Leviathan Hobbes spells out how a methodical process of connecting names into propositions, and propositions into deductive proofs known as syllogisms, results in scientia. Reason, he says, is:
attayned by Industry; first in apt imposing of Names; and secondly by getting a good and orderly Method in proceeding from the Elements, which are Names, to assertions made by Connexions of one of them to another; and so to Syllogisms, which are the Connexions of one Assertion to another, til we come to a knowledge of all the Consequences of names appertaining to the subject in hand; and that is it, men call SCIENCE.
(2012, 72; 1651, 21)
When Hobbes claims to have inaugurated a scientia civilis, he means a body of conclusions about the commonwealth that can be deduced syllogistically from methodically attained premises that ultimately derive from definitions. Hence, though I will follow convention and translate “scientia” and the corresponding verb, “scire,” as “scientific knowledge” and “to know scientifically,” I do not thereby speak of experimental science in our sense. For other forms of knowing, which Hobbes labels cognitio, I employ the broader term “cognition.”
1.2 Hobbes’s Method for Scientific Knowing
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,