Thomas Hobbes and Nominalist Logic

|||Hobbes, Thomas, and Edwin M. Curley. Leviathan. Indianapolis (Ind.): Hackett Publishing Company, 1994.|||

Nature itself cannot err; and as men abound in copiousness of language, so they become more wise, or more mad, than ordinary. Nor is it possible without letters for any man to become either excellently wise, or (unless his memory be hurt by disease of ill constitution of organs) excellently foolish. For words are wise men’s counters, they do but reckon by them; but they are the money of fools, that value them by the authority of an Aristotle, a Cicero, or a Thomas, or any other doctor whatsoever, if but a man. Thomas Hobbes, The Leviathan, I.4.

In this article, I would like to give brief treatment to a trend—not a full exposition, nor a full refutation. My reflections are guided by the greater sagacity of others on these matters, and I want to acknowledge that fact from the beginning. In such critical matters as metaphysics and logic, the philosopher must be very careful. For our purposes, I am merely going to sound out some general issues that arise in a particular manner of conceiving of logic.

There are a number of rather cheap ways to differentiate Aristotelian and modern logic, among which one can find the assertion that one is “intensional” and the other “extensional.” What is meant by this? To be honest, the very expression itself does cast the net so wide that one can give almost any meaning he or she wishes to the two terms—intension and extension. One might wish to say that symbolic logic only talks about classes of individuals, while ancient logic was concerned with essences and meanings. This not quite correct—and it likely will end in a poor definition of the formal object of logic. Still, stereotypes and popular wisdom almost always have some kernel of truth—or at least an insight that ought not to be ignored. Can this be said here, and if so, what are the general—by which I mean very general—implications of extreme forms of symbolic thought in logic?

I have heard an astute commentator remark that it is possible to read Hobbes as a type of ne plus ultra of the general élan of modern thought. With a certain grim logic, many of his positions unfold almost mechanically. This is particularly the case in a text like the Leviathan, which bears the marks of a new kind of thinking, one imbued with the rigors of thinking more geometrico—in the deductive, geometric manner of proceeding. We often think of Hobbes as the father of empiricism, but things are not quite so simple. Like so many of his time—for a number of reasons both speculative and historical—he was taken in by the demonstrative power of geometry. Merely to cite one remark of such approbation, consider his words concerning definitions: “And therefore in Geometry, (which is the only Science that it hath pleased God hitherto to bestow on mankind,[sic]) men begin at settling the significations, they call Definitions; and place them in the beginning of their reckoning.”

What one might call “nominalist logic” is quite akin to mathematical reasoning. Of course, as Henry Veatch remarked, “Unfortunately, the term ‘nominalism’ is very imprecise, covering a great multitude of rather different philosophic sins and perhaps even a few philosophic virtues.” Still, certain trends are fairly called “nominalism,” among which is an emphasis on the act of “naming” as that which gives universality to a group of particulars. For instance, in Hobbes, we find an expression like, “There is nothing in the world Universal but names.” Perhaps this is expected and seemingly insignificant—the English are all a bunch of nominalists after Ockham, right? Matters just aren’t so simple, though. Even sound Peripateticism will admit that there is nothing universal qua universal in the order of existing beings. As “bobcat” exists in individual animals, it is particular. However, as it is considered by the mind, it is universal—at least so would go an extremely summary form of the more developed Thomistic position. Still, how does it exist in these two manners, and what does that mean? Alas, to answer that adequately, one will need to travel far and wide into the treatises on “separate substances,” esse intentionale, and other such topics. These are, of course, too varied for a short essay.

However, the logic of the nominalist position is often an expression of something quite different from this type of level-headed consideration of the hoary problem of the universals. Often, the assertion, expressed in a form akin to that taken from Hobbes above, is a cipher for a denial of formal causality. What is really means is something like, “There are individuals, and I name them. That is really all I can do to account for how the mind works.” Now, even in Hobbes, there are myriad ambiguities about similarity between beings and how such naming occurs—such things are ultimately related to formal causality. Still, the élan of such thought is such that it inexorably leads to a striking form of “mathematicization” of reasoning, as can be seen in a passage like: “In sum, in what matter soever there is place for addition and subtraction, there also is place for Reason; and where these have no place, there Reason has nothing at all to do. Out of all of which we may define, (that is to say determine,) what that is, which is meant by this word Reason, when wee reckon it amongst the Faculties of the mind. For reason, in this sense, is nothing but Reckoning (that is, Adding and Subtracting) of the Consequences of general names agreed upon, for the marking and signifying of our thoughts; I say marking them, when we reckon by our selves; and signifying, when we demonstrate or approve our reckonings to other men.”

What is interesting is that such an approach to reason seems rather intuitive. For instance, consider the classic example: “All men are mortal. Socrates is a man. Therefore, Socrates is mortal.” It would seem that this could be recast: “For all X, if X is a man, then X is mortal.” Since Socrates is a man, thus he is a mortal. Is this not the same as the standard syllogism? Well, at least hidden in such nominalist logic would be some form of reasoning that could be recast as, “For all things X, if X is a member of the set of human beings, then X is a member of the set of all things mortal.” What is hidden from view—by the common sense language—is the status of X. What is it?

Let us take an illuminating example cited by Veatch. At one point of his intellectual development, Bertrand Russell puzzled over the form of expressions like, “Sea-serpents do not exist.” What is one to make of this form of proposition? Are we asserting that sea-serpents exist only then to deny that existence? Certainly not! Instead (Russell remarks), the proposition should be understood as expressing, “There exists an X, such that X is a sea-serpent and X lives in the sea.” Here, just as much as in the case of the recast syllogism above—though it was more hidden there—the argument of the “logical function” is really just a bare particular—naked, unclad, and lacking formality, or so it would be claimed. Now, one can begin to wonder how the whole system fits together and how propositions can be tied together as a full system. There are various attempts to fit together such a logic, but unless one is to fall prey to a species of absolute voluntarism, some explanation must be given for formal similarity. A positivistic solution—the myth of “sense data experience”—may be suggested. I am wholly unconvinced that it provides the analytical resolution necessary to explain even an expression as simple as, “I see this spot.”

Without some account of formal causality, there will be no account for intelligibility—in a sense, that is all that formal causality is meant to specify. To say, “This three-dimensional matter” is already to speak of “that which” it is and that “out of which” it is “made” or fashioned. Two principles are involved, and only one of them provides an account of intelligibility. One cannot reduce the logic of grammar to a calculus unless one wants to claim that logic is completely disinterested in essence or form—and there is a long history of Aristotelian logic that clearly is not so reductionist.

Now, I am not spurning this kind of thought completely. However, I am calling it out for what it is: A surreptitious mathematizing of thought. In fact, it is a telling example of how the mind proceeds in those intermediate sciences that deal with sense data as well as the objects of mathematics that cannot actually exist outside of the mind. (Classical mechanics as well as modern physics is an example of such “subalternate” sciences.) They are idealizations that have more flesh than geometry—and for that reason, they do treat reality and can be used to “save the phenomena” in generalized laws. Regarding quantified set-theoretic logic (whatever its particular form), it is not logic in the traditional sense but instead some form of subalterned mathematical knowledge. It has a usefulness, but it does not map onto an account of reason and the way that being is understood qua rationally knowable. Still, just as the specter of the atomists will remain a constant temptation to the human imagination, so too will such a nominalist form of thinking be a tempting “quick fix” to the explanations of how “logic works.”

For the purposes of this article, I will feel that I have accomplished my goals if I have effectively warned my readers against conceiving logic as mere talk of particulars and universals without perhaps also talking about (e.g.) intentionality, predicables, categories, and formal causality.

About Matthew Minerd Matthew Minerd Matthew Minerd, PhL is a PhD student at The Catholic University of America. His research and reading interests are the history of the Thomistic Tradition, 20th Century French Thomism, and sundry topics metaphysical and ethical. Follow Matt on Google+