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With the domain of philosophical ratiocination clearly delimited, Hobbes in Chapter 6 of De corpore derives what every method has in common from his definition of Philosophy. This generic definition of method superficially echoes Scholastic views of scientific demonstration.

Therefore, the Method of philosophizing is the shortest investigation of the effect through causes having been cognized, or of the causes through the effect having been cognized. We are then said to know a certain effect scientifically [scire] when we both cognize its causes [and] that they are; and in which subject they inhere, and in which subject they introduce the effect, and in what manner they make it. Thus, scientific knowledge is τοῦ διότι or of causes; every other cognition which is called τοῦ ὅτι is sense, or imagination or memory remaining from sense.

(Hobbes 1999, 57–8; OL I.58–9, translations of this edition are mine)⁶

τοῦ διότι is Aristotle’s term for propter quid demonstrations whereby effects/consequences are syllogistically deduced from causes/reasons. Methodical philosophizing thus produces scientia, i.e., valid causal syllogisms, in the shortest way possible. Hobbes signals that though the final demonstration will be propter quid, the methodical process of arriving at such proofs can take its starting point either from the cognition of causes and deduce their effects, or from the cognition of an effect, and deduce its (possible) causes.⁷ The mere non-deductive cognition of something lies outside the domain of scientific knowledge although, as Hobbes highlights, ratiocination or computation must begin from the cognition we acquire by sensation that there is an object. Knowing the nature of its causes, that the causes exist, where they reside, and where/how they generate the effect, however, cannot be attained by experience alone. It requires syllogistic demonstration, which Hobbes regards as computation. Hobbes broadens scientia by applying scientific reasoning to the commonwealth, as well as natural bodies, thus yielding conclusions in practical philosophy that have the same status as knowledge of the natural world. But his scientia is narrower than our science since experiential forms of cognition, though they provide starting points for syllogisms, are not themselves part of scientific knowledge. The latter affirms prior Aristotelian views, the former breaks with it.⁸

Hobbes also replaces the starting points of syllogistic deductions typical of Scholastic scientific knowledge. Scholastic principles are universal claims about existing things known by means other than proof and consist in fundamental truths about the most general kinds of being. These include definitions of corporeal versus incorporeal substance that are further qualified to yield definitions of animate versus inanimate corporeal substances, and eternal versus finite incorporeal substances, and so on down the line. At each level, one can, taking the appropriate definition as one’s first premise, then demonstrate propter quid the properties that are implied by the essence captured by the definition of that species of being. Accordingly, from the definition of a human being as a rational animal, one can infer that humans are both mortal and capable of understanding. From such properties contained in the essence of a human being one then deduces further effects. There were, naturally, many obstacles to doing this in practice as well as doubts raised about the accurate capturing of essences by definitions. However, in principle, one could, by syllogizing, eventually deduce a comprehensive, consistent structure of true conclusions about the natural world, all ultimately derived from the same first principles. Hobbes’s characterizations of scientific knowledge and method signal that he retains this structure but rejects the existing foundation as untrue. Removing Scholastic metaphysics, and incorporeal substance from the domain of philosophy allows Hobbes to replace Scholastic definitions based on genera and species of substance with a “true foundation,” consisting in definitions of geometrical objects.⁹

Hobbes further rejects Euclid’s definitions of the simplest geometrical entities, like point and line, instead embracing genetic, or generative definitions given by Hero of Alexandria.¹⁰ So, Hobbes not only proposes a different foundation from which syllogistic reasoning begins, but his foundational definitions or first principles are not standard Euclidean definitions, like the definition of a line as a breadthless length. Hobbes could be averting the criticism that the most basic Euclidean definitions do not capture the essential properties of geometrical entities. If Hobbes’s foundational geometrical definitions correspond to essential features of bodies, as did the first principles of the Scholastic structure of scientific knowledge, then his move is to recast essences as procedures or recipes for the production of an object.¹¹ Following Hero, the proper definition of a geometrical object spells out how it is constructed: “a line is made by the motion of a point, superficies by the motion of a line, and one motion by another motion, & c” (EW I. 70–1). Based on such generative definitions, the passages quoted suggest that Hobbes regards scientific knowledge as a unified structure of conclusions ultimately deducible from generative definitions of geometry. As he outlines, one begins with lines or lengths generated from points in motion, and surfaces generated from long bodies – which once demonstrated, then allow one to construct definitions of the more complex phenomena of the science of motion, itself produced by the effects of one body’s motion on other bodies. Next, the science of motion provides the starting points for demonstrating the phenomena of physics, which are produced by the motions of the parts of bodies, including our sense organs. Likewise, De corpore suggests that having arrived at definitions of human passions, we can progress all the way up to civil science. Hence demonstrative knowledge of all sciences, including politics, will necessarily be generated from geometrical foundations and form a unified whole.

Interpreting Hobbes’s method as this kind of a generative construction fits one sense of “demonstration.” When discussing the proper method of demonstration in teaching, which he holds to be the same as the method of discovery, Hobbes invokes the original sense that “demonstration” had in ancient geometry:

that which the Greeks called ἀποδέιξις, and the Latins demonstratio, was understood by them for that sort only of ratiocination, in which, by the describing of certain lines and figures, they placed the thing they were to prove, as it were before men’s eyes, which is properly ἀποδεικνύειν, or to shew by the figure;

(EW I.86)

If scientific knowledge consists in demonstrations that prove effects from definitions specifying generative causes, in this geometrical sense of making objects visible (concretely or in the imagination) through construction, then Hobbes’s hierarchical structure of knowledge appears as a successive placing before our eyes of ever more complex objects that are built up from previously shown objects, just as a square is constructed from four lines, and the lines, in turn, are drawn by moving a point.¹² The Commonwealth would sit at the pinnacle of this hierarchy, as the most complex object, built up of human bodies (themselves complex bodies generated by motions) whose passions and desire for peace make a social contract necessary. Two mechanical analogies suggest that Hobbes employs demonstration in this sense to methodically arrive at civil science. But since only artificial bodies of geometry and politics can be thus constructed this would imply that either physics lies outside of science, or Hobbes has distinct methods for theoretical and practical science.¹³ I argue, instead, that Hobbes has one method, but not a constructive method in this sense.

Hobbes’s use of mechanical analogies give the impression that civil science employs a method of mechanical construction at odds with method in physics. In De cive, Hobbes claims to have started from the matter of civil government “and thence proceeded to its generation and form, and the first beginning of justice. For everything is best understood by its constitutive causes” (EW II.xiv). Immediately thereafter he makes an analogy to a watch, which one must take apart to understand the matter, shape, and motion of the wheels. Similarly,

so to make a more curious search into the rights of states and duties of subjects, it is necessary, I say, not to take them insunder, but yet that they be so considered as if they were dissolved; that is, that we rightly understand what the quality of human nature is, in what matters it is, in what not, fit to make up a civil government, and how men must be agreed amongst themselves that intend to grow up into a well-grounded state.

(EW II.xiv)

In Leviathan, the Commonwealth or State is likened to an artificial person, which one can dissect into its component parts by analogy to the parts of an automaton. This analogy likewise suggests a kind of reverse-engineering methodology not possible with natural phenomena. Here too Hobbes employs Aristotelian notions of a form that is generated, and the matter, or constitutive causes, which once extracted through resolution, can then be recomposed in the correct way. A common interpretation equates Hobbes’s reference to resolution in this passage with his method of analysis in De corpore and aligns the re-composition with synthesis. Next I show that analysis and synthesis in De corpore are not a material resolution and re-composition. Here I argue that these analogies are rhetorical.

The automaton analogy precedes Hobbes’s description of the structure of his work, the Leviathan. He frames it in terms of the four causes familiar to his Aristotelian-schooled readers. First he treats of human beings, the matter, i.e., material cause, of this artificial body. Next, Hobbes invokes how the commonwealth is made by covenants, which to his readers would evoke its efficient cause. The last two sections of the book explain what a Christian commonwealth is and what the kingdom of darkness is, i.e., the final and formal causes (2012, 18; 1651, 2). Hobbes’s automaton analogy is a rhetorical visualization for the organic structure of his work, informing readers that he will present his theory starting from material and efficient causes and concluding with final and formal causes of the Commonwealth. Just as he does not thereby commit himself to a method that employs Aristotelian causes, his mechanical analogies do not commit him to a method of geometrical construction. Indeed, Hobbes’s De corpore clarifies that knowing scientifically is to syllogize from cause to effect.

The section that follows Hobbes’s etymological tracing of “demonstration” back to the ancient Greek geometrical term reveals a different sense of “demonstration”:

It is proper to methodical demonstration, First, that there be a true succession of one reason to another, according to the rules of syllogizing delivered above.

Secondly, that the premises of all syllogisms be demonstrated from the first definitions.

(EW I.87)

The formal definition of “demonstration” Hobbes gives just before he invokes its ancient origins confirms that it is “a syllogism, or series of syllogisms, derived and continued, from the definitions of names, to the last conclusion” (EW I.86). Hobbes’s recounting of the ancient geometrical sense of “demonstration” is thus a historical side bar to motivate putting geometry at the foundation of scientific knowledge by appeal to the ancients. Once geometry makes visible its foundational definitions, scientific reasoning proceeds syllogistically.

The rhetorical purposes of the watch and automaton analogies, combined with Hobbes’s formal definitions of scientific knowledge and “demonstration” caution against taking mechanistic resolution and re-composition as Hobbes’s method for civil science.¹⁴ Nonetheless, De corpore’s analogy between all definitions and geometrical ones reinforces the impression that Hobbes’s method of demonstration is one of construction:

But definitions of things, which may be understood to have some cause, must consist of such names as express the cause or manner of their generation, as when we define a circle to be a figure made by the circumduction of a straight line in a plane, & c.

(EW I.81–2)

But Hobbes also affirms the Scholastic view that principles are indemonstrable, adding that there are no principles aside from definitions (EW I.80, 82). Properly speaking, definitions are not demonstrated; hence their generation is not scientific ratiocination or computation. So, though one might make visible the definitions of natural and civil philosophy in a way that parallels geometrical construction of a figure, this is only a demonstration in a loose, analogous sense. Hobbes’s analogies thus do not support the bifurcation into a demonstrative method of construction in civil science versus the physicist’s method.

With this confusion removed, can we now articulate a unified method that would legitimize Hobbes’s claim to inaugurate a moral science based on the true foundations of natural philosophy? Even having restricted scientific knowledge derived from the primary geometrical definitions to Hobbes’s narrow sense of propter quid demonstrations, this remains challenging. If the success of Hobbes’s project rests on the capacity of his method to provide a true foundation of definitions or principles about universal causes from which, through a unified chain of syllogisms, ever more specific and complex effects are deduced, then it seems to fail. Notwithstanding that all scientific knowledge is knowledge of bodies, there are key differences between the aspects of body that each individual science takes as its object.

Natural philosophy scientifically knows what follows from the accidents of natural bodies whereas civil philosophy scientifically knows what follows from the accidents of the artificial body that is the commonwealth. Within natural philosophy, geometry, which lies at the base of the hierarchy in De corpore, takes as its object the accidents common to all bodies whereas physics takes as its object qualities, i.e., accidents of bodies as sensed by humans. This implies that the application of Hobbes’s generic method varies with object. As scholars have long realized, Hobbes’s actual procedure in physics differs from that of geometry and civil science since we are not privy to the underlying causes of the bodily qualities we sense.¹⁵ In physics one cannot define a quality by mentally constructing it, as one does with the generative definition of a square or when one imagines a commonwealth coming into being. Rather one must begin from observed effects, like the reddish hue of the setting sun or the passion of joy we feel when we watch it, and reason hypothetically to their possible causes. Since physics lies in the middle of the hierarchy of scientific knowledge providing the bridge between geometry and practical philosophy, if one assumes that unity means the sciences present a unified content, via an axiomatic-deductive method whereby all their conclusions trace back through a seamless chain of deduction to the same foundational definitions, then the divergent methodical procedure necessitated by the objects of physics appears to disrupt the unity of the whole.

In the face of these problems, one can 1) deny that Hobbes maintains a unity of theoretical and practical philosophy or 2) affirm a looser unity by denying that it is conditioned upon an axiomatic-deductive method. Advocates of 2) present evidence of Hobbes’s commitment to a non-deductivist unity. I draw on two recent views of this unity to propose a third. 2a) reads Hobbes’s sciences as unified not by a systematic content ultimately deduced from first principles, but by a common “demonstrative” method analogous to the geometrical method of construction.¹⁶ This strikes me as the correct strategy; however, though one finds procedures resembling constructions throughout Hobbes’s works, they cannot, as per his formal definitions constitute scientific demonstrations. Hence though they loosely connect practical philosophy with geometrical procedures, they cannot account for a moral science in Hobbes’s sense. 2a) also excludes physics from science. 2b) holds that Hobbes maintains the possibility of scientifically deducing a consistent body of theoretical and practical knowledge from first principles but includes alternative starting points and methods for non-philosophers to gain knowledge of practical philosophy.¹⁷ This too is promising, but to the extent that there is one method, it is an ideal that does no work. In practice, Hobbes proceeds as though physics and politics are independent domains with their own methods.

Despite these problems, 2) is better supported than 1). Hobbes’s view of scientific knowledge and generic definition of method point to one type of cognitive activity that constitutes scientific knowledge of all philosophical subjects. Regardless of whether one studies natural or artificial bodies, starts from cognitions of causes or effects, formal definitions or true cognitions attained by introspection, the process of methodical computation that charts the shortest route between causes and effects should be identical. This fits Hobbes’s aim of inaugurating a civil science to exorcise the Scholastic philosophy Empusa. Absent a unity of method for science, the boundaries between practical philosophy and religion will blur as non-scientific forms of cognition can then be invoked to confuse the rights and duties of subjects. Hobbes’s approach to identifying and removing the source of civil strife then falls apart. Hence overall 2) is the correct approach. I now draw on Hobbes’s context to propose a third variation, 2c).

Key is recognizing that Hobbes’s generic definition of method is just that. He next distinguishes method into what his contemporaries call universal method versus a method of proof for solving particular problems, known as particular method. Universal method was typically a preliminary hierarchical ordering of the concepts and definitions required for the discovery or teaching of knowledge of a subject, or both. It is distinct from method as a set of rules for scientific proofs, as found in Aristotle’s Posterior Analytics.¹⁸ Nonetheless, the two methods go hand in hand since universal method provides the systematic framework within which one generates different kinds of proofs by the particular method. This provides a third kind of unity for all scientific knowledge, rooted in method, with universal method providing a hierarchically ordered set of principles and definitions one requires as starting points for the deductive arguments one then makes in different domains to answer particular questions. Interpretation, 2c), allows for one computational activity that unifies all the sciences: namely, the rules of syllogistic reasoning for making valid propter quid demonstrations once one has the true principles, and applies the relevant definitions to the problem at hand. But to avoid willy-nilly attempts at deduction from any definitions, Hobbes’s method includes a preliminary methodical resolution of ideas and orderly composition into definitions, starting from the simplest concepts of geometry. This ensures unity at the level of first principles and the definitions one is permitted to take as starting points for scientific demonstrations at each level of inquiry. 2c) has been overlooked because just as Hobbes uses “demonstration” equivocally, he characterizes both activities as “computation” and labels methodical procedures that make up both the ordering computation and the syllogizing computation as analysis and synthesis.¹⁹ The two branches of method have thus been confused for one. I now disentangle them.