealed,
for example, that light has an internal constitution characterized by
the proportions, in it, of the distinct homogeneal (or
"uniform") kinds, which have different degrees of
refrangibility (Schliesser 2004).



To see why Hume cannot "approve", going beyond external
properties of bodies, let us take a brief detour through some core
elements of Hume's epistemology. For Hume, we build up our
causal theories from experience of particular events (see, for
instance, the demands at THN 1.3.14.6-15 and also the footnote
at EHU 11.26). This is an important constraint for Hume because it
allows him to ask who has ever perceived an instance of a power or
force in action. This is crucial for Hume's attack on
theoretical and invisible entities.



For Hume all our simple ideas are derived from impressions (THN
1.2.3.2-3). Hume's attacks on notions of substance, mode,
essence, force, power, self, and--of course--God, all rely
on his rhetorically powerful ability to ask to what impression such
notions can be traced (e.g., THN 1.1.6; 1.2.5.28; 1.4.14, and
1.4.5.3-4; on idea of God, see EHU 2.6). For, "[I]deas
always represent the objects or impressions, from which they are
derived" (THN 1.2.3.11). In the scholarly literature, this has
become known as the "copy principle" (Garrett 1997:
chapter 2). If no such objects or impressions are to be found, then
one must conclude that such ideas are the product of "passions
and emotions" (THN 1.1.6.1), a "trivial suggestion of the
fancy" (THN 1.4.7.6), or "some imperfection in [the]
faculties [of mind]" (THN 1.1.7.8). The thrust of Hume's
account is to make talk of, say, substance or force (power, God, etc.)
seem either meaningless or restricted to the particular qualities of
bodies from which the idea is derived (THN 1.1.6.1; EHU 4.2.16). At
best, they have reference to "an effect, or some other event
constantly conjoined with" the cause (EHU 7.2.29; for a more
detailed account, see the entry on Hume ).
 Thomas Reid, who saw what was at stake, described the strategy as
"a tribunal of inquisition erected by certain modern
philosophers before which every thing in nature must answer"
(*An Inquiry into the Human Mind: or the Principles of Common
Sense*, Chapter 6, Section VIII). 



Hume's "science of man" will not permit a realist
interpretation of forces as real causes (see, for different arguments,
Broughton 1987; Bell 1997). When the sciences talk about forces or
powers, these words must be reinterpreted (for example, the note to
EHU, 4.2.16 tells us to look for this in section 7 of EHU). According
to Hume, word's like "force" and "power"
have, at best, a reference to "an effect, or some other
event". And 



> 
> 
> Force, Power, Energy...[these] words, as commonly used, have very
> loose meanings annexed to them; and their ideas are very uncertain and
> confused. (EHU 7.2.29; cf. THN 1.3.14.27) 
> 
> 
> 



Hume denies here the fundamental achievement of the
 *Principia*.[4]
 Rather, he offers a reinterpretation of Newton (Hazony &
Schliesser 2016).



This is made very clear by his addition to the *Treatise*: I
must, he writes, 



> 
> 
> confine our speculations to the appearances of objects to our senses,
> without entering into disquisitions concerning their real nature and
> operations. 
> 
> 
> 



Hume is willing to grant that Newton has experimentally discovered
various "principles". But given Hume's aversion to
talk of forces, it is likely that he thinks these principles must be
understood at best as a means to keep track of the phenomena. This is,
in fact, for Hume the 



> 
> 
> *Newtonian* philosophy ... rightly understood ...
> Nothing is more suitable to that philosophy, than a modest skepticism
> to a certain confession of ignorance in subjects that exceed all human
> capacity. (THN 1.2.5.26n12; emphasis in original) 
> 
> 
> 



In context, Hume re-describes the Newtonian commitment to a vacuum. So
when, elsewhere, Hume describes the "philosopher" [i.e.,
Newton] who had "determined the laws and forces, by which the
revolutions of the planets are governed and directed", (EHU 1.8)
his language of "forces" must be interpreted in light of
his deflationary commitments.



One may think that Hume's use of "Newtonian
philosophy" in the addition to the *Treatise* suggests
that Hume has described Newton's natural philosophy as Newton
understood it (as understood by Hume). But this is not likely because
elsewhere he writes, 



> 
> 
> It was never the meaning of Sir ISAAC NEWTON to rob second causes of
> all force or energy; though some of his followers have endeavoured to
> establish that theory upon his authority. (footnote at the end of EHU
> 7.1.25: a note on Hume's Terminology: God is the "first
> cause;" "second causes" are ordinary finite causes
> that operate in nature) 
> 
> 
> 



So, first, Hume's Newton accepts some real causes in nature;
Hume's Newton is neither a skeptic about causation nor an
occasionalist (Leibniz had raised this concern in his exchange with
Clarke). Second, Hume is careful to distinguish Newton from the
Newtonians (for more evidence on this, see
 section 4.2).



Thus, a more likely interpretation is that Hume believes he has
offered a prescriptive interpretation of how Newtonian philosophy
should be viewed in light of the results of his "science of
man" (which shows the limitations of our cognitive capacity),
and his restrictive form of Empiricism which contribute to his
"modest" (or "mitigated") skepticism. Hume may
well have thought himself as an internal critic or "cautious
Newtonian". For Hume and Newton both appeal to the authority of
experience. Nevertheless, the "copy principle" guides how
Hume believes how "experiment" or
"experience"--authoritative for Newton as well as
Hume--should be analyzed. This may be why Hume claims that Boyle
and Newton have shown the road to the "true philosophy",
not that they completed it. One way to understand Hume's
"science of man" is to see it, then, as the fulfillment of
the Newtonian philosophy, "rightly understood", that is,
by Hume.



While Hume does not match Berkeley's detail in offering
arguments or in explaining how to reinterpret Newtonian invisible
entities, Hume does not accept that we can know that invisible causal
forces operate in a largely empty universe as anything other than
useful means to track the appearances. In fact, there is no room in
Hume's explanatory model for invisible forces acting as causes.
This becomes clear if we reflect on a passage that has received
intense scrutiny in the context of the problem of induction (which we
ignore for present purposes; for Hume's skepticism see
 section 4.2):



> 
> 
> We are determined by custom alone to suppose the future conformable to
> the past. When I see a billiard-ball moving towards another, my mind
> is immediately carry'd by habit to the usual effect, and
> anticipates my sight by conceiving the second ball in motion. There is
> nothing in these objects, abstractly considered, and independent of
> experience, which leads me to form any such conclusion: and even after
> I have had experience of many repeated effects of this kind, there is
> no argument, which determines me to suppose, that the effect will be
> conformable to past experience. The powers, by which bodies operate,
> are entirely unknown. We perceive only their sensible qualities: and
> what reason have we to think, that the same powers will always be
> conjoined with the same sensible qualities? 
> 
> 
> 
> Tis not, therefore, reason, which is the guide of life, but custom.
> That alone determines the mind, in all instances, to suppose the
> future conformable to the past. However easy this step may seem,
> reason would never, to all eternity, be able to make it. (THN Abstract
> 15-16)
> 
> 
> 



Hume here is calling attention to the (terse) argument of
*Treatise* 1.3.6. Our interest is in his claim that 



> 
> 
> [t]he powers, by which bodies operate, are entirely unknown. We
> perceive only their sensible qualities: and what reason have we to
> think, that the same powers will always be conjoined with the same
> sensible qualities? 
> 
> 
> 



In dialectical context, Hume is here presupposing (i) an explanatory
model familiar from Locke (and Spinoza, Aristotle, Boyle, etc.) in
which hidden powers (insensible qualities) of an entity are (causally)
responsible for the sensible qualities. So, it is completely natural
for early modern natural philosophers to say that these sensible
qualities express the essence. These hidden powers may be (part of)
the essence of the entity or (as Newton suggests about gravity in the
third rule of reasoning) universal qualities of an entity. So,
Hume's implied targets accept something akin to (i). That is not
insignificant because (i) is the main explanatory template of early
modern science.



Now, if one accepts (i), then the problem of induction reveals two
(related) problems: (a) one concerns the connection *among*
sensible qualities, and (b) the other concerns the connection between
hidden qualities and the visible qualities. So, if one accepts (i),
one might have thought, for example, that routinely (if not
exception-less) conjoined sensible qualities must always presuppose
the same combination of hidden/invisible qualities that produce them.
So, one could solve the problem associated with (a) by an appeal to
hidden qualities. In thinking this one could, in fact, appeal to a
same effect/same cause principle of the sort Newton articulates in the
second rule of reasoning: "to the same natural effects we must,
as far as possible, assign the same causes". To be sure,
Newton's version of the rule recognizes exceptions and is
clearly regulative ("as far as possible") and it does not
rely on (i). Rather, in Newton the rule is a direct consequence of a
parsimony principle ("admit no more causes of natural things
than such as are both true and sufficient to explain their
appearances").



But as Hume discerns, the explanatory model of (i) lacks resources to
secure anything like "same visible effect/same hidden
cause". That's because Hume thinks there is always a
barrier in moving from sensible qualities to the structure of hidden
qualities. (In the literature on Newton, who also rejects (i), this is
called the "transduction problem" since an influential
article by McGuire 1970a.) Hume makes this point fully explicit in the
first *Enquiry*: "he has not, by all his experience,
acquired any idea or knowledge of the secret power, by which the one
object produces the other" (EHU 5.4).



This is why Hume's philosophy of science is so deflationary: all
any science can show is the relations that obtain among visible
qualities, and perhaps those that can be represented on an analogy
with them (see Landy 2017). These relations can be grouped together
and given names ("elasticity, gravity, cohesion of parts,
communication of motion by impulse") and be treated as
"causes" of the phenomena, but these names do not signify
or explain features of hidden powers. In Hume's philosophy of
science, science remains at the surface. Hume made the point explicit
in a note added to the *Treatise*: 



> 
> 
> If the Newtonian philosophy be rightly understood it will be found to
> mean no more. A vacuum is asserted: That is, bodies are said to be
> plac'd after such a manner, as to receive bodies betwixt them,
> without impulsion or penetration. The real nature of this position of
> bodies is unknown. We are only acquainted with its effects on the
> senses, and its power of receiving body. (THN 1.2.5.26n12 (App.))
> 
> 
> 



This barrier between visible and hidden qualities/powers is
independent of the more fundamental problem of induction that even
when one grasps, in some way, the structure of the hidden qualities
ordinarily responsible for conjunction of sensible qualities, one
cannot feel secure about their presence and role in any claim one
makes about sensible qualities. For, a different set of hidden
qualities may be responsible for any ordinarily conjoined set of
sensible qualities. (Hume here discerns the outlines of the problem of
multiple realization as a general metaphysical problem.) That, in
addition, nature may change its course (and so change the
configuration of hidden qualities that produce sensible qualities)
means that the main explanatory framework of early modern science (i)
is without foundation (see also Belkind 2019).


## 4. In What Sense Was Hume a Newtonian?


### 4.1 Experimentalism



It is often argued that the subtitle of the *Treatise*,
"Attempt to Introduce the Experimental Method of Reasoning into
Moral Subjects", shows Hume's self-conscious debt to
Newton. Experiments certainly play an important role in Newton's
science. But only after 1712 does Newton refer to his own philosophy
as "experimental" (in the context of his polemic with
Leibniz; see Shapiro 2004). In general, Newton emphasizes the
mathematical nature of his philosophy; he calls attention to this in
the full title of the *Principia*: Mathematical Principles of
Natural Philosophy.



However one interprets Hume's "experimental method",
it is in no sense mathematical. Hume's so-called
"experiments" do not have the tacit logic of Newtonian
experiments; they almost never offer measurements (which are very
important for Newton's focus on successive approximation); they
do not connect to a tight mathematical structure (Smith 2002).
Moreover, by the standards of Newtonian natural philosophy, many of
Hume's so-called "experiments", for all their
ingenuity (see, e.g., the eight experiments at THN 2.2.2), have a
rather simple structure. They are more akin to systematic observations
(cf. THN I.8, 1.3.8.3, 1.3.12.11, 3.3.1.10). In fact, there is
(almost) nothing to distinguish Humean "experiment" from
normal, daily experience. In Hume the word "experiment"
seems to be nearly synonymous with "experience", which is
not uncommon in the period. This interpretation is also suggested by
Hume's description of his experiments as being based on "a
cautious observation of human life" (THN
"Introduction"). This is why Hume can claim that 



> 
> 
> experimental inference and reasoning concerning the actions of others
> enters so much into human life, that no man, while awake, is ever a
> moment without employing it. (EHU 8.1.17) 
> 
> 
> 



Even if we allow for some hyperbole, it would betray considerable
ignorance to confuse Newton's "experimental method"
with ordinary human "experimental inference and
reasoning".



So it is not so much the production of data that makes Hume's
method experimental rather than his way of "processing"
the data gathered in various forms of experiments. This method can be
reconstructed as a version of analysis and synthesis inspired by
Newton's *Opticks* (see
 section 4.8
 below), that begins with phenomena from the historical and everyday
observation of human behavior, and its analysis proceeds by such
"experiments ... judiciously collected and
compar'd" (THN I.10), in order to arrive at analogies
among various instances "from the observation of several
parallel instances" (EHU 8.13). The products of comparative
analysis so conducted are the principles of various faculties, like
perception, imagination, reason, etc., whose interaction results in
ideas and impressions causing behaviour, but their contribution can
hardly be measured and the principles of their interaction can hardly
be quantified--not even in principle (see also Hume's
anti-mathematicism discussed in
 section 4.7).
 So their relations cannot be represented in an algebraic way, in
terms of relations of quantities, so they cannot be mathematized
either. Instead, they remain qualitatively different principles of
human nature, and the explanation of human phenomena consists in a
description of how these principles with their distinctive
characteristics figure in producing them.



These findings are generalized by induction: "What I discover to
be true in some instances, I suppose to be so in all" (THN
2.1.5.1), and consequently, they are fallible, and the account of
human nature founded on them may be misconstrued (THN 1.2.5.19). Even
if it is sometimes possible 



> 
> 
> to attain what natural philosophers, after Lord BACON, have affected
> to call the experimentum crucis, or that experiment which points out
> the right way in any doubt or ambiguity. (EPM 5.17) 
> 
> 
> 



It is rarely so. Therefore, inquiry into moral matters is just as
open-ended as inquiry into natural matters, and the cure is the same
here as there, pretty much as Newton envisaged: it is in further
enquiry (Smith 2002: 160-161). So, for Hume experimental
findings can and need to be further refined by methods that rightly
belong to the family of Newtonian successive approximations: by
exploring exceptions and limitations, or by eliminating superfluous
conditions in order to identify the efficacious one (Demeter 2019b). One could see this feature
of Hume's method as anticipating Mill's method of
difference as much as resembling Newton of *Opticks* (see
 Section 3.3 of the entry on John Stuart Mill).


### 4.2 Skepticism



In our analysis of Hume's "science of man", we have
already encountered Hume's claim that we are unable to penetrate
into the internal constitution of matter
 (section 3).
 So, however else Hume's skepticism is understood--and it
has been the subject of intense scholarly discussion (including the
so-called "New Hume" debate, see Read & Richman 2000)
during the last three decades--the science of man has skeptical
implications with regard to his interpretation of Newton's
philosophy. Hume's evaluation of Newton is an additional source
of evidence in understanding the nature of Hume's skepticism.
This evidence reveals that in evaluating Newton's achievement
Hume is pessimistic about the extent and possibility of knowledge of
nature. It also shows that Hume rejected important Newtonian
standards/criteria in evaluating the claims of natural philosophy.



In *The History of England*, Hume writes:



> 
> 
> Boyle was a great partizan of the mechanical philosophy: a theory,
> which, by discovering some of the secrets of nature, and allowing us
> to imagine the rest, is so agreeable to the natural vanity and
> curiosity of men...While Newton seemed to draw off the veil from
> some of the mysteries of nature, he shewed at the same time the
> imperfections of the mechanical philosophy; and *thereby* restored her
> ultimate secrets to that obscurity, in which they ever did and ever
> will remain. (HE VI, 542; emphasis added)
> 
> 
> 



This quote reveals crucial details about Hume's position in
three areas: a) Hume's understanding of the relative merits of
Newton's philosophy and the mechanical philosophy of Boyle; b)
Hume's attitude toward criteria of intelligibility; c)
Hume's skepticism.



First, Hume treats Newton's account as a refutation of the
mechanical philosophy. Yet, while as we have seen
 (section 3),
 Hume certainly saw it as part of the road to "true
philosophy", he does not view Newton's achievement as a
decisive advance in knowledge of nature but, instead, as decisive
evidence for the claim that nature will remain unknowable in
principle. Hume understands Newton's success as a double-edged
sword: even if Newton removed a source of error and/or enlarged our
knowledge, he did so at the cost of undermining any hope of
establishing what we might call a "final theory" (see the
 entry on physicalism).
 Moreover, it is by no means clear whether Hume is willing to accept
Newtonian natural philosophy as a form of knowledge. A natural reading
of the passage is to conclude that Hume views Newton as successfully
(to use an anachronistic term) falsifying the mechanists'
program, while Hume hedges his bets on offering any evaluation of the
positive side of Newton's system (notice also the grudging use
of "seemed").



The way to make sense of Hume's remarks in *The History of
England* is that they reveal that he implicitly accepts the
Mechanists' insistence--explicitly associated with
Boyle--that theirs was the only program that offered the
possibility of intelligible explanation (even if in the hands of many
of its practitioners it only offered hope of post-facto rational
reconstruction; see also Hume on Causation in
 section 4.4).
 Hume's treatment of Boyle reveals that he thought it was a good
thing Newton falsified the mechanical philosophy. Hume acknowledges
that the mechanical philosophy could offer some successful
explanations. But he emphasizes that its practitioners were likely to
overestimate--on psychological and methodological
grounds--its potential. Hume appears to have assimilated
Newton's devastating criticisms of the mechanical
philosophy.



Furthermore, the passage in *The History of England*, lends
support for a skeptical interpretation of Hume's philosophy.
Hume thinks the Newtonian project will enable some knowledge of nature
at the cost of keeping a "final theory" permanently
unavailable to human inquiry. Earlier Hume had offered a positive
account of the explanatory principles knowable to mankind: 



> 
> 
> Elasticity, gravity, cohesion of parts, communication of motion by
> impulse; these are probably the ultimate causes and principles which
> we shall ever discover in nature; and we may esteem ourselves
> sufficiently happy, if, by accurate enquiry and reasoning, we can
> trace up the particular phenomena to, or near to, these general
> principles. (EHU 4.1.12) 
> 
> 
> 



Let's leave aside, for the moment, the ultimate metaphysical
status of "ultimate causes and principles" in Hume's
thought. He is willing to accept that some limited set of fundamental
scientific laws (i.e., "ultimate causes and principles")
are available to human researchers. (Hume hedges his bets a bit; note
his use of "probably".) Moreover, these four principles
are all associated with Newton's project; the mechanical
philosophy had only accepted communication of motion by impulse as an
explanatory principle. Of course, Hume treats these laws not so much
as describing genuine "causes" or "powers" of
nature, but rather--in opposition to Newton's own view
which insisted on the reality and causal nature of forces (Janiak
2007)--as a way to keep track of the appearances (recall
 section 3
 above).



Finally, these passages show that Hume rules out that we could ever
hope to explain the causes of these laws (or unify them in some more
ultimate principle). Newton would agree he did not know the cause of
these laws ("General Scholium", *Principia*), but
he would treat it as a question open to further research and
speculation. In the context of a discussion of the doctrine of
occasionalism, Hume shows he is aware of this: 



> 
> 
> Sir Isaac Newton (tho' some of his Followers have taken a
> different Turn of thinking) plainly rejects it, but substituting the
> Hypothesis of an Aetheral Fluid, not the immediate Volition of the
> Deity, as the Cause of Attraction. ("A Letter From a Gentleman
> to his Friend in Edinburgh", THN p. 429) 
> 
> 
> 



This quote is revealing in two more ways: besides showing that Hume
may have been aware of some of Newton's attempts at articulating
a mechanism for the operation of attraction (i.e., Newton's
letters to Bentley or Boyle; see Newton 2004), Hume recognizes that
Newton's followers can deviate from Newton (recall
 section 3).



In light of the text of *The History of England* (VI, 542)
quoted at the start of this sub-section, it is clear Hume thinks that
Newton's laws are not sufficient for explaining all of nature.
So without (yet) taking a stance on how to interpret Hume's
treatment of induction or his account of causation, one can
distinguish two further strands of Hume's skepticism: i) Hume
treats Newton as showing conclusively that the domain of possible
knowledge will leave parts of nature unknown forever; ii) in
particular, this will include the cause(s) behind our fundamental
principles. The combination of (i-ii) entails that Newtonian
natural theology--a very popular eighteenth century intellectual
enterprise (see the
 entry on natural theology and natural religion)--is
 based on shaky foundations.



Together with Hume's emphasis on accounting for the phenomena in
his interpretation of Newtonian philosophy, Hume is far removed from
Newton's realist ontology of interacting forces (Janiak 2007;
Smeenk & Schliesser 2013). Two further sources for this difference
are revealed when we analyze Hume's departure from
Newton's account of causation
 (SS4.4)
 and Newton's rules of reasoning
 (SS4.5).


### 4.3 Fallibilism



One of Hume's great claims to fame is his articulation of what
has come to be known as the "problem of induction", or, to
use language closer to Hume's: the problematic status of
inferences. An informal way to express his insight is that no claim to
knowledge of matters of fact ought to be thought of as definitive
because in all of our inductive reasoning (or inferences) we
presuppose that the future will be the same as the past. But we can
never be certain that the future will be the same as the past because
the evidence for the assumption is based on the uniformity of nature
in the past. The uniformity of nature is presupposed in our knowledge,
but our belief in it cannot be secured by reason. Infamously, Hume
claimed the source of the belief is not reason but habit and our
confidence in it is derived from instinct (see Millican 1995). While
there is ongoing scholarly debate over the extent of Hume's
skepticism that follows from this insight, it is less controversial
that for Hume knowledge of matters of fact, whatever its ultimate
status in Hume's thought, is always tentative, subject to
revision. This is known as fallibilism. While Hume's argument
appears unique to him (although elements of it are prefigured in
Berkeley and the Dutch Newtonian, Willem 's Gravesande), the
position is anticipated by Newton.



Newton's fourth rule of reasoning reads:



> 
> 
> In experimental philosophy, propositions gathered from phenomena by
> induction should be considered either exactly or very nearly true
> notwithstanding any contrary hypotheses, until yet other phenomena
> make such propositions either more exact or liable to exceptions.
> (Newton 2004, *Principia*, Book III, Rule IV)
> 
> 
> 



The rule is that we should treat well-confirmed propositions as true
(or nearly true) until there are deviations that promote new research,
which, in turn, lead us to refine our original propositions or reject
them for new ones (Smith 2002). But while one has a theory, one must
not be distracted by possible differing explanations for the found
regularities until one has empirical reason. One accepts a theory as
true as a means to developing a better theory. As Newton writes in the
"Preface" to the *Principia*, "the principles
set down here will shed some light on either this mode of
philosophizing *or some truer one*" (emphasis added). Thus, Newton accepts that
physical inquiry is forward-looking and may be open-ended; not only
its theories may evolve, but also its methods. Rule IV implicitly
accepts that the future may bring surprises and new evidence, and,
thus, anticipates Hume's fallibilistic insights. As commentators
on Hume have noted, this strand of Hume's skepticism is shared
by Newton. It is less clear if Hume learned it from Newton because
there is no evidence that he was acquainted with Newton's fourth
rule of reasoning (added to the third edition of the
*Principia*); there is no equivalent in Hume's rules of
reasoning to Newton's fourth rule. In the section on
Hume's Rule of Reasoning
 (SS4.5),
 the significance of the absence of an equivalent to Newton's
rule 4 in Hume's thought is explored.


### 4.4 Causation



In
 section 3,
 we saw that Hume rejected Newtonian forces as real causes; he argues
that we must reinterpret forces and powers as being ideas about
effects (see also Hazony 2014; Hazony & Schliesser 2016). In that
section no reference to Hume's widely discussed views on
causation was made. In this section Hume's account of causation
is analyzed. Given our focus on the Hume-Newton relationship no stance
on the most controversial issue in Hume scholarship are taken: are
causes mere (psychological) regularity or are they found in nature.
However, recall that Hume insists that 



> 
> 
> It was never the meaning of Sir ISAAC NEWTON to rob second causes of
> all force or energy; though some of his followers have endeavoured to
> establish that theory upon his authority. (footnote at EHU 7.1.25)
> 
> 
> 
> 



So Hume's Newton accepts some real causes in nature.



Hume's account of causality covers at least five related issues:
(1) how we acquire an idea of cause; (2) what we mean by
"cause;" (3) how we reason about causes; (4) whether
causes are in the mind or in nature; (5) how we could infer the
existence of causes. In this section, we explore how Hume's
treatment of what we mean by "cause" illustrates
Hume's critical response to and departure from Newton's
philosophy (see also Schliesser 2007). Hume's treatment of
causation straightforwardly rejects at least two kinds of causes that
appear in Newton's philosophy: final causes and simultaneous
causes (Schliesser 2009). Moreover, we show that the structure of
Humean causes is deeply indebted to the Pre-Newtonian mechanical
philosophy associated with Boyle.



Hume analyzes how "our" notion of causality--one
applying to events that are contiguous, exhibit temporal priority of
the cause, and have constant conjunction (THN 1.3, Sections 2, 6, and
15)--is derived from experiencing constant conjunction of objects
that produce a union in the imagination (THN 1.3.6.16). Hume's
account is causal in its own terms, that is, his two definitions of
the meaning of "cause" (THN 1.3.14.31) are patterned on
the chain of events that he thinks lead people to acquire the idea of
cause. Hume's analysis is a first approximation of and unifies
what "Moderns" tend to mean by "causation". In
his hands, a redefined version of Aristotelian "efficient
causation" is the only kind of causation available for use (THN
1.3.14.32). There is, thus, a stipulative quality to Hume's
discussion (see also the treatment of his Rules of Reasoning, THN
1.3.15 discussed in
 section 4.5).
 One of the tacit targets of Hume's approach is Newton. For
Hume's treatment of causation rules out the permissibility of
Newton's appeal to "final causes" in the
justification of the (inductive and probable) argument from design in
the "General Scholium" of the *Principia*:
"we know [the Deity] only by his most wise and excellent
contrivances of things, and final causes" (for discussion, see
Stein 2002).



Moreover, while Hume and Newton both appeal to the authority of
"experience", there are further serious tensions between
Hume's account of causation and the contents of Newton's
natural philosophy. For Newton, the behavior of the moon in its orbit
and that of, say, apples falling on the earth have the same cause:
namely, the force of gravity, or weight, towards the earth
(*Principia*, Book III, Scholium to Proposition IV, Theorem
IV). This conflicts with the contiguity requirement, which Hume
considers "essential" to "causation" (THN 1.3.2.6).
It is hard to see how contiguity could be made consistent with the
universal nature of attraction. The most distant particles of the
universe attract each other. (The contiguity requirement notably
disappears in EHU.) More important, according to Newton the
acceleration produced by the exercise of a force is simultaneous with
that exercise--thus defying temporal priority (Smeenk &
Schliesser 2013). Hume claims that temporal priority of the cause is
"of no great importance" (THN 1.3.2.8), yet it appears
explicitly or implicitly throughout his treatment of causation. Be
that as it may, Hume explicitly attacks the possibility of an effect
being simultaneous with its cause (THN 1.3.2.7-8; Ryan
2003).



Finally, there is a fundamental structural similarity between Humean
causes and the causes favored by pre-Newtonian Mechanical philosophers
(i.e., Boyle, Huygens, etc; for a different argument, see McGuire
1972). They have the same structure: i.e., priority of the cause over
the effect, contiguity, and constant conjunction. Now, to be sure,
Hume is aware that Newton decisively refuted the Mechanical
Philosophy's program which insisted that explanations be cast in
terms of the impact of colliding bodies
 (section 4.2).
 Hume rejects the ontological and explanatory reductionism of the
Mechanical philosophy. Hume introduces eight "rules by which to
judge of causes and effects" (see
 section 4.5
 below) because it is "possible for all objects to become causes
or effects to each other" (THN 1.3.15). This is why Hume's
list of "ultimate causes" and "general
principles"--"Elasticity, gravity, cohesion of parts,
communication of motion by impulse" (EHU 4.1.12)--is more
inclusive than the Mechanical philosophy would allow.



So, even if we leave aside the controversial question to what degree
Hume would allow the existence and our potential knowledge of real
causes in nature (as discussed in the "new Hume" debate),
his analysis of what we mean by "cause" is hostile to
Newtonian natural philosophy. Hume rules out final and simultaneous
causes. The former play only a role in Newton's theology and
natural religion, but the latter are an integral part of what we could
his "science".


### 4.5 Rules of Reasoning



Consider these passages:



> 
> 1. The cause and effect must be contiguous in space and time.
> 2. The cause must be prior to the effect.
> 3. There must be a constant union betwixt the cause and effects. It
> is chiefly this quality, that constitutes the relation.
> 4. The same cause always produces the same effect, and the same
> effect never arises but from the same cause. This Principle we derive
> from experience, and is the source of most of our philosophical
> reasonings. For when by any clear experiment we have discovered the
> causes or effects of any phaenomenon, we immediately extend our
> observation to every phenomenon of the same kind, without waiting for
> that constant repetition, from which the first idea of this relation
> is derived.
> 5. There is another principle, which hangs upon this, viz. that
> where several different objects produce the same effect, it must be by
> means of some quality, which we discover common amongst them. For as
> like effects imply like causes, we must always ascribe the causation
> to the circumstance, wherein we discover the resemblance.
> 6. The following principle is founded on the same reason. The
> difference in the effects of two resembling objects must proceed from
> that particular, in which they differ. For as like causes always
> produce like effects, when in any instance we find our expectation to
> be disappointed, we must conclude that this irregularity proceeds from
> some difference in the causes.
> 7. When any object encreases or diminishes with the encrease or
> diminution of its cause, it is to be regarded as a compounded effect,
> derived from the union of the several different effects, which arise
> from the several different parts of the cause. The absence or presence
> of one part of the cause is here supposed to be always attended with
> the absence or presence of a proportionable part of the effect. This
> constant conjunction sufficiently proves, that the one part is the
> cause of the other. We must, however, beware not to draw such a
> conclusion from a few experiments. A certain degree of heat gives
> pleasure; if you diminish that heat, the pleasure diminishes; but it
> does not follow, that if you augment beyond a certain degree, the
> pleasure will likewise augment; for we find that it degenerates into
> pain.
> 8. The eight and last rule I shall take notice of is, that an
> object, which exists for any time in its full perfection without any
> effect, is not the sole cause of that effect, but requires to be
> assisted by some other principle, which may forward its influences and
> operation. For as like effects necessarily follow from like causes,
> and in a contiguous time and place, their separation for a moment
> shews, that these causes are not compleat ones. (THN 1.3.15)
> 
> 
> 



In *Treatise* 1.3.15, Hume states eight "rules by which
to judge of causes and effects" (see the block-quote above)
because it is "possible for all objects to become causes or
effects to each other". The source of these rules is ambiguous.
Although they "might have been supply'd by the natural
principles of our understanding" (THN 1.3.15.11), Hume provides
no evidence for this. Nevertheless, Hume thinks it is
"proper" to employ them in his "reasoning"
(THN 1.3.15.11; 1.3.15.2). Earlier in the Treatise, he was even more
adamant about the regulative character of these rules: 



> 
> 
> We shall afterwards take notice of some general rules, by which we
> ought to *regulate* our judgment concerning causes and effects; and
> these rules are form'd on the nature of our understanding, and
> on our experience of its operations in the judgments we form
> concerning objects. (emphasis added, THN 1.3.13.11; see de Pierris 2001) 
> 
> 
> 



So, while these rules may be derived from reflection on how our minds
work or some may be derived "from experience" (THN
1.3.15.6), they prescribe how we should ascribe causes to
"objects" in the world, especially in "most of our
philosophical reasonings". But on Hume's definition of a
cause (rules 1-3), rules 4-8 are at most useful
stipulations (Hume uses "to fix" at THN 1.3.15.2) that
help one identify causal relations. This is not the place to resolve
how Hume is entitled to the normative character of these rules (see
Martin 1993). Now we examine these rules and their debt to
Newton's.



The first three rules define what it is to be cause and effect: as we
have seen, they must be contiguous in space and time; the cause must
be a prior to the effect; there must a constant union between cause
and effect (THN 1.3.15.3-5). With the exception of these first
three (see
 section 4.4),
 Hume's rules of reasoning have a strong resemblance to
Newton's four "Rules for the Study of Natural
Philosophy" outlined at the start of Book 3 of the
*Principia* (third edition). For example, Hume's fourth
rule, "The same cause always produces the same effect, and the
same effect never arises but from the same cause", is explained
by 



> 
> 
> [F]or when by any clear experiment I have discover'd the causes
> or effects of any phaenomenon, I immediately extend our
> observation to every phenomenon of the same kind. 
> 
> 
> 



This echoes Newton's second rule of
 reasoning,[5]
 especially in its generalizing tendency, which Newton explicitly
asserts in his third
 rule.[6]
 That is to say, in his fourth rule, Hume makes explicit what is
implied by the simplicity of nature assumption in Newton's first
 rule:[7]
 that the same cause always produces the same effect. Also,
Hume's fifth rule is an articulation of Newton's first and
third rules. Hume's sixth rule is itself an extension of
Hume's fifth.



Hume's seventh and eighth rules do not directly echo
Newton's four rules. Hume admits, however, that one should be
cautious in applying and extending the seventh rule because one cannot
extrapolate from a "few experiments" (THN 1.3.15.9; he
appeals to the rule at 2.2.8.4). The example Hume offers (on the
relationship between heat and pleasure/pain) is about a mental
phenomenon. Even so we think there is an important critical
relationship between Hume's Rule VII and Newtonian gravitation
(what follows is taken over from Hazony & Schliesser 2016). This
relationship is not explicit in his text, it is established by
Hume's wording, which closely follows Newton's phrasing in
discussing gravity in the *Principia*: In his Book 3,
Proposition 7, Corollary 1, Newton describes gravitation as an action
in which "every attraction toward a whole arises from the
attractions toward the individual parts". In Rule VII, Hume
speaks in these same terms, arguing that a quality that
"encreases or diminishes with the encrease or diminution of its
cause", should be "regarded as a compounded effect,
deriv'd from the union of the several different effects, which
arise from the several different parts of the cause". And,
elsewhere in the *Treatise*, Hume writes explicitly of the
force of gravitation using just this language (THN 1.3.2.16). On the
face of it, then, Hume's Rule VII seems to adopt Newtonian
language in order to provide an alternative description of the kind of
extrapolation involved in establishing Newtonian gravitation.



But only the first half of Rule VII is compatible with Newton's
science. In the latter half, Hume turns against Newton, warning
against the attempt to "draw such a conclusion from a few
experiments" (THN 1.3.15.9). Indeed, we know quite well that
effects can vary proportionately within a certain range of experience
and yet behave completely differently outside of this range. Hume
gives the example of our experience of fire. 



> 
> 
> A certain degree of heat gives pleasure; if you diminish that heat,
> the pleasure diminishes; but it does not follow, that if you augment
> it beyond a certain degree, the pleasure will likewise augment; for we
> find that it degenerates into pain. 
> 
> 
> 



This argument, made with respect to heat, is no less applicable to the
Newtonian force of gravitation: what appears to be a strictly
proportional relation over a given range of experience can turn into
something quite different when one strays from this range.



What we have, therefore, is as follows. Newton's Rule III, which
is the basis for the claimed universality for his law of gravitation,
is met and replaced by Hume's Rule VII, whose intent is in a
certain sense precisely the opposite: The so-called universal law of
gravitation must be regarded only as characterizing a certain range of
human experience and no more. Extension of this law beyond our
experience (or beyond what "perceptible models" allow for,
see Landy 2017), whether into the heavens or the microworld, cannot be
admitted into science (except as "hypothesis"). And the
same will have to be said for all other qualities that are attributed
to bodies significantly outside of the bounds of our actual
experience. What to Newton is nothing less than the "foundation
of all natural philosophy"--his Rule III--is in
Hume's philosophy shown to be unnecessary for scientific
reasoning and of questionable validity.



This suggests that it is Newton's Rule II that Hume considers to
be "Newton's chief rule of philosophizing"--an
interpretation that fits well with what Hume writes about method in
both the *Treatise* and in his later writings. It also
reinforces the view that Hume rejects Rule III as being that part of
Newton's philosophy that is worthy of being adopted and
imitated. Indeed, Hume's point is precisely that it is
Newton's Rule II, chiefly, that we should be interested in. Rule
III, with its extravagant claims concerning the presence of supposedly
essential qualities in every body in the universe far from common life
is one we can afford to set aside. The view we have presented here is
at odds with that of Graciela de Pierris, who builds her discussion of
Hume's debt to Newton around Hume's putative embrace of
Newton's Rule III as the cornerstone for his philosophical
method (de Pierris 2006:
306-310, 312; for detailed criticism see Hazony & Schliesser
2016).



Hume's eighth rule is, as Hume himself implies, a refinement of
Hume's fourth rule; it prevents over-zealous causal ascription
to an object. (In his explanation of the rule, Hume presupposes the
spatial and temporal contiguity requirement of cause and effect, but
it is not an essential feature of the rule.) But the first part of it
("an object, which exists for any time in its full perfection
without any effect") appears to target non-Newtonian theological
or Spinozistic arguments, so will not be discussed here.



On Hume's interpretation, Newton's second rule is the only
rule that is said to be derived (un-controversially) "from
experience" (THN 1.3.15.6). It is a crucial rule because the
fifth and sixth rules are, by Hume's lights, extensions of the
fourth (THN 1.3.15.7-8). Moreover, the conjunction of
Hume's fourth and seventh rules produces a new rule: "An
effect always holds proportion with its cause" ("Of
Interest", EMPL 297). We can call this Hume's ninth rule.
If one assumes (or prescribes) that linear causal relationships are
the only possible ones, this new rule allows Hume to rule out
competing claims that posit the existence of causal relationships that
are not "proportional". Hume can use the rule as a
constraint on theory. It plays a prominent role in Hume's
political economy when he rejects Mercantilism and, more important for
our present purposes, in his criticism of the use of analogy in the
Newtonian argument from Design (see EHU XI, and *Dialogues*
Parts V-VII).



Hume's ninth rule also has Newtonian debts. Since the time of
Aristotle, many philosophers have asserted proportionality between
cause and effect in one fashion or another. Hume's ninth rule
echoes, for instance, a principle Leibniz uses quite frequently: the
principle of the equality of cause and effect. It is the basis of
arguments Leibniz gives for his conservation principles (e.g.,
Specimen Dynamicum). But Leibniz's formulation is in terms of
equality and not proportionality. Unlike Leibniz and other Cartesians,
Newton preferred to reason in terms of proportionality. Although
Hume's ninth rule is not derived from any of Newton's
official Rules of Reasoning, Newton does implicitly use a rule like
Hume's ninth throughout the *Principia*. For example, the
importance of a proportion between cause and effect is emphasized
throughout the treatment of the behavior of bodies in resisting fluids
(e.g., the Scholium to Proposition 40, Book 2, Section 7, especially
Experiment 14), which, given the importance, for Hume, of treating
money as a fluid ("Of the Balance of Trade", EMPL
312-315; see Schabas 2001) may have caught Hume's
attention. Hume also treats resistance in his footnote to the EHU,
7.1.15. Moreover, there is a prominent place in the *Principia*
(the Scholium following Proposition 69, Book I, Section 11), where
Newton implicitly transforms a version of Hume's seventh rule
into Hume's ninth rule in which proportionality is emphasized.
In this Scholium, Newton starts employing the language and emphasizing
the importance of proportionality. This is not ruled out by
Newton's own "rules", but it was not emphasized
there. This passage could have attracted Hume's attention for
two reasons: it is one of the few explicit methodological passages in
the *Principia*, and it offers an account of what Newton means
by "attraction". Hume was almost certainly aware of this
passage because the proper meaning of "attraction" is
discussed, with explicit appeal to Newton's intentions, in
Hume's footnote to EHU 7.1.25. Hume makes the ninth rule
explicit and uses it as a constraint with which competing theories (in
political economy, the argument from design, etc) can be ruled out.
Hume's use of it in his attack on the design argument is an
instance where Hume attacks Newton with Newtonian tools.



Moreover, there are two connected, important further differences
between Hume's and Newton's rules. First, Hume never quite
endorses the universal reach implied by Newton's third rule. For
Newton we extend the known qualities of bodies within our experimental
reach to all bodies in the universe. While it could be compatible with
Newton's third rule, Hume's fourth rule does not go that
far. There is one instance where Hume appears to accept an implication
of Newton's rule: "The production of motion by impulse and
gravity is an universal law, which has hitherto admitted of no
exception" (EHU 6.4). Leaving aside the fact that this would a
very puzzling way to express the inverse-square law, the context makes
clear that Hume has in mind causes that "are entirely uniform
and constant" on Earth, not their universal reach; this is why
in context his other examples involve the burning of fire and the
suffocation of every human creature by water. There is textual support
to suspect that Hume would deny the universal scope implied by
Newton's third rule. Hume states a "maxim" in a
footnote to section XI of EHU which argues against inferring new
effects from any cause only "known only by its particular
effects". This denies Newton's strategy of making ever
more audacious inferences (about planetary motions, the tides, the
shape of the Earth, comets, etc) based on the acceptance of universal
gravity (recall Hume's treatment of Newton's methodology
in HE, VI, 542, discussed in
 section 3).[8]
 The argument in favor of the "maxim" reveals the tension
with Newton's third rule:



> 
> 
> To say, that the new effects proceed only from a continuation of the
> same energy, which is already known from the first effects, will not
> remove the difficulty. For even granting this to be the case (which
> can seldom be supposed), the very continuation and exertion of a like
> energy (for it is impossible it can be absolutely the same), I say,
> this exertion of a like energy, in a different period of space and
> time, is a very arbitrary supposition. (EHU 11.26)
> 
> 
> 



Newton's first three rules offer a bold methodological program
that attempts to unify science across different periods of space and
time; it is a bet on the causal unity of nature. The maxim cautions
against overconfidence in this regard. Hume's caution is
prophetic because it turns out that sub-atomic entities behave very
differently than macroscopic bodies. However, it is not entirely
certain if one should ascribe the "maxim" in the footnote
to Hume because it is offered in the voice of a "friend",
who is pretending to be Epicurus.



Second, Hume lacks an equivalent to Newton's Rule 4. Hume is not
alone in ignoring rule 4. Even Reid and Priestley, who have much to
say about the authority of Newton's Rules of Reasoning, tend to
ignore the fourth rule (Tapper 2002). Adam Smith seems to have been
one of few eighteenth century figures to have taken it seriously
(Schliesser 2005a and 2005b). Recall (from
 section 4.2)
 that Newton's Rule IV can be viewed as (1) an encouragement to
find and exploit known deviations from the regularities one has
established in order to make them "more exact". (2) A
proposal about how to treat a theory, that is, as true until proven
otherwise. Hume seems to have not appreciated the first point at all
(Schliesser 2004). On the second point, we have seen that Hume shares
Newton's commitment to fallibilism. But this common commitment
also hides an important difference between Hume and Newton which is
connected to the observation just made about the contrast between
Newton's third rule and the maxim in the footnote to section XI
of EHU. Newton's fallibilism includes commitment to the truth of
the propositions within one's scientific theory until it is
proven to be false. Newton realizes that induction can never be
certain for all time; he does anticipate Hume in this respect. But it
is also an expression of Newton's "scientific
naturalism". Empirical science is authoritative until one has
empirical reason to refine theory. This means that at any time one
risks the danger of going beyond one's evidence, but this is the
methodological price one must pay to make further progress. In his
eagerness to combat Newtonian superstition, Hume is willing to be more
cautious.



Hume's omission of an equivalent rule has several implications
for his philosophy and its relationship to Newton's. First Hume
replaces the authority of natural philosophy by his own criterion, the
"copy principle", when it comes to existence claims (see
 section 2, of the entry on Hume).
 Only the ideas that can be traced to a distinct impression will be
permissible. Thus, Hume's "science of man", or
"true philosophy", offers to evaluate the claims of
natural philosophy from a privileged position. This is the sense in
which Hume is not a scientific naturalist.



Second, without commitment to the truth of a "scientific"
theory, Hume has conceptual elbow room for a distinction between the
provable, experimental claims of common life (including some parts of
natural philosophy) and the lesser, probable commitments of the more
abstract parts of natural philosophy. This, too, is a result of
Hume's "science of man". Recall (from
 section 1)
 that the Humean practitioners of "mitigated scepticism"
will not 



> 
> 
> be tempted to go beyond common life, so long as they consider the
> imperfection of those faculties which they employ, their narrow reach,
> and their inaccurate operations. 
> 
> 
> 



The distinction between a provable common life and the far less
probable parts of natural philosophy runs through all of Hume's
major works. Yet, its implications for Hume's attitude toward
Newtonian natural philosophy are not discussed until the Dialogues.
There, Cleanthes, the spokesperson for a Newtonian natural religion,
attacks the Humean position:



> 
> 
> They are even obliged to acknowledge, that the most abstruse and
> remote objects are those, which are best explained by philosophy.
> Light is in reality anatomized: The true system of the heavenly bodies
> is discovered and ascertained. But the nourishment of bodies by food
> is still an inexplicable mystery: The cohesion of the parts of matter
> is still incomprehensible...In reality, would not a man be
> ridiculous, who pretended to reject Newton's explication of the
> wonderful phenomenon of the rainbow, because that explication gives a
> minute anatomy of the rays of light; a subject, forsooth, too refined
> for human comprehension? And what would you say to one, who having
> nothing particular to object to the arguments of Copernicus and
> Galileo for the motion of the earth, should withhold his assent, on
> that general principle, That these subjects were too magnificent and
> remote to be explained by the narrow and fallacious reason of
> mankind?... In vain would the sceptic make a distinction between
> science and common life, or between one science and another. The
> arguments, employed in all, if just, are of a similar nature, and
> contain the same force and evidence. Or if there be any difference
> among them, the advantage lies entirely on the side of theology and
> natural religion. Many principles of mechanics are founded on very
> abstruse reasoning; yet no man, who has any pretensions to science,
> even no speculative sceptic, pretends to entertain the least doubt
> with regard to them. The Copernican system contains the most
> surprising paradox, and the most contrary to our natural conceptions,
> to appearances, and to our very senses: yet even monks and inquisitors
> are now constrained to withdraw their opposition to it.
> (*Dialogues* Part I)
> 
> 
> 



Cleanthes points out that if philosophy asserts the distinction
between common life and science, philosophy would set itself against
some of the best supported parts of natural philosophy which are often
most removed from common life. We may naturally think that the Sun is
in motion, but the reality behind the appearances can be very
surprising. Cleanthes's point is that philosophy cannot hope to
argue against the authority of science without looking as backward as
monks and inquisitors (who attacked Copernicanism).



For our purposes, there are three important features in
Cleanthes's discussion. First, he claims that the same kind of
correct reasoning applies to all domains. This is a very popular
argument among religious Newtonians (e.g., Reid). So just because
science deals with uncommon domains and obscure topics, it can still
contain "just reasoning". This is, in fact, one of the
major assumptions behind Hume's own Rules of Reasoning. So,
Cleanthes uses Hume's philosophy to undercut part of
Hume's anti-Newtonian strategy. Even if Philo were not bound by
Hume's philosophy (and there is no evidence he should be
considered a strict spokesperson for Hume), as a defender of the
epistemic priority of common life he has no resources to claim that
there is a different, correct form of reasoning for areas beyond
common life. Second, if there is a debate between science and common
life, the advantage is with science. No skeptic, who at least pretends
to be informed, is seriously willing to doubt the results of natural
philosophy. That is, by the last third of the eighteenth century
natural philosophy has an authoritative claim to knowledge even if it
is founded on very uncommon, "abstruse" principles. Third,
Cleanthes assimilates the success of natural philosophy to theology
and natural religion; he does not recognize a principled distinction
between science and religion. If Philo attacks natural religion he
attacks science itself. Contemporary advocates of "intelligent
design", who claim that it should be treated as a scientific
theory (see the
 entry on teleological arguments for God's existence),
 follow the same strategy as Cleanthes.



Initially it seems that Cleanthes's argument is left without a
response. So there appears no room for a principled difference between
common life, on the one hand, and natural philosophy and natural
religion, on the other hand. In the remainder of the Dialogues, Philo
makes sure not to be thought of as attacking natural philosophy again.
In the context where the intellectual authority of science has become
unchallengeable, Philo's best hope lies in driving a wedge
between natural philosophy and natural religion. This may explain why
in undermining Newtonian natural religion, Philo does not draw on some
core elements of Hume's philosophy: the "copy
principle" or Hume's attack on the permissibility of final
causes. Rather, throughout the Dialogues, Philo offers more narrow
arguments attacking the content of natural religion. So, while in Part
I of the Dialogues Philo has no immediate response to
Cleanthes's argument, later in the Dialogues he continues to use
some distinction between the secure reasoning available in common life
and those too far removed from it. For example, by using Hume's
ninth rule, Philo is critical of the use of analogy in making claims
about the nature of the first cause. Philo relies on common sense to
formulate the problem of evil--if God is all powerful then he is
responsible for natural and moral evil (see Part XI). At the end of
the Dialogue, Philo is willing to grant Cleanthes "*that the
cause or causes of order in the universe probably bear some remote
analogy to human intelligence*" (Part XII; emphasis in
original). So,
while Philo is unable to draw a conclusive, principled distinction
between natural philosophy and natural religion, he reduces the latter
to a very minimal thesis.



It may, of course, be possible that by the end of his life, Hume had
limited his aims to removing the "superstitious" elements
in Newtonianism (recall his criticism of Newton in Section 1). Perhaps he had given up on
claiming the priority of the science of man over natural philosophy.
But it would be a mistake to identify the posthumous Dialogues as
Hume's final, definitive philosophy. Hume appended an
"advertisement" to EHU, which was printed at the start of
the posthumous 1777 edition. After distancing himself (to some degree)
from his "juvenile work", the *Treatise*, he says
about EHU: "Henceforth, the Author desires, that the following
Pieces may alone be regarded as containing his philosophical
sentiments and principles". EHU contains, of course,
Hume's copy principle and the attack on final causes. Perhaps,
the closing remarks of Philo, where he apologizes for 



> 
> 
> intervening in the education and instruction of his [i.e.,
> Cleanthes's] pupil [i.e., Pamphillus--the official narrator
> of (and witness to) the dialogues among Philo, Cleanthes, and Demea],
> 
> 
> 
> 



should be taken more seriously by more of Hume's readers. The
Dialogues are Hume's efforts to educate the students of natural
religion; they are not a statement of Hume's positive
"science of man" or "true metaphysics".


### 4.6 Mathematics



There has been a persistent strain of criticism of David Hume that has
insinuated that he simply did not understand Newton or lacked
mathematical competence. But when Hume (or any other historical
figure) deviates from Newton this need not entail lack of
understanding, it can, depending on other evidence, also be taken as
informed criticism (Schliesser 2011). In Hume's case, critical
scholars also draw on a (1772) letter to William Strahan in which he
mentions a 1755 draft essay "On the Metaphysical Principles of
Geometry" that he withdrew upon the advice of his friend the
mathematician Lord Stanhope, "who convinced me that either there
was some defeat in the argument or in its perspicuity" (Newman
1981). This remark is taken as evidence of Hume's acknowledged
lack of competence in mathematics. But it could also be taken at face
value and an expression of scholarly integrity: he accepted a
compelling criticism.



However far his understanding of complex mathematics reached, he
advanced a radical sceptical challenge for mathematics, and thereby he
also undermined knowledge claims associated with demonstrative
reasoning (Meeker 2007). The sceptical problem arises from the
inexactness of geometrical ideas and the fallibility of our reasoning
processes. Geometry for Hume is about actual figures and shapes whose
ideas cannot be perfectly exact because our perceptual abilities are
limited, and reasoning based on these ideas inherits this inexactness.
Ideas relevant for arithmetic, i.e., numbers, do not suffer from this
imprecision, but arithmetical reasoning is just as fallible as human
reasoning in general. The outcome of our demonstrative reasoning must
be judged by a probabilistic judgment on the reliability of our
reasoning faculties, which in turn must be judged by a further
probabilistic judgment on the probabilistic judgment on the
reliability of our faculties. The apparent demonstrative certainty of
our mathematical reasoning degenerates into probability, and we are
left with fallible and uncertain conclusions even in our demonstrative
sciences (THN 1.4.1.2-6).



But Hume does not stop there: he offers a sceptical solution to this
challenge (Demeter 2019a). First he offers an *individual*
remedy for the mathematician: to go back and to check again his
reasoning, because "[e]very time he runs over his proofs, his
confidence increases" (THN 1.2.4.23). Secondly, *social*
processes are more effective in reducing doubt, because his certainty
is increased "still more by the approbation of his friends; and
is rais'd to its utmost perfection by the universal assent and
applauses of the learned world" (THN 1.4.1.2). Even if all
demonstrative knowledge remains probabilistic in this approach too,
the certainty of mathematical reasoning reaches its peak due to the
acknowledgment of epistemic peers.



The popularity of a mathematical proof (or demonstration) among
experts in the field naturally speaks in favor of the proof. This
feature is not peculiar to mathematical conclusions, because as Hume
points out: "I feel all my opinions loosen and fall of
themselves, when unsupported by the approbation of others" (THN
1.4.7.4). What makes mathematics peculiar is that, in addition to
individual reasoning, the approbation of the mathematician's
close circle of "friends", and the approval of the
scholarly community seem to be the *only* sources of
justification in matters of mathematics.



By connecting mathematical certainty to the approbation of others Hume
gives an essentially social character to mathematical knowledge. No
matter the different metaphysical and epistemic pedigree of its
branches, it is their practices that determine the certainty of
mathematical conclusions (THN 2.3.10.2). In practice geometrical
reasoning is elevated to the same level of certainty as our reasoning
in arithmetic and algebra--and his may be one way to explain why
the *Enquiry* (EHU 4.1, 7.1-2, 12.20) lists all of them
as demonstrative. The limitations of our practices, arising from human
nature, condemn all branches of mathematics to eventual fallibility
and uncertainty. But that is not the main lesson we should draw here.
What really matters is that despite this fallibility we
*generate* certainty through our predominantly social
practices. So geometry *in practice* can be as certain and
demonstrative as arithmetic is *in principle* demonstrative,
but in practice, fallible. Taken together, the metaphysics and
practice of mathematics leads us to pretty much the same epistemic
grounds in all branches of mathematics.



Hume's reservations about the demonstrability of mathematics
imply a critique of Newton's programme of mathematizing natural
philosophy (for details see Hazony & Schliesser 2016). This
criticism is not wholly implicit; rather Newton is very clearly the
target of remarks made in the context of Hume's discussion of
the principle of "infinite divisibility" in the paragraphs
subsequent to THN 1.2.4.17:



> 
> 
> we are not possess'd of *any* instrument or art of
> measuring, which can secure us from all error and uncertainty...
> we therefore suppose some imaginary standard of equality, by which the
> appearances and measuring are exactly corrected, and the figures
> reduc'd entirely to that proportion... But tho' this
> standard be only imaginary, the fiction however is very natural; nor
> is any thing more usual, than for the mind to proceed after this
> manner with any action, even after the reason has ceas'd, which
> first determin'd it to begin. This appears very conspicuously
> with regard to time; where tho' 'tis evident we have no
> exact method of determining the proportions of parts, not even so
> exact as in extension, yet the various corrections of our measures,
> and their different degrees of exactness, have given us an obscure and
> implicit notion of a perfect and entire equality. The case is the same
> in many other subjects. A painter forms the same fiction with regard
> to colours. A mechanic with regard to motion. (THN 1.2.4.24)
> 
> 
> 



Instead of introducing certainty into natural philosophy as Newton
claimed, mathematics, albeit a useful device "in almost every
art and profession" (THN 2.3.3.2), is thus grounded in natural
fictions. It has a limited contribution to the advancement of
knowledge. Mathematics in Hume's eyes is only another human
cognitive enterprise that has no potential to make other fields of
knowledge immune to human fallibility. This is in sharp contrast with
the cognitive optimism Newton expresses in the Preface to the
*Principia* and several other passages about the role of
mathematics in natural inquiry (see Guicciardini 2009, esp. ch. 13
& 14; Zemplen & Demeter 2010). Newton is confident that
by making the method of inquiry mathematical, natural philosophy can
be infused with certainty and demonstrativity. This confidence is
undermined by Hume's account of how mathematical knowledge is
possible at all.


### 4.7 Analysis and synthesis



What is distinctive about the method of the *Principia* is what
I.B. Cohen termed the "Newtonian style". Its constitutive
feature is the mathematization of nature, i.e., "dealing
mathematically with the realities of the external world". This
meant much more than deriving numerical results from experiments, or a
focus on measurement, or a commitment to a means of exposition that
proceeded from definitions and axioms. Instead, it meant taking
*mathematics as the model of reality*: constructing "the
mathematical analogue of a natural situation" and then to
advance from this idealized case by the addition of further conditions
toward more accurate mathematical analogues of actual situations
(Cohen 1980: 51, 151, see also Smith 2002; Smeenk & Schliesser
2013). There are no traces of this approach in Hume, so if one takes
the *Principia*'s "Newtonian style" as the
essence of Newton's method, then one should also conclude that
Hume's experimental method is not Newtonian. (For a contrasting
view see de Pierris 2015 who credits Hume with a
*Principia*-style Newtonian inductive methodology, and for a
critique of her views see Landy 2017.)



As McGuire (1970b: 182) points out "Newton did not see any
dichotomy in method between that used in the *Principia* and
that found in the *Opticks*". But even if he considered
his methodology fundamentally the same in both works, and he treated
mathematical and experimental analyses as contributing to inquiry in
the same manner, this was perceived differently by subsequent
generations. In Query 31 Newton himself introduces two different ways
of analysis that "may proceed from compounds to ingredients, and
from motions to the forces producing them" (*Opticks*, Query 31 added in 1718, Newton 2004:
139; for a discussion
see e.g. Ducheyne 2012; Demeter 2016): the first way allows for a
qualitative analysis that does not require the centrality of a
mathematical framework of analysis. The crucial element is indeed
common to their methodology, namely the idea of *causal
analysis*--this is the core of Newtonian analysis, and these
are the terms in which Colin Maclaurin (1775: 8-10) introduces
the Newtonian method to his contemporaries. Nevertheless, it is
immediately clear from this passage that an analysis "from
compounds to ingredients" must proceed differently and find
different causes from an analysis "from motions to the forces
producing them": they will be different with respect to both the
*method* of analysis, and the *nature* of the causes
that can be so analysed.



From the angle of Newton's Preface to the first edition of the *Principia*, 



> 
> 
> the basic problem of philosophy seems to be to discover the forces of
> nature from the phenomena of motions and then to demonstrate the other
> phenomena from these forces. (Newton 2004: 41) 
> 
> 
> 



So its method is focused on analysing the causes of *motions*
in terms of *forces*, a quantifiable natural kind that is
defined in terms of other quantities. So defined, the problem cries
out for a mathematical apparatus, and so it fosters what I.B. Cohen
termed "the Newtonian style" in philosophy: taking
mathematics as the model of reality, constructing "the
mathematical analogue of a natural situation", and then
producing from this idealized case by the addition of further
conditions more and more accurate mathematical analogues of actual
situations (Cohen 1980: 51, 151). Through this series of
"successive approximations", Newton's axioms or laws
of motion function as "inference tickets" that allow for
drawing conclusions from motions to forces and *vice versa*,
and also from macrophysical to microphysical forces composing them
(Smith 2002: 143, 155-159; Smeenk & Schliesser 2013).



The analysis of compounds to ingredients, followed in the
*Opticks*, looks for parts, components, constituents etc., and
accompanies the mathematical methods of analysis where they prove to
be inadequate in themselves. The qualitative component of analysis is
intended to reveal the *composition* of optical and, especially
in the Queries, chemical phenomena. The paradigmatic cases are, of
course, Newton's prism experiments that revealed the composition
of white light. In the first two books of the *Opticks* Newton
himself uses the method of analysis of compounds into ingredients
"to discover and prove the original differences of rays of
light" (Query 31, Newton 2004: 140), that is to discover
qualitative differences that persist due to the lack of their analysis
in the "Newtonian style". Most notable among them, as the
*experimentum* *crucis* had revealed, are colours that




> 
> 
> are not *Qualifications of Light*, derived from Refractions, or
> Reflections of natural Bodies (as 'tis generally believed,) but
> *Original* and *connate properties*, which in divers
> Rays are divers. (Newton 1671/72: 3081; for discussion and context see
> Ducheyne 2012: 190-192)
> 
> 
> 



In this vein, the *Opticks* provides a more appropriate setting
for understanding the character of Hume's experimentalism than
the context of the *Principia*. As Colin Maclaurin put it in
his 1748 account of Newton's discoveries: while the
*Principia* inquires into forces acting between bodies in great
distance, the *Opticks* explores the "hidden parts of
nature", which are not so easily "subjected to
*analysis*" because of the subtlety and minuteness of the
agents (Maclaurin 1775: 21). The principles of human nature that Hume
endeavours to explore also belong to the hidden parts of nature that
can be explored by a method of qualitative *analysis and
synthesis* similar to the one advertised in Query 31. (Landy 2017
offers a consonant reconstruction of Hume's philosophy of
science as aiming at the exploration of hidden processes of the
mind.)



The *Treatise* begins with setting up a "scheme of
fundamental 'elements'" for analyzing human
phenomena in terms of ideas and impressions. Humean analysis begins
with phenomena from the historical and everyday observation of human
behavior, and the analysis proceeds by "experiments ...
judiciously collected and compar'd" (THN I.10), in order
to arrive at analogies among various instances "from the
observation of several parallel instances" (EHU 8.13). The
products of comparative analysis so conducted are the principles of
various faculties, like perception, imagination, reason, etc., whose
interaction results in ideas and impressions causing behaviour, but
their contribution can hardly be measured and the principles of their
interaction can hardly be quantified--not even in principle, so
they cannot be mathematized either (see also
 section 4.6
 above). Instead, they remain qualitatively different principles of
human nature, and the explanation of human phenomena consists in a
description of how these principles with their distinctive
characteristics figure in producing them (Demeter 2016).



The methodological core thus consists in collecting relevant
phenomena, finding analogies between them, and ascribing those
analogies to similar causes, thereby reducing a variety of phenomena
to regular principles underlying them (THN App.3, Abs.1, EHU
4.12)--while knowing that our knowledge cannot transcend what we
can infer on an analogical basis from the effects themselves (THN
I.8). Just as comparing rays of light reveals their determinable
properties which, once determined, can be used in constructing
explanations, the comparison of instances of human behavior reveals
the principles of human nature with increasing generality and
exactness. Salient human phenomena are collected from history and
observation, then compared; if analogies and similarities are found,
they are ascribed to some principle of human nature that are also
compared, grouped and resolved into more general ones (see also
Section 4.8 below). This process results in determinable properties of
human nature like the faculties of reason, sympathy, moral sense etc.;
determining how these properties are actually instantiated in
different social, historical, individual, etc. circumstances provides
the explanatory raw material for singular phenomena (EHU 8.7, 8.9).
Thus we reach the principles of human nature that are the proper aim
of inquiry in the science of man. These principles can be used, at the
stage of synthesis, to explain why our impressions and ideas follow
one another in the order they do.



The outcome of these procedures is the refinement of the theory of
human nature. While exploring exceptions and eliminating superfluous
conditions it turns out, for example, that some principles of human
nature are universal, some others are particular (THN 1.4.4.1). Some
principles of imagination are then constitutive of human nature, but
some others are just contingent on culture or history, or even
idiosyncratic, and can lead to local superstitions or philosophical
chimeras, like presupposing "substance" as the bearer of
properties in scholastic metaphysics. The universal principles provide
the fundamental framework of determinable human properties that are
actually determined by social and historical circumstances. This
explains why certain virtues, like courage, are evaluated differently
in different historical periods (EPM 7.11-14), and also why a
creature without sympathy, however contingent its degree and direction
may be, would count as a "monster" and not a
"man" (EPM 6.1-2). Sympathy is a universal principle
of human nature, but the principles of the degree and direction of its
sensitivity are determined by the conditions within which it is
developed and refined through social interaction (EPM 5.41-42).
This amounts to saying that Hume's account of human nature has
both universalistic and contextualist elements, and this is the
outcome of his experimental methodology: it is through a series of
successive approximation through a comparative study of changing
circumstances that the universal and contingent principles of human
nature can be distinguished.



Analysis and synthesis so understood constitutes the core of
"the experimental method of reasoning" that distinguishes
Hume's enterprise from the alternative approach that Newton
(2004: 121) had termed "hypothetical philosophy". Hume is
aware of this distinction and explicitly sides with the
experimentalist camp. His methodological pronouncements and
commitments situate him in the context of "methodological
Newtonianism" characteristic to Scottish moral and natural
philosophers, who "dealt with aspects of philosophy for which
Newton had not laid down the specific postulates upon which future
theories were to be built" (Donovan 1975: 29, see also Demeter
2016).


### 4.8 Analogy



As Hume repeatedly emphasizes, it is impossible to reveal the
"ultimate causes of our mental actions", and we have to be
content with "experience and analogy" in explaining any
act of the mind "by producing other instances, which are
analogous to it, and other principles, which facilitate its
operation" (THN 1.1.7.11). Finding analogies between different
instances gives one the chance to explain causes and reduce them to
"more general principles" (THN App. 3). For Hume,
*analogical reasoning* is the key to most of our everyday and
philosophical conclusions in empirical matters. Causal reasoning is
partly but crucially founded on our capacity to recognize resemblances
among different instances, and to extend our inferences based on
previous observations to similar but unobserved instances. Thus, the
recognition of resemblances is at the heart of our reasoning
concerning any matter of fact, and the limits of this kind of
reasoning are exactly where our capacity to recognize resemblances
ends (THN 1.3.13.25). The proper method of both natural and moral
philosophy is 



> 
> 
> to reduce the principles, productive of natural phaenomena, to a
> greater simplicity, and to resolve the many particular effects into a
> few general causes, by means of reasonings from analogy, experience,
> and observation. (EHU 4.12, 11.30; THN 1.1.7.11) 
> 
> 
> 



It is history--natural and civil as well--that provides the
pool of observations from which philosophers--natural and moral
ones as well--relying on analogies can establish explanatory
principles. Finding analogies between different instances gives one
the chance to explain causes and reduce them to "more general
principles" (THN App.3).



In the *Dialogues*, and especially in the sections criticizing
the design argument, Hume seems to be more critical of analogical
reasoning than he is in his other passages of similar methodological
relevance; nevertheless, Philo pronounces "analogies and
resemblances" reliable enough to serve as the "sole proofs
of the Copernican system" (*Dialogues* 2.26). Given that
in Hume's epistemology the category of *proof* provides
the highest level of epistemic certainty available for any piece of
empirical knowledge, analogical reasoning is a highly esteemed way of
reaching theoretical conclusions in exploring the principles of nature
and human nature (EHU 6n10). Hume's doubts in the
*Dialogues* concerning analogical arguments from design
primarily do not arise from the weaknesses of analogical reasoning,
but mainly from the uniqueness of the world, which does not provide a
sufficient pool of instances among which analogies can be found (EHU
11.26).



Although the cognitive role of analogy is central, it relies on
subjective judgment and so it can have idiosyncratic manifestations.
Things are similar in an infinite number of ways, and only some of
these similarities can be exploited with the hope of cognitive benefit
(THN 1.1.5.3). As any thing may resemble any other in an infinite
number of ways only some resemblances can explain associative
relations between ideas. Resemblances of cognitive relevance are
therefore not passively detected, but they are actively produced by
memory: we remember past instances *as* resembling (THN
1.4.6.18). Depending on the resemblances one recognizes among
particular instances, one can end up with different and potentially
conflicting conclusions concerning the causes of phenomena. Therefore,
as Hume puts it:



> 
> 
> No questions in philosophy are more difficult, than when a number of
> causes present themselves for the same phaenomenon, to determine which
> is the principal and predominant. There seldom is any very precise
> argument to fix our choice, and men must be contented to be guided by
> a kind of taste or fancy, arising from analogy, and a comparison of
> similar instances. (THN 3.2.3.4n71)
> 
> 
> 



This is one reason why "Tis not solely in poetry and music, we
must follow our taste and sentiment, but likewise in philosophy"
(THN 1.3.8.12). And while the subjectivity of analogical reasoning is
a source of creativity and insight, it also puts the objectivity and
certainty of Newton's epistemic ideal beyond reach.