Habit and Generalization

1 Introduction

Both terms in our title, “habit” and “generalization,” are ordinary language expressions that take a peculiar and abstract sense in Peirce’s thought. This brief paper has the goal of clarifying their meanings and mutual relationships in order to shed light on some crucial points of Peirce’s thought in connection with various philosophical issues of great interest and relevance at present.

From various standpoints ,the concepts denoted by these two terms prove to be fundamental for understanding Peirce’s ideas, and eventually for further development of these ideas by other thinkers. They are logically interrelated and entangled with other key notions of Peirce’s philosophy, within a tightly knit fabric of conceptions that mutually support and reinforce each other. Here I will try to highlight some of these interconnections with the intention of elucidating some consequences of adopting these concepts, and of adumbrating the perspectives they disclose to us.

In what follows I try to attain a unified vision, one that leads to a focal point where several of Peirce’s most important ideas converge. This outlook comes from the realization that his thought moves toward a goal that he constantly suggests but does not quite articulate explicitly ^– at least in any of the numerous writing I have had occasion to examine. The unstated objective I am referring to is no other than the goal of generalizing the very idea of generalization. The self-referential nature of this project is consonant with similar notions that emerge, here and there, in Peirce’s works, and which appear here under the rubric of “the habit of acquiring habits.” ^[2]

2 Habits

The “habit” we are here dealing with is the outcome of an extreme generalization of the meaning of that term in its ordinary sense. For instance, I have the habit of going for a walk with an umbrella when I notice the appearance of very dark clouds in the western sky. As a consequence of having gotten very wet on memorable occasions, I have acquired this habit because it habitually rains when such clouds show themselves.

In the case of a person or any other organism, the habit is simply an acquired or innate tendency to display a certain kind of behavior each time circumstances of a well-determined character occur. Dogs chase after cats through a habit that seems innate, but Pavlov’s unfortunate dogs kept on acquiring new habits at the ringing of a bell.

When we apply the term “habitually” to the rain we are generalizing the concept of habit through analogy, starting from the behavior of organisms and coming to include totally different physical phenomena. We can rest content with this analogy or venture further, toward a higher-order generalization. This higher-order generalization will be more abstract and will be applicable to many situations not directly related to organismal behavior or weather contingencies, although these particular instances will be retained as special cases. This is precisely the route that Peirce invites us to take. As we will see later, generalizing the notion of habit entails an operation of a special kind, due to the fact that habits are themselves generalizing agents. So, we are engaged in a higher-order generalization, a sort of meta-generalization. Once the notion of habit is thus generalized, its connotational range swells to cover such diverse instances as those of symbol, rule, propensity, and law of nature.

3 Generalizations

The operation of generalizing is possibly the most essential function of the human intellect. In science and philosophy, the development of thought is marked by the progressive generalization of concepts, hypotheses, arguments, and theories.

From the beginning, Peirce generalizes the idea of generalization from its role as a logical function to extend it to the mental operations that support it, encompassing the entire psychic range of mental functions. He considers that the tendency to generalize is nothing else but the “law of mind”:

The one primary and fundamental law of mental action consists in a tendency to generalization. Feeling tends to spread; connections between feelings awaken feelings; neighboring feelings become assimilated; ideas are apt to reproduce themselves. These are so many formulations of the one law of the growth of mind. When a disturbance of feeling takes place, we have a consciousness of gain, the gain of experience; and a new disturbance will be apt to assimilate itself to the one that preceded it. Feelings, by being excited, become more easily excited, especially in the ways in which they have previously been excited. The consciousness of such a habit constitutes a general conception. (CP 6.21, 1891)

During a second stage Peirce generalizes the form of generalization that characterizes the life of signs and the mind toward their manifestation as features of life in general, in the evolution, development, and growth of organisms and their associations. From a sufficiently general standpoint, signs can be considered to be living beings and vice versa:

Every symbol is a living thing, in a very strict sense that is no mere figure of speech. The body of the symbol changes slowly, but its meaning inevitably grows, incorporates new elements and throws off old ones. (EP2, 264; CP 2.222, 1903)

Conversely, organisms and their associations are signs, and are animated through the interplay of numberless semiotic transactions. These have become the field of research of biosemiotics, a recently developed scientific discipline of Peircean inspiration (see, e.g., Barbieri 2007; Hoffmeyer 2008; Fernández 2010a, 2012a).

During a third and decisive step, Peirce generalizes the form of generalization that characterizes biological evolution to reach the all-encompassing realm of cosmic evolution. This supreme generalization, which harbors equally the lineages of signs, organisms, and stars, becomes at this point evoked by the term “habit” in its most general acceptation: the habit of acquiring habits. According to Peirce, at the very origination of time the universe emerged from a chaos conceived as totally void of determination and, concomitantly, as a plenum of totally undetermined possibilities. The following fragment from 1898 states in concise and summary form the roles played by habit, generalization, and the “habit of acquiring habits” within the evolutionary cosmology advocated by Peirce:

Qualities are already possible. Actual existence has begun. Accidental reactions are taking place. Several continua are established. A tendency toward generalization is operative.

But as yet no thing can be said to exist; much less any personal consciousness. The accidental reactions are purely accidental, unregulated in any degree by law, the work of blind and brutal chance.

But now the tendency toward generalization which is already operative, and which indeed is more ancient than actual existence itself, begins to group the accidental reactions into fragmentary continua. Into continua, because such is the logical nature of generalization. Into fragmentary continua because the tendency to generalization has to fight the lawless brutality of chance with its youthful freakishness and ebullient vivacity. At first, during the early eternities, those generalizations and continua are smashed as soon as they appear. For they are themselves of a haphazard kind with no vitality. But in this endless haphazard shindy between generalization and chance this generalization happens to come about, namely a limited but still a general tendency toward formation of habits, toward repeating reactions that had already taken place under like circumstances. Now the difference between this generalization, this tendency toward law, and the rest was that this was one which by its own law was always tending to grow stronger. […] until at length, […], there came to be a decided and so to say a sensible degree of tendency in nature to take habits.

This was the earliest of the laws of nature and was and still is continually strengthening itself. A habit of acquiring habits began to be established, and a habit of strengthening the habit of acquiring habits, and a habit of strengthening that habit, and so on ad infinitum.

The acquiring [of] a habit is nothing but an objective generalization taking place in time. It is the fundamental logical law in course of realization. (NEM 4, 139–140, 1898)

4 Habits and laws

Peirce’s speculative cosmology as sketched in the above-cited fragment was for many years a target of derision and contempt by scientists and philosophers moved by a strong antipathy toward some philosophic conceptions that ground his cosmological speculations.

In previous work I’ve had occasion to explain in some detail how this attitude is changing in consequence of several discoveries made in the physical sciences during the last century. It is not appropriate to repeat here the substance of those reflections, and those interested will find them conveniently available in electronic version (Fernández 2010a, 2012a). With regard to the questions that concern us here, it will be sufficient to review summarily a few issues pertaining to the evolution of the laws of physics.

There is a remarkable fact that has gone generally unnoticed and should, in my opinion, have deep consequences for the philosophy of the physical sciences. I refer to the rupture in the long tradition of an ahistorical stance in these sciences. As a matter of fact, since the emergence of modern science in the seventeenth century and in contrast to other disciplines ^– particularly the biological sciences since before Darwin ^– evolutionary ideas have failed to find a niche in the explanatory schemes of the physical sciences. In their simplest form, these schemes are based on the conjunction of two antithetical factors: the initial conditions of a phenomenon or process and the laws of physics.

The initial conditions represent singular and contingent determinations, which are usually subject to manipulation and quantitative recording during the preparation of experiments. They define the initial state of a physical system (for example, the speed and direction of a projectile as it emerges from a cannon at a given instant).

In contrast, in traditional physics the laws of nature are immutable principles of a universal and necessary nature, located within an abstract hierarchy of ascending generality. When the state of a system is given, as defined by the initial conditions, the laws of physics allow us to compute univocally the future states of the system (in the previous example, the parabolic path, the location, and velocity at each instant, according to Galileo’s law).

It is a striking fact that in recent times theoretical physicists, confronted with the need to explain unexpected and recalcitrant experimental data, have rediscovered some ideas advanced by Peirce in his speculations — ideas they had previously found philosophically repugnant.

Among such rediscovered ideas, there are two that tend to reinforce each other: the reality of objective chance (randomness independent of limitations to our predictive powers) and the mutability of the laws of physics (according to Peirce, more restrictive laws evolve from others, less restrictive, that allow a wider margin of causal indetermination).

At present, the idea that laws evolve has finally found favor among physicists and cosmologists of sound scientific reputation. Among them Leo Smolin is an eminent researcher who is well known through his proposals for reconciling relativistic gravity theory with quantum physics. He has developed the conception of a mechanism, analogous to that of natural selection in biology, to explain the evolution of physical laws in the remote past (Smolin 1997, 2012). Smolin quotes Peirce in his works and gives him due credit for anticipating such evolution. Remarkably, his theories lead him to contemplate early stages of cosmic evolution where the dichotomy between laws and initial conditions, noted above, is no longer absolute.

From Peirce’s point of view, the laws of physics are not abstract principles that mysteriously govern the phenomena without participating in them. They are, on the contrary, habits imputable to natural entities and processes as tendencies or dispositions to behave in the same general way every time circumstances of a certain general kind repeat themselves.

5 Generalization and the life of science

Up to this point I have only restated some ideas of Peirce, without attempting to go beyond what he has said and what can be inferred with sufficient certainty from his texts. In order to develop and extend Peirce’s ideas in the light of new conceptions and discoveries that emerged after the end of his career, it is necessary to advance new hypotheses that those findings may suggest or make necessary. Due to the limited scope of this essay, we shall be limited to bringing up a few observations and to advancing some ideas that they motivate, in the hope of exploring these ideas in future investigations.

The notion of generalization, together with some other closely related conceptions such as abstraction and unification, underwent notable alterations and development during the last century, in the wake of new discoveries within disciplines where the operation of generalizing plays a prominent role. This is especially the case in physics, mathematics and logic.

The discovery of the unsuspected heuristic power of an important kind of generalization was crucial for the development of quantum mechanics in the first three decades of the twentieth century. Physicists were encountering phenomena that were not predictable, and frequently not even intelligible, in the light of classical conceptions. It became necessary to find a guide for modifying and extending the older theories so as to explain and understand those new and enigmatic phenomena.

That guide was found in the principle of correspondence, first stated by Niels Bohr. In its original form, this principle promulgated the framing of hypotheses that were generalizations of the laws of classical physics, in the sense that they would reduce to those classical laws at the limit of large quantum numbers (high energies, large orbits, etc.), by making similar predictions, frequently in the form of statistical averages. ^[3]

This kind of reduction is not a peculiarity of the relations between classical and quantum physics. On the contrary, it is found to be a general phenomenon: new theories include as limit approximations the theories they are meant to replace. Examples are legion. Newtonian mechanics, for instance, appears as a valid approximation to the explanations given by the special theory of relativity, and yields practically equivalent predictions when dealing with speeds that are much lower than that of light. Galileo’s law of fall is an approximate limit case of a similar law derivable from Newton’s laws, etc.

Several philosophers of science have proposed generalizations of Bohr’s principle under the title of a “generalized correspondence principle” to raise it to the status of a heuristic formula applicable to the sciences in general (see, e.g., Post 1971; Radder 1991; Fernández 1993). ^[4] The generalized correspondence principle is actually a heuristic application of a philosophical realization, fruit of a reflection on the historical development of scientific theories. This reflection scans a chronicle of progressive replacement of precedent theories by new and superior ones that become their generalization.

From a Peircean perspective this reflection confirms the creative ascendance of the tendency toward generalization, which is the analogue within the intellectual realm of the creativity deployed by nature in the evolution of living forms. According to this analogy, the evolutionary novelties that made possible, for instance, the emergence of bacteria, have become incorporated as “limit cases” within the cells that make up the tissues of our bodies.

Scientists are continually seeking concepts, hypotheses, and theories capable of explaining the phenomena with the greatest possible generality and so to obtain the deepest unification of the most diverse findings under a single conceptual structure. New theories are thus generated with the power of explaining not only what was left unexplained in previous ones, but also the reasons why the replaced theories were able to yield correct results within their former range of application.

The mathematics and logic of the twentieth century have generated an amazing deluge of theoretical creativity in conceptions of unmatched generality and universality, which would have delighted Peirce. We should mention, among many others, the discoveries of metamathematics, algebraic geometry, category and topos theory, non-standard analysis, and the “motifs” and “schemes” of Grothendieck. All of these extend or promise to extend embryonic conceptions of Peirce that he was unable to elaborate. At the present time, the extremely technical and abstract nature of these ideas place them out of reach for all but professional mathematicians. ^[5]

6 To conclude

As is well known, Peirce’s logical and mathematical investigations, especially his unfinished theory on the mathematical continuum, and his existential graphs, led him to his doctrine of synechism, and to consider mathematical continuity as the highest form of generality.

Today we are acquainted with other lofty forms of generality that were not anticipated by Peirce. Among these, the mathematics and physics of the first half of the twentieth century brought to light the enormous generalizing power of the notion of symmetry, understood as a property of the phenomena that is left invariant under certain transformations. It is not an exaggeration to state that this conception is the leading idea of twentieth century physics and that it took over the role played by the concept of energy toward the end of the previous century (see, for example, Fernández 2012b).

Some authors have recently developed Eugene Wiener’s thesis that considers symmetries as a form of meta-laws, in the sense that their generalizing power stems from the fact that they constrain laws in ways analogous to the way laws constrain physical phenomena (see, e.g., Lange 2007). In the second half of the twentieth century the associated notion of symmetry breaking emerged as a powerful unifying force by playing a key explanatory role within previously separated theories in physics, chemistry, and biology.

These considerations have led me to speculate on the possibility of extending Peircean synechism toward a wider conception that could include the generalizing functions of ideas concerning symmetry and other kinds of invariance. In a recent paper (Fernández 2012c), I propose to interpret habit acquisition in terms of symmetry breaking. I thereby hope to add a modest contribution to the gigantic task of consolidating and extending the Peircean enterprise of generalizing generalization.