## 1. The Criteria for Scientific Knowledge



The fundamental aspects of Hobbes' materialism are well known.
Hobbes believed that everything that exists is a body, and that bodies
are sometimes in motion and sometimes at rest. Furthermore, he held
that the only essential property of body is extension, or magnitude.
All other apparent properties of bodies, such as those of color,
taste, and firmness, are the result of motions from bodies being
continued through media to humans' sense organs. These motions,
when continued into the bodies of perceivers, are constitutive of
conceptions, or
 ideas.[2]
 Ideas of the objects of sense are caused by motions from things
outside of perceivers and those continued motions constitute ideas and
serve to individuate one idea from another. Thus, all ideas in the
human mind are either from sense perception or derived from ideas
gained from sense perception (*Leviathan* I; LEV 22).



This account of the origin and nature of ideas shows Hobbes'
clear empiricist leanings; however, Hobbes does not hold that knowers
should uncritically accept what the ideas of sense objects seem to
represent. Like many other philosophers in the seventeenth century,
Hobbes held that our knowledge of the external world was not direct
but was instead mediated by ideas. This recognition that "we
compute nothing but our phantasms or ideas" (Hobbes
1642-43 [1973: 450]; cf. OL
 I.82)[3]
 resulted in two worries about human knowledge.



First, knowers must examine what resemblance ideas in the mind have to
objects in the outside world. This worry seems similar, at first
glance, to the concerns of Descartes' meditator in the
*Meditations on First Philosophy* (1641), but Hobbes aimed to
provide a solution that made no reference whatsoever to God or to
anything at all immaterial, such as a soul. In the early work
*Elements of Law*, composed in 1640 and published in 1650 (EL),
Hobbes offered arguments that attempted to show that ideas are
distinct from that which they purport to represent, and he claimed
that as a result we could know that the so-called secondary qualities,
such as color, taste, and sound, were not in bodies. To do this, he
used everyday experience to provide evidence for his claims:



> 
> 
> Every man hath so much experience as to have seen the sun and other
> visible objects by reflection in the water and in glasses, and this
> alone is sufficient for this conclusion: that colour and image may be
> there where the thing seen is not. (*Elements of Law* II.5; EL
> 3)
> 
> 
> 



He used similar considerations in *Leviathan* I, concluding
that we can know, for example, that color and sound are not in bodies
since if they were "they could not bee severed from them, as by
glasses, and in Ecchoes by reflection" (LEV 24).



A second worry that follows from Hobbes' view that we have only
mediated access to bodies in the world relates to the possibility of
gaining knowledge of the causes of natural events. Most of the ideas
that knowers possess of bodies are received passively. When interested
in the cause of some phenomenon, all one may examine are ideas caused
by the motions of the bodies involved. However, when interested in,
say, the cause of billiard ball *B* being put into motion after
apparent contact with moving billiard ball *A*, one does not
find an idea of *A* being the cause of *B*'s
motion. Even if one were to look to a lower 'level', as it
were, smaller than billiard balls by use of a microscope, one would
not find any idea of *A*'s motion causing
*B*'s motion. Hobbes diagnosed this lack of causal
knowledge by highlighting that human agents are not the makers of
natural phenomena. He thought that makers gain this causal knowledge
by attending to their constructions through the process of creating
something. Since we lack the ideas of the causes of individual
phenomena from our experience, Hobbes claimed that we cannot know
their actual causes at all. All that we may know are possible causes.
Hobbes asserted in *Six Lessons to the Professors of
Mathematiques* (1656) that because "of natural bodies we
know not the construction but seek it from the effects" we can
know "only of what [the causes] may be" (EW VII.184).



This second worry brings to the fore Hobbes' condition for the
possibility of scientific knowledge, namely, the possession of
(actual) causal knowledge. He claimed that



> 
> 
> we are said to know [*scire*] some effect when we know what its
> causes are, in what subject they are, in what subject they introduce
> the effect and how they do it. Therefore, this is the knowledge
> [*scientia*] tou
> dioti or of causes. (OL I.59)
> 
> 
> 



Having scientific knowledge required one to know the actual causes of
a phenomenon, not its mere possible causes. However, the only way to
possess such causal knowledge is to act as a maker, as God did in the
case of natural things.



This restriction that Hobbes made allowed him to consider only
geometry and civil philosophy as bodies of scientific knowledge, since
in only these two disciplines do humans make the objects that they
study. In *Six Lessons to the Professors of Mathematiques*,
Hobbes distinguished these two disciplines from all others by
connecting them to making:



> 
> 
> Geometry therefore is demonstrable for the lines and figures from
> which we reason are drawn and described by ourselves and civil
> philosophy is demonstrable because we make the commonwealth ourselves.
> (EW VII.184)
> 
> 
> 



In the three following sections, this entry considers ways in which
these two bodies of scientific knowledge are used within other
disciplines to provide an epistemic grounding for the explanations
therein. In natural philosophy, or physics, Hobbes borrowed
geometrical principles to provide the cause--the reason
'why'--for many phenomena, while the making of the
commonwealth, and its laws, out of the state of nature was the genesis
of the science of civil philosophy.


## 2. The Use of Mathematics and Hypotheses in Scientific Explanations



There has been debate among scholars of Hobbes' thought about
the relationship of the different parts of his philosophy to one
another. Much of the focus has been upon the methodological statements
in Part I of *De Corpore*, and scholars have traditionally
divided over whether Hobbes understood philosophy as unified or
disunified. However, more recent scholarship has drawn attention to
Hobbes' practice of explanation, such as the explanations found
in *De Corpore* Part IV, and has argued that aspects of both
the unified and disunified views track Hobbes' discussions and
practice while those views on their own miss that Hobbes explicitly
borrowed principles from mathematics to use in natural philosophy (and
provided citations to show this activity). This section will discuss
these three approaches to understanding how the parts of Hobbes'
system fit with one another and then provide an example of an
explanation in Hobbes' natural philosophy from *De
Corpore* XXV.



First, the unified view. A significant number of scholars have argued
that Hobbes understood his philosophy as unified by deductive
connections between the different parts (for example, Martinich 2005;
Peters 1967; Shapin & Schaffer 1985; Watkins 1965). A stronger
version of this unified view understands Hobbes to be a type of
reductionist, wherein descriptions of macroscopic bodies, such as
humans and rocks, ultimately reduce to microscopic bodies responsible
for all phenomena (for example, Hampton 1986; Ryan 1970). For example,
Alan Ryan articulates the reductionist view as follows:



> 
> 
> Hobbes believed as firmly as one could that all behaviour, whether of
> animate or inanimate matter, was ultimately to be explained in terms
> of particulate motion: the laws governing the motions of discrete
> material particles were the ultimate laws of the universe, and in this
> sense psychology must be rooted in physiology and physiology in
> physics, while the social sciences, especially the technology of
> statecraft, must be rooted in psychology. (1970: 102-103)
> 
> 
> 



There is some textual support for understanding the parts of
Hobbes' system as either deductively or reductively linked
together since he did at times talk of the parts of philosophy as
beginning in first philosophy and leading from one to another. For
example, he asserted in *De Corpore* VI.6 that by beginning at
first principles, one will move from first philosophy to geometry, and
from geometry to physics. He continued by claiming that "after
physics we come to morals" and, indeed, Hobbes claims that moral
philosophy must be studied after physics because the passions have
"their causes in sense-experience and imagination" (CSL
299; OL I.64).



However, immediately following these statements that seem to indicate
that Hobbes took his philosophy to be tightly knit together, he argued
that "civil and moral philosophy do not so adhere to one
another, but that they may be severed" (EW I.73). This
separation is permissible, Hobbes claimed, because in addition to
learning moral philosophy from first principles each individual could
simply study the motions of their own mind and gain knowledge of the
same principles. That such separation could occur is difficult to
explain for a strong version of the unified view because it makes it
appear that Hobbes thought that one could develop civil philosophy
simply by introspecting, entirely independently of any work in moral
philosophy, natural philosophy, and first philosophy.



A further difficulty for the unified view is that even if Hobbes did
see the connection between, say, physics and moral philosophy as
deductive, it is not obvious how that deduction would work because
moral philosophy must add content about human passions (endeavors)
that is not contained within--and thus not deducible
from--physics. For example, although the concept
'endeavor' is introduced in physics, for it to be used in
moral philosophy the concepts of 'appetite' and
'aversion', which are properties of human bodies, must be
added to it for use (Malcolm 2002: 147). One way to avoid this
difficulty for the unified view would be to provide evidence that
Hobbes made explicit the reduction relationship between concepts like
'appetite' and 'aversion' and the concept of
'endeavour', showing how one can reduce claims about human
bodies to claims about microscopic bodies. Hobbes does not appear to
do this anywhere in the corpus. However, even if a strong version of
the unified view faces this difficulty, the presence of
'endeavor' throughout Hobbes' philosophy shows that
it was a foundational concept (see Jesseph 2016).



The second major view of the relationship of the parts of
Hobbes' philosophy to one another is what we can call the
disunified view (for example, see Robertson 1886; Taylor 1938;
Warrender 1957). Some of the motivation behind the disunified account
seems to be a desire to free Hobbes from what is prima facie a case of
deriving normative claims relating to the commonwealth in civil
philosophy from descriptive claims related to human psychology and,
ultimately, more general claims in natural philosophy (especially
Taylor 1938). However, in its attempts to rescue Hobbes from a version
of the so-called naturalistic fallacy, the disunified account fails to
take seriously Hobbes' claims about the unity of his philosophy.
Furthermore, it neglects that many of Hobbes' contemporaries
(for example, Bramhall) saw Hobbes' views in natural philosophy
as having far-reaching consequences for other areas of philosophy.



A third view has more recently been offered that seeks to carve a
middle path between the unified and disunified interpretations. We can
call this view the mixed-mathematics view (for example, Adams 2016,
2017; Biener 2016). This understanding of Hobbes' system agrees
with the worry raised above for the unified account that
'higher' levels, such as geometry, do not contain the
concepts used in 'lower' level explanations. For example,
although geometrical principles are used in Hobbes' optical
explanations those geometrical principles do not contain concepts such
as 'light' or 'color'. Some evidence for this
lack of containment claim can be found on the well-known "Table
of the Several Subjects of Science" in *Leviathan* IX.
The "sciences" on this table are listed on the right-most
section and their subjects are to the immediate left. The subject of
the science of optics, for example, is all of the "consequences
from vision", and these stem from "Physics or consequences
from qualities". The science of geometry, however, has as its
subject the "consequences from quantity, and motion
determined... by figure" and these stem not from physics
but from "consequences from the accidents common to all bodies
natural; which are quantity and motion".



Instead of seeing this "adding to" as evidence for the
disunified view, the mixed-mathematics view understands Hobbes having
seen certain disciplines as providing causal principles (what he
called the 'why') while other disciplines provided the
facts relevant to a given domain (what he called the
'that'). Textual support for this understanding of
Hobbes' system can be found in Hobbes' methodological
statements about natural philosophy as well as in his practice of
explanation.



As mentioned already, Hobbes identified scientific knowledge
(*scientia*) with knowing causes, and in his discussions he
used language germane to Aristotle's distinction between the
'why' and the 'that'. We have seen already
Hobbes' commitment to knowing through the causes, but the
complete passage from *De Corpore* VI.1 provides further detail
about Hobbes' views on the two types of knowledge, as
follows:



> 
> 
> We are said to know [*scire*] some effect when we know what its
> causes are, in what subject they are, in what subject they introduce
> the effect and how they do it. Therefore, this is the knowledge
> [*scientia*] tou
> dioti or of causes. All other knowledge
> [*cognitio*], which is called tou
> oti, is either sense experience or imagination
> remaining in sense experience or memory (*De Corpore* VI.1; CSL
> 287-289).
> 
> 
> 



Two types of knowledge thus emerge. There is knowledge from sense
experience, retained as imagination and eventually as memory (more
below on how this can develop into prudence), and there is scientific
knowledge. When reflecting in *De Homine* on the status of
claims in physics, Hobbes claims that what he calls "true
physics" must be a mixture of *both* of these types of
knowledge:



> 
> 
> [...] since one cannot proceed in reasoning about natural things
> that are brought about by motion from the effects to the causes
> without a knowledge of those things that follow from that kind of
> motion; and since one cannot proceed to the consequences of motions
> without a knowledge of quantity, which is geometry; nothing can be
> demonstrated by physics without something also being demonstrated
> *a priori*. Therefore physics (I mean true physics) [*vera
> physica*], that depends on geometry, is usually numbered among the
> mixed mathematics [*mathematicas mixtas*]. [.] Therefore those
> mathematics are pure which (like geometry and arithmetic) revolve
> around quantities in the abstract so that work [in them] requires no
> knowledge of the subject; those mathematics are mixed, in truth, which
> in their reasoning some quality of the subject is also considered, as
> is the case with astronomy, music, physics, and the parts of physics
> that can vary on account of the variety of species and the parts of
> the universe. (MC 42; OL II.93)
> 
> 
> 



These two statements concerning the status of different types of
knowledge and the requirement to mix "quantities in the
abstract" with "some quality of the subject" in
physics can aid in making sense of Hobbes' actual explanatory
practice. What does it mean for physics to be "mixed
mathematics"? For Hobbes it means that for many explanations one
will first establish that some fact is the case by appealing to sense
experience, but to give the reason why one must borrow a principle
from geometry.



At several places in *De Corpore*, Hobbes appears to carry out
the mixed-mathematics ideal by showing, with a citation, that he used
a causal principle from geometry within an explanation that included
details about the "quality of the subject." For example,
in *De Corpore* XXV, the chapter with which Hobbes began Part
IV, Hobbes appears to have done just this when he explained sensation.
In that explanation, he appealed both to "qualities of the
subject", such as the claim based upon experience that "we
may observe... that our phantasms or ideas are not always the
same" (EW I.389), and by citing and using causal principles from
earlier in the work (see discussion of this explanation in Adams
 2016).[4]



Such behavior--borrowing and citing a principle within an
explanation--would be difficult to explain on the picture offered
by the unified view since Hobbes offers no justification for this
practice other than phrases such as "I have shown
besides...". There is no deduction anywhere offered within
Hobbes' actual explanatory practice that would give reason to
think that Hobbes understood the use of these principles from
elsewhere in the work in that way. Likewise, it is difficult to make
sense of this activity within Hobbes' actual practice if we
adopt the disunified view of Hobbes' philosophy, since by using
principles from elsewhere in the system, and especially by explicitly
citing them, Hobbes is signaling that the parts of his system did fit
together, even if not in the strong reductive sense of the unified
view. The next section will describe Hobbes' view that work in
first philosophy and geometry must be done prior to experiments.


## 3. Hobbes on Experimentation: Conflict with Robert Boyle and the Royal Society



Hobbes' conflict with Robert Boyle concerning the nature of
natural philosophy in general, and the air-pump experiments in
particular, took place over several years and in a series of
 publications.[5]
 Hobbes wrote *Dialogus Physicus* (1661; a second version
appeared in
 1668)[6]
 as a dialogue aimed at criticizing Boyle's *New Experiments
Physico-Mechanical* (1660). Boyle responded to various criticisms
in works such as *An Examen of Mr. T. Hobbes his Dialogus Physicus
de Natura Aeris* (1662), *An Examen of Mr. Hobbes'
Doctrine about Cold* (1665), and *Animadversions upon Mr.
Hobbes' Problemata de Vacuo* (1674). The most comprehensive
and influential treatment of this period of Hobbes' life is
Shapin and Schaffer's *Leviathan and the Air-Pump*
 (1985).[7]
 This section will focus upon Hobbes' criticisms of the air-pump
experiments in the *Dialogus Physicus* with an aim of showing
how they illuminate our understanding of Hobbes' natural
philosophy.



Most generally both Boyle and Hobbes viewed the natural world as
composed of bits of matter in motion. Even if there were some points
of agreement between the versions of mechanical philosophy offered by
both Boyle and
 Hobbes,[8]
 there are important differences. A crucial difference between the two
relates to the status (or lack thereof) of Laws of Nature. While Boyle
talked about the laws of nature as established by God (see the section on
 Laws of Nature in the entry on Boyle),
 Hobbes restricted discussion of laws to the laws of human conduct
discovered by those who escape the state of nature and create a
commonwealth. In contrast to laws of the natural world, Hobbes
articulated *a priori* principles of motion at the foundation
of his physics in *De Corpore* VIII.19 and IX.7. Rather than
being known as laws of motion, issued by some divine lawmaker, these
Hobbesian principles of motion are explicated by thought experiments
and seem to rely upon a version of the principle of sufficient reason
(Jesseph 2006: 132). Although Hobbes held that they were true of all
human experience, since Hobbes holds that we cannot know the actual
causes of natural phenomena he would have to admit that nature might,
unbeknownst to us, act otherwise. However, despite these differences,
the primary dissimilarity that emerges between Hobbes and Boyle
concerning the air-pump experiments is one of method as it relates to
the status of experiments/experience (see the section on
 Philosophy of Experiment in the entry on Boyle).



Given that Hobbes was convinced of the impossibility of knowing the
actual causes of natural phenomena, he held that any phenomenon admits
of multiple possible explanations. This should not be taken to imply
that Hobbes saw all explanations, and thus all possible causes or
suppositions, as standing on equal footing. Instead, Hobbes held that
work in first philosophy and geometry must be completed prior to
attempting to make any explanations in natural philosophy. This seems
to be what Hobbes meant in the *De Homine* extended quotation
provided above when he said that "nothing can be demonstrated by
physics without something also being demonstrated *a
priori*" (MC 42; OL II.93). When giving an explanation,
Hobbes held that one should ideally appeal to those causes that are
demonstrable from geometry when mixed with facts and rule out those
that are not intelligible according to geometrical principles.



In contrast, Boyle's method prescribed that instead of bringing
causal principles to an experiment and expecting to explain some
phenomenon by appeal to those principles, one should attempt to arrive
at a supposition that would explain a phenomenon only after repeated,
careful experiments. Thomas Sprat detailed the care taken in the
design of experiments and the manner in which Royal Society members
were formed into committees that shared parts of an experiment so that
"[b]y this union of eyes, and hands" they were able to
gain "a full comprehension of the object in all its
appearances" (Sprat 1667: 85).



We can make sense of Hobbes' direct criticisms of Boyle's
prioritization of experiment with this methodological difference in
mind. Hobbes' view of the foundational role played by first
philosophy and mathematics over experiment/experience is clear when he
claimed in *Dialogus Physicus* that



> 
> 
> ...ingenuity is one thing and method is another. Here method is
> needed. The causes of those things done by motion are to be
> investigated through a knowledge of motion, the knowledge of which,
> the noblest part of geometry, is hitherto untouched. (DP 347; OL
> IV.236)
> 
> 
> 



According to Hobbes, then, one must have geometrical principles
already in place to aid in choosing a supposition before engaging in
experiments. Unlike the Royal Society's aim to have multiple
members examine the same object, Hobbes emphasized the need for
individual conceptual clarity, something that could be accomplished
from an armchair.



This criticism from Hobbes, and Boyle's rebuttals relying upon
evidence from experiments, could be seen as a conflict of
Boyle's experimental natural philosophy against a form of
speculative natural
 philosophy.[9]
 However, it is important to avoid taking Hobbes' criticisms of
Boyle's method to imply that Hobbes completely eschewed
experiment/experience while engaging in natural-philosophical
explanations. Indeed, Hobbes held that both natural history and civil
history are "useful (no, indeed necessary) for philosophy"
(CSL 189; OL I.9). Experiment/experience play the role of establishing
that some phenomenon occurs, what we have seen Hobbes called the
'that', but one should never hope, according to Hobbes, to
glean a possible cause from mere observations, even if those
observations were carefully documented and repeated many times.



This is clear when in the *Dialogus Physicus* Hobbes, speaking
through speaker A, often granted the observational reports of the
experimenters without question. For example, speaker A does not
question what the experimenters claim they observed regarding a
bladder that had been placed inside the air-pump and weighed, noting
"They can be certain that the scale in which the bladder is, is
more depressed than the other, their eyes bearing witness" (DP
369; OL IV.261). Instead of criticizing the experimenters'
reliance upon observations, speaker A argues that the experimenters
cannot know, in the case of this explanation, what the cause of the
scale being depressed is because their posited cause (the
"natural gravity" of the air) does not allow them to
explain why the scale is depressed after the air-pump is engaged. In
contrast, speaker A offers a possible cause that is borrowed, with an
explicit citation, from Hobbes' geometrical account of
"simple circle motion" and "fermentation"
developed in *De Corpore* 21.5 (Adams 2017).


## 4. Hobbes on the Value of Using *Scientia* in Natural Philosophy



The preceding sections have outlined Hobbes's views concerning
*why* principles from geometry can be used within explanations
in natural philosophy and his claim that before engaging in
experimentation one must have principles from geometry ready for use.
Still one might wonder why Hobbes thought that this approach, inspired
by "mixed mathematics", would be more successful than the
methods of Boyle and his colleagues in the Royal Society. Indeed, what
was the aim of engaging in natural philosophy according to Hobbes?
This section describes Hobbes' view that the aim of natural
philosophy is to bring positive benefits to humans' quality of
life and then contrasts Hobbes's view on the usefulness and
limitations of "prudence" with the usefulness of natural
philosophy that employs *scientia*. 



As mentioned already, Hobbes is well known for holding that all ideas
in the mind are either from sense or derived from those that are
(*Leviathan* I; LEV 22). Hobbes also linked
"trains" of ideas in the mind to sense by asserting that
just as "we have no Imagination, whereof we have not formerly
had Sense, in whole, or in parts; so we have no Transition from one
Imagination to another, whereof we never had the like before in our
Sense" (*Leviathan* III; LEV 38). Hobbes divided these
trains of ideas into those that are guided and those that are
unguided. Unguided trains explain what happens when the human mind
wanders from idea to idea, such as when daydreaming. Hobbes described
these unguided trains as the "wild ranging of the mind",
and he noted that some might think that the connecting points in such
trains are by chance even if they are not. He compared such unguided
trains to a dialogue between conversants that began on one topic (the
present civil war) but over time seemed to drift to other topics by
chance (concluding with a question about the price of a Roman penny).
Although the connecting points between these topics of conversation
(and the trains of ideas they signify in each conversant's mind)
may not be immediately obvious, Hobbes suggested that there was a
coherence to each transition. Hobbes traced this coherence in the
example he provided as follows:



> 
> ... the Thought of the warre, introduced the Thought of the
> delivering up the King to his Enemies; The Thought of that, brought in
> the Thought of the delivering up of Christ; and that again the Thought
> of the 30 pence, which was the price of that treason: and thence
> easily followed that malicious question; and all this in a moment of
> time; for Thought is quick. (*Leviathan* III; LEV 40).
> 



Hobbes intended the comparison between this example of a conversation
and the way that unguided trains of ideas move from idea to idea to
have a general output: no matter how seemingly disconnected the links
of any train of ideas may seem, there is always a coherent
explanation, whether it is obvious or not, that would explain them.




In contrast to the seemingly disconnected wanderings of the mind that
occur with unguided trains, Hobbes saw guided trains of ideas as
transitions from idea to idea that were investigated by the mind with
some end or goal in view. Say that someone desired to eat a delicious
dish that incorporated a particular type of meat and certain spices
and herbs. If they desired to bring about that result, they would
search through the trains of ideas in their mind, received from past
sense experiences, until they found trains that terminated in that
goal. When they found a train that had the end result that they were
seeking, they would trace back, idea by idea, until they found a
"beginning" that was within their current ability to
produce (*Leviathan* III; LEV 40). Continuing the example of a
desired dish, say that the individual found that a prior train of
ideas that termined with the desired end began with harvesting a
particular herb at a particular time of year. They would attempt to
bring that "beginning" about and, if successful, would
move on to the next idea in the train. There are no guarantees that
this would work, since the links in the train may be merely
probablistically connected to one another. Hobbes held that humans and
non-human animals shared this form of reasoning, which he identified
as a type of causal inquiry: "...when of an effect
imagined, wee seek the causes, or means to produce it"
(*Leviathan* III; LEV 40). Given the limitations mentioned
already related to knowing the causes of natural phenomena, Hobbes
could only have meant that *possible* causes can be identified
by this process.



Hobbes connects prudence with an ability to engage in this type of
reasoning on a broader scale. Individuals who have acquired much
experience, and thus have a large stock of trains of ideas at their
disposal, can make predictions about future events that may occur. For
example, on the basis of cooking hundreds of dishes with hundreds of
ingredients, a prudent individual could look at a given list of
ingredients and predict whether the outcome will likely be delicious
or not. Hobbes thought that the more experience such an individual
had, the better the prediction would be: "...by how much
one man has more experiences of things past, than another; by so much
also he is more Prudent" (*Leviathan* III; LEV 42).
Prudence is valuable for the human knower, but no matter how useful
prudence may be, Hobbes thought that it could never arise above being
based upon mere associational connections between ideas. Instances of
*A* have always been followed by *B*, so the prudent
person would reason, thus the *A* that has presently occurred
will likely be followed by *B*. Hobbes thought that this type
of prediction by means of associations amounted to a mere presumption
of what the future would look like (*Leviathan* III; LEV 44).
In other words, this inference required "supposing like events
will follow like actions" (*Leviathan* III; LEV 42), but
that supposition might prove false and the inference would fail.
Furthermore, any difference between prior antecedents and a current
initial condition could result in a failure on the part of the prudent
individual to predict successfully, as Hobbes noted:
"...the omission of every little circumstance altering the
effect, frustrateth the expectation of the most Prudent"
(*Leviathan* XLVI; LEV 1052). While useful in many everyday
situations, Hobbes thought that prudence showed its limitations when a
knower encountered a novel situation.



If predictions made upon the basis of associations among ideas were
the extent of human knowledge of natural phenomena, it would seem that
Hobbes should have wholeheartedly endorsed the approach of the
experimental philosophy championed by Boyle and others. What are
Boylean experiments if not repeated experiences in which one tries to
control for potential confounding variables, at least according to how
*Hobbes* saw them (Boyle would not agree with this
characterization; see the section on
 Philosophy of Experiment in the entry on Boyle)?
 Hobbes saw experienced-based prudence as useful, but he denied that
it counted as true knowledge of the future, which he held was
available only to the one by whose "will" an event happens
(*Leviathan* III; LEV 44). Hobbes's solution for moving
beyond mere associations required knowers to play an active role by
creating artificial objects (like the objects of geometry). Such
knowledge (*scientia*) was more useful for predictions because
it provided power to its holders, as he noted in *De Corpore*
1.6: "knowledge is the for the sake of power [*Scientia
propter potentiam*]" (OL I.6).



Unlike association-based predictions, which are limited by the extent
to which the prior antecedents resemble a current scenario and rest on
a presumption that the future will resemble the past, knowing the
causes of some event because one brought it about by one's will
allowed one to understand its true nature. Hobbes thought that this
"power" provided direct benefits that improved the quality
of human living, such as the marking of "moments in time"
and "mapping the face of the earth" (OL I.6-7). Similarly,
the science of civil philosophy (discussed more in the next section)
could help prevent civil war and other calamities (OL I.8). Hobbes
recognized that many citizens may not see the value of
*scientia* because they fail to understand it: "For
Science is of that nature, as none can understand it to be, but such
as in good measure have attayned it" (*Leviathan* X; LEV
134). Furthermore, he admitted that many citizens would confuse the
cause of success in the "arts of publique use"; although
the reason why such arts produce effective fortifications and other
"Instruments of War" lies in their use of principles from
the science of geometry, many will think that the inventor of such
instruments is responsible and because of this "the Midwife [the
artificer] pass[es] with the vulgar for the Mother" when the
"mother" is really mathematics (*Leviathan* X; LEV
134).



If the solution to moving beyond association-based prudence was to use
geometrical principles within natural philosophy, why did Hobbes think
this? As mentioned already, in *Six Lessons* (1656) Hobbes
claimed that because "of natural bodies we know not the
construction but seek it from the effects" we can know
"only of what [the causes] may be" (EW VII.184). A claim
like this might make it seem like the natural philosopher simply
guesses cause *might* be responsible for a given phenomenon,
but Hobbes held that not all possible causes are on equal epistemic
footing. Hobbes's method of natural philosophy that mixes
mathematical principles (the 'why') with observations from
experience (the 'that') rejected what Hobbes thought of as
a merely passive approach to understanding nature. In contrast, in the
Letter to the Reader of *De Corpore* Hobbes compares
philosophizing to God's act of the creation of the world:



> 
> 
> If you are going to pay serious attention to philosophy, let your
> reason hover over the confused abyss of your thoughts and experiences.
> The confused things must be shaken violently, distinguished, and
> ordered, having been marked with their own names, that is, in method
> [*Methodo*] it must be according to the creation of things
> themselves. (OL I. Letter to Reader)
> 
> 
> 



Unlike what Hobbes saw as the passive approach of conducting and
observing experiments, which would provide associations in the form of
trains of ideas and eventually prudence, Hobbes thought natural
philosophy should imitate God's activity. The only way for
natural philosophy to provide the benefits that Hobbes saw following
from it was for it to combine observations with certain knowledge from
*scientia*. The result was that explanations in natural
philosophy were epistemically between mere associational prudence and
the certainty of *scientia*. We could thus characterize
explanations in Hobbes' natural philosophy as having
hypothetical certainty. The natural philosopher cannot know with
certainty that nature behaves as an explanation claims. However, given
that they borrow causal principles from geometry, they can know that
*if* nature behaved as they suppose, *then* certain
consequences would follow of necessity.


## 5. The Prospects for a Science of Civil Philosophy



Hobbes thought that he would be renowned as the founder of civil
philosophy just as he saw Copernicus as having initiated the
"beginning of astronomy", Galileo as having opened the
"gate of natural philosophy universal" with an account of
the "nature of motion", and William Harvey as having first
discovered the "science of man's body" (see the
dedicatory epistle to *De Corpore*; EW I.viii). He asserted
that while "Natural Philosophy is... young", civil
philosophy itself is "no older than... [his] own book De
Cive" (EW I.ix). As a student of historical texts in their
original
 languages,[10]
 Hobbes was well aware of many works from antiquity to his own time
addressing issues relevant to civil philosophy. By claiming civil
philosophy was his invention, he intended to deny that any of those
preceding works counted as philosophy.



What did Hobbes see as distinguishing his work in civil philosophy
from all predecessors? As points of contrast, Hobbes mentioned the
Sophists who "taught ... [only how] to dispute" and
Christian theologians who introduced "school divinity", by
which Hobbes meant the blending of teachings from Scripture with
Aristotle's philosophy. For the latter, Hobbes saw the best
"exorcism" to be the distinction between the subject
matters of religion, which were the "rules for honouring
God", and philosophy, which was concerned with the
"opinions of private men" (EW I.xi). What distinguished
religion from philosophy in this sense, Hobbes continued, is that
philosophy provides either demonstrations from definitions or
demonstrations from "suppositions not absurd".



So far it seems that there are two criteria relevant to civil
philosophy that Hobbes saw as setting his apart from all other
attempts. First, Hobbesian civil philosophy is a science
(*scientia*) because human makers have the ability to know the
actual causes of the objects of study since they construct them.
Second, to count as philosophy and not mere superstition or sophistry,
Hobbesian civil philosophy must provide demonstrations.



How exactly Hobbes' use of 'demonstration' should be
understood as it relates to civil philosophy has been a subject of
debate among Hobbes scholars over the past several decades. Much of
the focus of this debate has been concerning the Laws of Nature in
*Leviathan* XIV and XV. Why restrict the scope of demonstrable
civil philosophy to two chapters of *Leviathan*? Why not
include, for example, *Leviathan* Parts III ("Of A
Christian Commonwealth") and IV ("Of The Kingdom of
Darkness")? Alternatively, why not also include chapters from
Part II ("Of Commonwealth"), especially chapter XVII
("Of the Causes, Generation, and Definition of a
Commonwealth")? One motivation for focus upon chapters XIV and
XV is that in those chapters Hobbes seems to have indicated that he
saw a deductive relationship between the laws of nature by using the
language one might expect in a demonstration. For example, Hobbes
described the second law of nature as being "derived from"
the first law (LEV 200). The remainder of this section will focus on
two ways of understanding Hobbes' civil philosophy as a
demonstration.



One way of understanding Hobbes' claim that civil philosophy is
demonstrable connects it to Euclidean geometry. This view has been
called the "definitivist" or "definitional"
view because of its emphasis on the importance of definitions in
Hobbes' philosophy. One articulation of the definitivist view
understands Hobbes' definition of 'law of nature' in
*Leviathan* as playing a role similar to an axiom in Euclidean
geometry (Deigh 1996). In *Leviathan* XIV, a law of nature is
defined as



> 
> 
> a Precept, or generall Rule, found out by Reason, by which a man is
> forbidden to do, that, which is destructive of his life, or taketh
> away the means of preserving the same; and to omit, that, by which he
> thinketh it may be best preserved. (LEV 198)
> 
> 
> 



The definivist further claims that like Euclidean axioms Hobbes did
not view this axiom--the definition of 'law of
nature'--as requiring demonstration; instead, he derived
the first law of nature from it and then derived the others one from
another. Why is Hobbesian civil philosophy a demonstrable science on
this view? Simply put, it is a demonstrable science because it follows
the method of Euclidean geometry, viewed by Hobbes and others as the
model of scientific knowledge on account of its clarity and
 rigor.[11]



A virtue of the definitivist view is that it takes seriously
Hobbes' claim that civil philosophy is demonstrable. However, a
difficulty faced by the definitivist view, along with any other that
understands Hobbes as drawing inspiration from Euclid, is that Hobbes
himself harshly criticized Euclidean definitions, arguing that
Euclid's definitions "ought not be numbered among the
principles of geometry" because they did not contain the causes
of what was to be constructed (EW VII.184). Furthermore, Hobbes
criticized the nature of the objects of Euclidean geometry. For
example, Hobbes argued against understanding lines as being without
breadth since there are no such bodies in nature (EW VII.202).
Additionally, Hobbes himself did not ground his own geometry in
undemonstrated axioms and held that even Euclidean axioms needed to be
demonstrated (OL I.72; OL I.119).



A second difficulty for the definitivist view lies in its inability to
accommodate the laws of nature as commands (Hoekstra 2003: 115). If
the laws of nature were derived from the definition of 'law of
nature', it would be difficult to see how they could then take
the form of instructions to perform some action. Indeed, the laws of
nature take the form of instructions to do this or that, such as the
first law of nature



> 
> 
> That every man, ought to endeavour Peace, as farre as he has of
> obtaining it; and when he cannot obtain it, that he may seek, and use,
> all helps, and advantages of Warre. (LEV 200)
> 
> 
> 



Beyond the first and second laws of nature, the remaining laws contain
instructions concerning what should be done to accomplish peace, that
is, they command it, such as the third law of nature which commands
"That men performe their Covenants made" (LEV 220).



An alternative account, what has been called the "maker's
knowledge" view of Hobbes' civil philosophy, attempts to
connect Hobbes' demonstrations and definitions in geometry with
civil philosophy. This view avoids the two difficulties faced by the
definitivist account mentioned above and holds that Hobbesian civil
philosophy is demonstrable by appealing to Hobbes' own
understanding of what constitutes a demonstration (Adams 2019). The
remainder of this section will discuss two features of the
"maker's knowledge" account of Hobbesian civil
philosophy.



First, a requirement for geometrical definitions, which Hobbes
stressed in multiple contexts, is that they must provide the causes of
the things being defined. For example, Hobbes claimed that the
definition of 'line' should be as follows: "a line
is made by the motion of a point" (OL I.63). Likewise, a plane
is made by the motion of a line. Perhaps Hobbes understood all of the
laws of nature to be like this type of geometrical definition, but
instead of the definition of something like 'line' they
served as the definition of (and thus how to make) peace. That is,
when following all of the laws of nature one could make peace just as
by following the generative instructions contained in the definition
of 'line' one could make a line.



Second, a demonstration for Hobbes did not involve the derivation of
features by means of deduction. Such deductions would provide one with
knowledge of what was already contained in the starting proposition,
making it difficult to see how commands could be derived from the
definition of 'law of nature' in *Leviathan* XIV.
However, Hobbes explicitly said that demonstrations should be
synthetic, wherein one builds the complex thing to be demonstrated out
of simpler constituent parts. A demonstration, Hobbes asserted, should
be understood as a showing of some construction to someone else (OL
I.76) and, as a result, he claimed that "entire method of
demonstrating is synthetic" (OL I.71). By
'synthesis' Hobbes means that one shows how something is
put together to reach the desired end, one shows how that thing is
made.



The maker's knowledge view of Hobbes' civil philosophy
draws insight from these two points and understands Hobbesian civil
philosophy as demonstrable in the following way. Hobbes begins civil
philosophy at a starting point in the "natural condition"
of human bodies in *Leviathan* XIII, continues by considering
how those bodies could be moved (by commands in the laws of nature) in
ways that would be conducive of peace and, finally, are brought
together to compose the commonwealth.