Are the Laws of psychology Necessary?

There are laws of physics and laws of psychology, but are these laws of the same kind? Of course, they are about different things, but do they have the same modal status? Are they both nomologically necessary? The laws of physics are: they are universal and unalterable by human action. Everywhere you go the law of gravity holds; physical laws aren’t local. These laws are rightly called laws of nature—they characterize nature as a whole. They are as widespread as the universe itself (so far as we know). And no one can change them: nothing you can do will suspend the law of gravitation (or the electromagnetic laws, etc.).  The laws of physics are unconditional, ubiquitous, and immutable. They are not restricted to our solar system or even our galaxy. You can boldly go anywhere and they will be there waiting for you, always the same. But the same is not true of psychological laws: these laws are species-specific (in a broad sense of species). Some of them are species-specific in the usual sense of “species”, but if they apply more widely than this, they are still restricted to specific animal groups.  The law “Praise increases self-esteem” is presumably limited to humans, but other laws of psychology will be restricted to mammals or vertebrates or terrestrial life. Let’s take the example of memory laws, such as the frequency and recency laws: the more frequent or recent an experience the more it will be remembered. This law holds for many groups of animals, but does it hold for all? What about worms or wasps? Couldn’t there be a species that doesn’t exemplify these laws but still remembers things? It might obey the intensity law: the more intense the stimulus (louder, brighter) the more it will be remembered. What about laws relating emotion and memory—such as that strong emotion can enhance memory? That would hardly apply to an emotion-free organism that nevertheless remembers. Mr. Spock’s mind is free of emotion, so the laws governing it will not have an emotional component—it works by non-human psychological laws (he is not upset by insults). Thus, we have no trouble with the thought that in remote galaxies there might be minds that obey quite different laws from those with which we are familiar. Psychological laws are not going to be universal, invariant, built into nature; they are local, variable, parochial. They are more like anthropological laws, which vary with the society being considered: what holds of one society may not hold of another (science fiction is full of such societies). Psychological laws are not universal necessities.

Why is this? The answer, presumably, is that minds are adapted to specific types of environments and life-styles: what works for a mammal may not work for a mollusk. The laws of the octopus mind will not coincide with those of the bonobo mind. Just as an animal’s phenotype is shaped by its environment via natural selection, so the laws of that phenotype will be so shaped, including its mental phenotype. Psychological laws are evolved, selected, and modified over time. They are the children of selfish genes. Nothing like this is true of the laws of physics and chemistry. Artificial selection drives the point home: you could breed for certain psychological laws to obtain. Take the laws of conditioning, classical and operant: these hold for many animals, but we could intentionally breed them out and replace them with new laws. We could select for reproduction only dog minds that fail to acquire conditioned reflexes, or only pigeon minds that are bad at responding to positive reinforcement. We might get dogs that can never be made to salivate to bells, or pigeons that never learn to peck at levers that have supplied food pellets in the past. It all depends on genetics and brain wiring, which are manipulable. Likewise, we could breed for humans that don’t obey the frequency and recency laws of memory; or we could just interfere with the brain of humans to bring about this result. The laws depend on the mechanisms that depend on the selection history that depend on the environment. They are created by the local environment; they aren’t written into nature as such. Psychological laws are biology-dependent; they are contingent in that sense. Not even the laws of psychophysics are guaranteed to apply to all organisms capable of responding to a graded stimulus. Physiological laws are also species-specific, depending on the kind of body in question, and psychological laws are no different. The worm has a different physiology from the human and its mind (such as it is) is not operationally the same as a human mind—the governing laws are quite different.

Are there any psychological laws that apply universally? Does every animal act to fulfill its desires, say? This is certainly a very general law, but is it as universal as the law of gravity? Every physical body has mass (more or less) but not every organism has desires, though it will doubtless have biological needs. Some animals may be highly illogical, some models of rationality; some emotional, some clinical. It is hard to think of any psychological law that is written into nature—that is, intrinsically universal. Every mind obeys some set of psychological laws, but there is no set of psychological laws such that that set applies to all minds. Certainly, we can say that generally psychological laws are species-specific. The law of gravity (or the laws of motion in general) applies to every material body in the same way to the same degree, but psychological laws never apply identically to every organism with a mind. Bodies are nomologically homogeneous, but minds are not. Animal minds vary tremendously, and so do the laws governing them. Zoology isn’t like chemistry: the elements always behave in the same way—not so animals. Our Earth-centered zoology may have little application to the animals on other planets, but our chemistry will carry over nicely. Strange beasts, familiar chemicals. None of our species may exist on some distant planet, but surely our chemicals will be all present and correct (ditto our atoms).

This means that psychology will never be quite like physics. Physics envy is folly. This isn’t because there are no psychological laws, or that all such laws are ceteris paribus not strict, or that psychological laws can never be quantitative in the way physical laws are; it is because they lack universality. Even if they exist in plenty and are strict and quantitative, they would not have the range of physical laws—they would always be contingent and parochial. Nothing wrong with that—we should give up our craving for generality—but it is misguided to try to imitate the universality of the physical sciences. If you imagine what psychology will look like in the age of intergalactic travel, it will surely be a multi-faceted subject: there will be departments of human psychology, of Vulcan psychology, of Klingon psychology—not to mention the many animal species that need a psychology department of their own. A comprehensive Department of Psychology will be a vast undertaking, including many divisions and subdivisions; but the physics department will be a small operation employing relatively few professors, physics being a smaller field. Pan-galactic zoology is a vast area of study well beyond the capabilities of even the most learned man or woman, while pan-galactic chemistry is relatively confined and manageable. So, zoology and psychology will never have the range of physics and chemistry, but it will outdo them in manpower and variety. There will be many more doctorates in those fields than in the physical sciences. Indeed, physics and chemistry may long ago have come an end, everything having been discovered, while zoology and psychology are still in their infancy, with many living planets awaiting investigation. Physical science comes to a natural end while psychological science marches on.[1]

[1] One reaction to these reflections would be to announce that there are no genuine psychological laws, the emphasis indicating that genuine laws must be universal. The question is somewhat verbal, but one sees the point of such a declaration. A local law sounds like a contradiction. We might also consider the question of whether local psychological laws must be backed by non-local physical laws, thus deriving the conclusion that minds must ultimately be physical (cf. Davidson). We also have psycho-physical laws on the books: these combine the local with the universal, inviting the question of whether they are local or universal. It is certainly true that the physical laws were there first and that the psychological laws somehow rest on them (psychological laws are physically supervenient). These are topics for further study.

Conceptual Analysis Mathematized

Frege mathematized meaning by invoking the concept of a function, the central concept in modern mathematics. Concepts are conceived as functions from objects to truth-values, etc. This enables Frege to give a systematic rigorous account of the workings of language, modelled on mathematical notation. I propose to do the same for conceptual analysis: the analysandum is viewed as a function from the elements constituting the analysans. For example, knowledge is a function from belief, truth, and justification to a propositional component (intuitively, the concept of knowledge viewed as a constituent of thought). There are several ways of constructing the arguments and values of such functions, but the important point is that the function exists: it takes us from the primitive elements of the concept to the concept itself. It operates as a kind of binding function: it unites the several elements into a conceptual whole, glues them together. Thus, the concept is not just a list or conjunction; there is a natural unity. We define the function as second-level because it takes first-level functions as arguments—since belief, truth, and justification are functions from objects to something else (truth-values or states of affairs). The idea is that complex concepts like knowledge are mappings from simpler concepts, themselves mappings from one kind of entity to another (ala Frege). There is a hierarchical structure, representable by a tree diagram, linking complex concepts to simpler concepts. Of course, the concepts used in the analysis will often have analyses of their own, so that the tree will be ramified and many-branched. We could assign a number to its complexity and compare analyses in respect of cardinality (the concept of a game, say, might be twice as complex as the concept of knowledge, computed according to the number of functions in the analysis). A whole proposition (thought) would combine several analyzable concepts (“John knows what a game is”) and this entity would contain the full analysis of all the concepts that compose it. It would be mathematically quite hairy. The structure is familiar from linguistics and descriptions of conceptual constituency; I am merely adding the Fregean apparatus of functions, arguments, and values. We view the basic concepts as inputs to a function that gives as output a complex concept containing the input concepts. Think of the concept-forming function as a binding function: it fuses the elementary concepts into a conceptual whole that is available for cognitive use. Geometrically, it is defined over a space of basic concepts (also functions) that can be assembled into complex wholes; it is not unlike atoms and molecules, or words and sentences, or organs and bodies. We have a kind of mereological mathematics applied to the conceptual domain. Concepts can share parts and hence be available for intersection—one concept may incorporate an element also possessed by another concept. Set theory may thus be brought to bear. Formal methods can be applied to the domain of concepts, because of their compositional structure. We get a mathematics of the conceptual—primitive perhaps but mathematically formulated. It will yield equations like “Knowledge equals the combination of Belief, Truth, and Justification” (K=BTJ), i.e., “The thought-content of the concept of knowledge is the value of a second-level function from first-level functions corresponding to the attributes of Belief, Truth, and Justification”. This should satisfy the ambitions of mathematically inclined analytical philosophers wedded to the project of conceptual analysis.[1]

[1] Nothing says that this is the only way to mathematize conceptual analysis; I offer it as one way to impose mathematical structure on the underlying reality—illustrative not definitive.

Analysis and Mathematics

Mathematics is an analytical discipline (a branch of it is even called Analysis). It analyzes shapes (geometry), numbers (arithmetic), populations (statistics), motion (calculus), logical relations (mathematical logic), chance (probability theory), games (game theory). The OED gives us two definitions of “analysis”: “a detailed examination of something in order to explain or interpret it” and “the process of separating something into its constituent elements”. Putting these together, we could say that analysis is the detailed examination of something in order to separate it into its constituent elements. Mathematics does this in a rigorous and precise way: it breaks entities into their parts and specifies the relations that constitute wholes. It isn’t interested in the meaning of these entities in human life, or their psychological significance, or their poetic resonance, or their historical influence; it wants to know their constituent structure, pure and simple. It takes an abstract domain and dissects it, probes it, disassembles it. It looks for primitive entities and relations and investigates how they combine to produce more complex entities. A mathematics text can always be called A Mathematical Analysis of X. But is all analysis mathematical analysis? That is by no means clear; it depends on our notion of analysis and our interpretation of “mathematical”. Chemical analysis is clearly mathematical: it uses numbers and geometric shapes, and it employs rigorous methods (the OED defines “mathematical” as “(of a proof or analysis) rigorously precise”). Economic analysis is typically quantitative and mathematically formulated (e.g., the laws of supply and demand). Anatomical analysis specifies bodily parts in numerical and geometric terms (size and shape). But what about psychoanalysis or textual analysis or conceptual analysis—are these mathematical?

It might be said that psychoanalysis is mathematical in that it divides the psyche into precisely three parts—the id, ego, and superego. It also specifies quantitative laws of motivation expressed hydraulically. It aims for rigor and precision (it tries to be mathematical). The mathematics is crude and simple, but it is still mathematical in form—it resembles a typical scientific theory. Psychoanalysis is a bit like evolutionary science in this way: it too is concerned with quantitative structural relations—the probability of survival given certain genetic and environmental conditions. Some biology is aptly described as mathematical biology. Textual analysis can certainly be mathematical, even if not all is—word frequencies, inscriptional forms, etc. Astronomy also analyzes the physical universe mathematically, though some is not mathematically formulated. Linguistics is partly mathematical, though not wholly. Logic is certainly analytical and has attained the status of a mathematical discipline. Genetics is pretty mathematical, as is psychology. The concept of the mathematical is broad and inclusive; it doesn’t need to approximate the equations of advanced theoretical physics. The human mind is quite mathematical, thinking habitually in terms of quantity and number—counting, measuring, computing. It is perfectly possible to be mathematical about the arrangement of your room or the structure of a piece of music or the shapes in a painting. We shouldn’t overintellectualize mathematics or equate it with what we learn in school in a mathematics class. Other animals have rudiments of it, as do pre-school children. Mathematical competence is arguably innate (remember the Meno). Mathematical thought is more pervasive than might be supposed. We think in terms of sets and their relations. We recognize the magnitude of multiplicities. We add, subtract, divide, and count. We symbolize and generalize, abstract and mathematize. We have mathematical minds, and we like to impose mathematical methods on reality.

I say all this in order to prepare the ground for a somewhat startling thesis: conceptual analysis is mathematical analysis. Analytic philosophy is mathematical philosophy. In analyzing concepts, we mathematize them, as we have so much else. We can approach the matter both historically and intrinsically. Historically, we have the figures of Frege, Russell, Wittgenstein, Carnap, Tarski, Quine, Kripke, Montague, and many others—all mathematicians by training and eager to apply its methods and attitudes to philosophy. Russell wrote Introduction to Mathematical Philosophy and Montague wrote Formal Philosophy. The shape of so-called analytical philosophy was certainly influenced by mathematics, modelled on it, inspired by it. Tarski’s theory of truth is a prime example. Carnap’s Aufbau is in this tradition. These philosophers wanted philosophy to be rigorous and precise, and mathematics was their paradigm. This conception of philosophy contrasts with other conceptions prevalent in the intellectual tradition: historical and cultural (Vico and Collingwood), psychological (Locke and Hume), religious (Aquinas and many others), linguistic (Austin and later Wittgenstein). It is ahistorical, anti-psychologistic, secular, and contemptuous of ordinary speech. It likes proof not poetry, dissection not description, abstraction not particularity. It is Pythagorean not Hegelian or phenomenological. It is about logic not life, entailment not lived experience. It prefers science to stories. It deals with the form of thought not the dynamics of action (the “deed”). It is formalistic not humanistic. It prefers rigor to uplift. It reveres Plato more than Aristotle, and has no time for Nietzsche. It is pure not applied. It is anti-biological. It is above politics. It is contemplative not practical. It deals in necessities not contingencies, essences not empirical facts. It is more rationalist than empiricist (Russell’s first book was on Leibniz). Thus, analytical philosophy is mathematically oriented, mathematically imbued; it grows from mathematics.

Viewed intrinsically, we can note that conceptual analysis is what the name implies—analytical; it breaks concepts into their more primitive elements. It reduces unity to multiplicity. This multiplicity has a number—the number of necessary conditions that constitute the concept. Thus, knowledge has three necessary conditions, according to the classical analysis—belief, truth, and justification. These conditions are recognized in their numerical dimension: this is a three-component concept. Each component is added to the others to produce the concept being analyzed. We could represent the analysis in the form of an equation: knowledge equals belief plus truth plus justification. This appeals to our mathematically inclined mind. We could say the same about the causal analysis of perception, Grice’s analysis of speaker meaning, Suit’s analysis of the concept of a game, or any other attempt at conceptual analysis. We could divide concepts into three-component concepts, two-component concepts (a bachelor is an unmarried man), and one-component concepts (primitive concepts like the good, according to Moore). That is, we could dwell on the numerical attributes of concepts. Concepts have a mathematics, according to the tenets of analytical philosophy, construed as methodologically mathematical. We already do this with regard to other points of conceptual analysis: we speak of one-place, two-place, and three-place predicates; we distinguish first- and second-order quantifiers; we call existence a second-level concept; we talk regularly of the finite and the infinite. Of course, we have a philosophy ofmathematics, as well as a generally mathematical philosophy. We are well aware that concepts have mathematical properties. Above all, we approach the task of analytical philosophy in a mathematical spirit—rigorously, precisely, as mathematically as we can. Some analytical philosophers even go so far as to apply mathematical model theory to philosophical issues (e.g., Montague). Such philosophers want philosophy to approximate to a mathematical science, and they are not wrong to be so motivated, because conceptual analysis fits the paradigm. This is why Russell’s theory of descriptions was so applauded by philosophers in the analytical tradition: it provides a mathematical analysis of the definite article (symbols, quantifiers, formality). Similarly, for Tarski’s theory of truth and Davidson’s attempt to convert it into a theory of meaning. If only we could employ calculus to resolve the problems of space and time, or the statistics of neurons to solve the mind-body problem! It is an entrancing vision. It beats windy pronouncements about the course of history, or the problematics of the text, or the puny joys of “experimental philosophy”. Mathematical philosophy sounds like the kind of philosophy a serious student might get behind. Okay, it hasn’t quite lived up to the hype, but its heart is in the right place—some distance from the actual heart (unless you are Plato or Pythagoras). It carries better credentials than merely descriptive ordinary language philosophy, which threatens to turn into a kind of localized anthropology. In any case, the analysis of concepts looks like a bona fide case of mathematical analysis: it is precise, abstract, systematic, and susceptible of proof.

How does the mathematical method arise in the human mind? We don’t know, but here is a promising suggestion: it arises from the language faculty. For the language faculty is itself mathematically structured: it consists of a finite array of primitive elements (words) that combine in a rule-governed way to generate an infinity of linguistic strings (sentences). We might plausibly regard the mathematical faculty as wholly or partially derived from the language faculty, arising at some point in evolutionary history. Without going into the matter further, we can entertain the hypothesis that our capacity to conduct conceptual analysis ultimately derives from our capacity for language; crudely, conceptual structure and composition mirror linguistic structure and composition, as seen through the lens of mathematics. The analytic-mathematical turn in philosophy owes its origin to the linguistic-mathematical turn in evolution: the human brain went linguistic and mathematical long ago and then much later it occurred to people to investigate the concepts involved in philosophical problems mathematically. Mathematics grew out of language millennia ago, developed in the course of human history, and then suggested itself as the royal road to philosophical enlightenment. According to this hypothesis, creatures without a language faculty will not develop a mathematical faculty, and will therefore not develop what we call analytical philosophy. This is a new type of “linguistic turn” in philosophy, happening perhaps millions of years ago not in the middle part of the twentieth century. First, we have the mathematical turn in philosophy that did happen in the twentieth century, but this turn depended on the prior existence of mathematics in the human mind, going back into deep evolutionary history, some time after the appearance of language in humans. From language to mathematics to analytical philosophy—the long curve of human intellectual history.

Mathematical-analytical philosophy was conceived as exclusionary—we should do that kind of philosophy and not the other kinds of philosophy. But this is not compulsory: we can let the mathematical kind of philosophy roam over its domain of operations but we can also make room for the historical, psychological, anthropological, spiritual types of philosophy. We can have existentialist philosophy as well as essentialist philosophy—the human condition and necessary and sufficient conditions. The humanistic and the formalistic. For example, we can philosophize about the role of games in human life as well as analyze the concept of a game in quasi-mathematical style. Collingwood can coexist with Russell, Sartre with Carnap. Doing analysis does not preclude investigating Dasein. We can talk about the structure of our concepts and the meaning of life. We can have analytical philosophy and the other kind (it has no accepted name)—historical, hermeneutical, humanistic, humid. We can have the dry and the moist, the desiccated and the succulent. By all means let’s take the gustatory turn! We can be both mathematical and musical (bacchanalian even). Punk philosophy is not out of bounds (it belongs with existentialist philosophy). We can talk about money and sexual perversion as well as knowledge and the form of the good. You could happily describe yourself as an analytical-humanistic philosopher. What you don’t want to be is a bullshit philosopher (either pedantically so or pretentiously so). There is more than one way of being good at philosophy.[1]

[1] Unfortunately, few people are good at both types of philosophy: if you are good at one, you tend not to be good at the other. Practically, I would encourage graduate schools in philosophy to educate students in both traditions, while allowing that students will generally be better at one sort of philosophy than the other. There is, however, no excuse for the dismal prose style of the typical product of an American philosophy graduate program. Someone should really do something about this.