October 25, 2015
This volume contains the mathematical and physical parts of Hobbes's Elements of Philosophy (= De Corpore). Hobbes was a poor mathematician and scientist, so studying the details is not very interesting. However, Hobbes's vision of a general philosophical method modelled on mathematics is quite interesting. This is what I shall focus on in my review.
Hobbes maintains that his Elements of Philosophy is "to an attentive reader versed in the demonstrations of mathematicians ... clear and easy to understand, and ... without any offensive novelty." (vii)
Thus he defines: "Philosophy is such knowledge of effects or appearances as we acquire by true ratiocination from the knowledge we have first of their causes or generation." (3)
This definition is explicitly modelled on mathematics: "How the knowledge of any effect may be gotten from the knowledge of the generation thereof, may easily be understood by the example of a circle: for if there be set before us a plain figure, having, as near as may be, the figure of a circle, we cannot possibly perceive by sense whether it be a true circle or no ... [But if] it be known that the figure was made by the circumduction of a body whereof one end remained unmoved" then the properties of a circle become evident. (6)
Another way of putting it is that "The subject of Philosophy, or the matter it treats of, is every body of which we can conceive any generation." (10) Just as the domain of geometry is the set of constructible curves.
As the circle example shows, motion is a basic form of generation. Indeed motion is the foundation of geometry and physics alike. "First we are to observe what effect a body moved produceth, when we consider nothing in it besides its motion; ... from which kind of contemplation sprung that part of philosophy which is called geometry." (71) Next "we are to pass to the consideration of what effects one body moved worketh upon another; ... that is, when one body invades another body which is either at rest or in motion, what way, and with what swiftness, the invaded body shall move; and, again, what motion this second body will generate in a third, and so forwards. From which contemplation shall be drawn that part of philosophy which treats of motion ... [and ultimately] comprehend that part of philosophy which is called physics. (71-72)
"And, therefore, they that study natural philosophy, study in vain, except they begin at geometry; and such writers or disputers thereof, as are ignorant of geometry, do but make their readers and hearers lose their time." (73)
"After physics we must come to moral philosophy; in which we are to consider the motions of the mind, namely, appetite, aversion, love, benevolence, hope, fear, anger, emulation, envy, &c." (72) "For the causes of the motions of the mind are known ... And, therefore, ... by the synthetical method, and from the very first principles of philosophy, [one] may by proceeding in the same way [as in geometry and physics], come to the causes and necessity of constituting commonwealths, and to get the knowledge of what is natural right, and what are civil duties; and, in every kind of government, what are the rights of the commonwealth, and all other knowledge appertaining to civil philosophy." (73-74)
Carefully enunciated definitions are another prominent aspect of mathematics that is to be carried over into general philosophy. "Whatsoever the common use of words be, yet philosophers, who were to teach their knowledge to others, had always the liberty ... of taking to themselves such names as they please for the signifying of their meaning, if they would have it understood. Nor had mathematicians need to ask leave of any but themselves to name the figures they invented, parabolas, hyperboles, cissoeides, quadratrices, &c. or to call one magnitude A, another B." (16) "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." (81-82)
Logical, syllogistic reasoning is another distinctive attribute of mathematics. In fact, "They that study the demonstrations of mathematicians, will sooner learn true logic, than they that spend time part in reading the rules of syllogizing which logicians have made; no otherwise than little children learn to go, not by precepts, but by exercising their feet." (54-55)