Because our behavior may respond to two kinds of teleology – *internal*, driving *goals* (control theory model) vs. *external* selective *functions*, either biological or social (Castelfranchi, 2001) – this is why there might be *conflicts* between one's internal goal and the *function* of one's action/behavior – also considering that we do not necessarily understand and thus intentionally pursue our biological or social functions. We may even act against the functions of our behavior. We may even cut the adaptive connection between our motives and their original functions, for example by deciding to have sex without inseminating or without establishing/maintaining any friendly/affective/supportive relation with our mate. As for social functions, an example of a conflict between our goals and our *role function* could be the goal that B be condemned while I'm his defense attorney.

As for social functions and roles in general, we play them (citizen, consumer, father, pedestrian,...) quite blindly; not because they are unconscious, or because just based on reinforcement learning or on mere "habituses" (in Bourdieu's view; see The Emergent, Collective, Self-Organizing Effects of our Behaviors), but because they are external to our minds. In fact, even our intentional and deliberated actions, evaluated on their (visible and

3For a deep philosophical and critical discussion of teleologies and the relation with causal explanation in natural sciences, see Larry Wright fundamental work (Wright, 1976). A remarkable attempt to deal with these problems also is Ruth Millikan's work.

conceivable) consequences, may "pursue" collective (good or bad) external "ends" (Castelfranchi, 2001).

For example, if we realize how marketing induces "needs," and deceives and manipulates us, we couldn't play well our most crucial "role" in/for society: the role of "consumers"!

Social functions are *parasitic* to cognition: they establish and maintain themselves *thanks to and through agents' mental representations but not as mental representations: i.e., without being necessarily known or at least intended.* "By pursuing his own interest he [the individual] frequently promotes that of the society more effectually than when he really intends to promote it." (Adam Smith; last sentence of cited paragraph in section "The Emergent, Collective, Self-Organizing Effects of our Behaviors.") However, it is possible, and even frequent, that – following our personal motives – we play our roles in contradiction with the mission and collective utility of our social function.

#### **GOALS VS. PSEUDO-GOALS**

It is also very important to disentangle true goals from *pseudogoals* (Miceli and Castelfranchi, 2012), that is, goals that only seem to be there and to regulate the system and its behavior. However, in fact they are not there as goal mechanisms, they are not represented in the system and "governing" it. They are just functional ways in which the system has been "designed" (by evolution, by learning, by the designer); they are the system's goal-oriented way of working, its operational rules. For example, a real thermostatic system (thermostat, thermometer, room, radiator, boiler, etc.) has been designed in order to reduce naphtha consumption, heat loss, etc. as much as possible. These are (pseudo)goals of the system, which works also in order to guarantee them; but they are not true cybernetic-goals like the set-point of the thermostat. They are not represented, evaluated, and "pursued" by the system action cycle.

Analogously, our minds have been shaped (by natural selection, or culture and learning) in order to have certain working principles and to guarantee certain functions, which are not explicitly represented and intended. It seems (from our behavior) that we have certain goals, but they are not real goals, only pseudo-goals. This is the case, in our view, of some well-known (and badly misunderstood) finalistic notions, like utility maximization, cognitive coherence, and even pleasure. No doubt, we often choose between different possible goals so as to maximize our expected utility, giving precedence/preference to the greater expected value; that is obvious and adaptive. However, this does not mean that we have "the" goal (the unique and monarchic goal) of maximizing our utility, indifferently to the specific contents and goods. On the contrary, we are moved and motivated by specific, qualitative terminal goals of ours (esteem, sex, power, love, etc.), but the *mechanism* that has to manage them has been designed and works so that it maximizes expected utility.

In the same vein, we maintain coherence among our beliefs, and need to avoid and eliminate contradictions. That is why we can reject certain information and do not believe all the data we get (sometimes even what we directly perceive; "we do not believe our eyes," literally); the new data must be plausible, credible, integrable, within the context of our preexisting knowledge; otherwise, we have to revise our previous beliefs on the basis of new (credible)

data. This coherence maintenance is frequently completely automatic and routinely. We have mechanisms for coherence check and adjustment. We do not usually have any real intention about the coherence of what we believe. Thus, knowledge coherence is a pseudo-goal of ours, not a real meta-goal guiding meta-actions.

### **PLEASURE**

Similarly, pleasure is not "the" goal of our activity, and the same holds for feeling pleasure (or avoiding feeling pain). "Pleasure" – as a specific and qualitative subjective experience, sensation (not as an empty tautological label for goal satisfaction) – normally is not a goal for us: it is not what we intend to realize/achieve while acting, what move us for performing that behavior. Of course, feeling pleasure or avoiding pain *might* become real goals and intentionally drive our actions: that is basically the mindset of the true hedonist, who acts for pleasure and not for whatever practical consequence his/her action accomplishes. But typically looking for pleasure and avoiding pain are not a unique final goal of ours (another monarchic view of mind and motivation): rather, they act as signals for learning, and they help us learning, among other things, how to generate and evaluate goals.

Those hedonistic philosophies that identify pleasure with motivation, and relate our goal-oriented activity to pleasure motivation, should address the following, evident objections:

i. As a matter of fact, several goals when attained do not give us any pleasure experience; they are just practical results, or consist in the pursuit of (often unpleasant) duties.

ii. If pleasure is so necessary for goal pursuit and motivated activity, why it is not necessary at all in cybernetic models of goal-directed activity and purposive systems? How is it possible to have a clearly finalistic and anticipation-driven mechanism, open to "success" and "failure," without any pleasure? In other terms, *what is the real function and nature of pleasure in a goal-directed system?* Moreover, pleasure seems to be present in nature (both phylogenetically and ontogenetically) well before mentally goaldirected actions. This also suggests that the function of pleasure has to be different; it does not seem to play the role of a goal.

In my view, pleasure is more related to the notion of "reward," of "reinforcement" and learning. Pleasure as an internal reward plays two fundamental roles: it attaches some value to some achieved state, which is important when the system can have more than one of such states, possibly in competition with each other; it signals that a given outcome (perhaps accidental) "deserves" to be pursued, is good, has to become a goal (that state, not the pleasure *per se*). In this view, pleasure is a signal and a learning device for goal creation/discovery and for evaluation. It seems very useful in a system endowed with a "generative" goal mechanism, and which needs different kinds of evaluation, more or less intuitive, fast, based on experience or on biological/inherited "preferences," and not just on reasoning (with its limits, biases, and slowness).

# **THE EMERGENT, COLLECTIVE, SELF-ORGANIZING EFFECTS OF OUR BEHAVIORS**

That is how complexity determines the "social order." Our claim on issue (D) is that we need an analytic and dynamic theory of the "invisible hand," aimed at identifying its underlying mechanisms. Otherwise we cannot understand societies, etc. We also have to understand the relation between the mechanisms regulating the social order and our intentions and mental representations: that is, how – without being understood and explicitly represented – the emergent structure/order feedbacks into and shapes our minds and behaviors; not just the "emergence" but also the "immergence" processes.

The *foundational* issue of the Social Sciences is the micro-macro link, the relation between cognition and individual behavior and social self-organizing phenomena or complex structures and organizations4; and institutional actions/phenomena (the two facets of "social order": the "spontaneous" one and the organized or at least institutionalized one; Tummolini and Castelfranchi, 2006). This is the main reason for the existence of the social sciences, what they have to "explain," diachronically and synchronically, in its origin and dynamics.

As remarked by Hayek (1996): "This problem [the problem of the unintentional emergence of order and of spontaneous institutions] is in no way specific to economics... *it is without doubt the core problem of the whole of social science."*

That is also why *Methodological Individualism,* although fundamental or better necessary, is not *sufficient* at all as a framework for explaining social interactions and phenomena (Conte and Castelfranchi, 1995).

Adam Smith's original formulation of "THE problem" is – to me – much deeper and clearer than Hayek's formulation.

The great question is how [the individual] *"which does neither, in general, intend to pursue the public interest, nor is aware of the fact that he is pursuing it,* ... *is conducted by an invisible hand to promote an end that is not part of his intention"* (Smith, 1976).

The problem is "*how"* the Invisible Hand does really work; in the end, we should (and could) explain the "mechanism" and its reproductive feedback on the agents' minds and behaviors.

In Smith's view of the "Invisible Hand":

The real problem is to understand how not only such process coexists with an intentional behavior but also exploits it (Castelfranchi, 2001).

Thus special attention should be devoted not only to the "emergent" bottom-up processes but also to the "immergent" ones: the top-down feedback from emergent phenomena to the agent control-system via learning or through understanding and intending (Conte et al., 2007).

In particular we have to identify which of the macro-level phenomena is or *has to be* mentally represented, understood, and even intended in order to reproduce itself and be effective (as it happens with norms), and to discriminate those that are unintended and blind, and presuppose some form of alienation (like social functions or institutional powers). What we have to explain is also how the Invisible Hand and spontaneous (selforganizing) social order are not so spontaneous and disinterested or optimal for the involved people but do systematically favor powerful agents. What is needed is a criticism to von Hayek's theory (or vulgate) about the spontaneous social order as the best *possible* outcome: the often implicit assumption that *an understanding of the social dynamics, deliberate planning, and intentional pursuuit of non-individual outcomes could never achieve better results*.

How much the epistemic and motivational representations that regulate our intentional conduct are *shaped by* the macro sociological, economic, anthropological, political levels? How the former *are functional to* the latters, not just mere complex effects and consequences?

That is: how could the Spontaneous Order not just*emerge* from our autonomous acts but *maintain and reproduce* itself without actively influencing and reproducing those acts? Which – however – are due to our cognitive representations and processes. Thus it has to shape and reproduce those cognitive mechanisms. *The Invisible Hand works also through and on our minds, by manipulating our mental devices in order to bring out the appropriate (not understood and unintended) outcomes.*

In fact, the problem is not just how a given *equilibrium* (like in simple Games) or *coherence* is achieved and some stable *order* emerges. In order to have a "social order" or an "institution" spontaneous emergence and equilibrium are not enough. They must be "functional," that is self-reproducing by a causal loop.

# **THE "***COGNITIVE MEDIATORS"* **OF SOCIAL PHENOMENA**

Social phenomena are due to the agents' behaviors, but... the agents' behaviors are due the *mental mechanisms* controlling and (re)producing them.

For example: Our Social Power lies in, consists of, others' *Goals* & *Beliefs*! How do they evaluate us and accept to depend on us. That's why we need Mind-Reading! Not only for adjusting ourselves to the others' interference, but for manipulating and exploiting the others or for helping or punishing them.

Social and cultural phenomena cannot be deeply accounted for without explaining how they work *through the individual agents' minds* (the mental "counterparts" or "mediators" of social phenomena).

Does this mean that social actors fully understand what they do/construct? No, not necessarily.

4See for example (with a more traditional approach) Sawyer, 2003 or Prietula et al., 1998; also related with agent-based simulation (Computational Science for Reconciling "Emergence" with "Cognition"). For interdisciplinary and integration based view close to our position, see also (Dale et al., 2013). Although in our perspective goal-directed behavior and intended results and self-organization and spontaneous social order are two complementary and interacting faces of sociality and social theory. We do not think that dynamical system theory is the framework for integrating human interaction "into a broader account." Also because the problem is not the coordination of motor, expressive, and linguistic "inter-action," but of social conventions, scripts, institutions, and collective self-organizing "order."We are more in agreement with the previous Dare's claim about the need for a "pluralistic" approach in Cognitive Science.

That's why we use the term: "mediators": because they are the mental ingredients necessary for producing that social phenomenon or structure without *(necessarily) being the mental representation (understanding or intending) of the social phenomena produced by the behaviors that they determine.*

So, I play and reproduce a"socialfunction"(of father, consumer, the witness of a promise, "public opinion," the follower of a leader, etc.) without necessarily understanding it, but with something specific, corresponding, in my head.

As we said, the problem is social functions impinge not only on our habits and automatic or ritual behaviors, but on our deliberated and intentional actions. Charging only the non-intentional, non- deliberate behaviors with those functional aspects is a simplistic solution: according to such a view, role-playing would just be implemented in "habituses" (Bourdieu and Wacquant, 1992). Thus, when a social actor is consciously deliberating and planning, he would not play a social role, he would be "free." I disagree with such a solution. Social actors play social roles and accomplish their social functions also through their deliberate, intentional actions, however they do so not deliberately. This is precisely the problem to be addressed; and it requires a sophisticated model of intentions. We are back to the issues of (C;Two Teleologies Impinging on Human Behavior).

*What is the relationship existing between the social system's goals and the goals internal to its members, which directly regulate their actions*?

Are social actors able to understand and represent explicitly in their minds the social system's goals? Or are the goals of the social system simply a projection of the goals of (some of) its members? Or, do the members' goals and plans happen to happily coincide with those of the social system? In other terms: do we intends all the goals we pursue?

*Functions establish and maintain themselves thanks to and through agents' mental representations but not as mental representations: i.e., without being known or at least intended.*

# **COMPUTATIONAL SCIENCE FOR RECONCILING "EMERGENCE" WITH "COGNITION"**

However, "necessary" doesn't mean "sufficient": Mind is not enough. For "explaining" what is happening at the societal and collective layers we have to model the mind of the actors, but this is insufficient. The"individualistic plus cognitive" approach – even if complemented with "collective intentionality," "joint action," "we intend," etc. – is not sufficient for a social theory and for modeling social processes. Social actors do *not* understand, negotiate, and plan all their collective behavior and cooperative activity. Society is not "team work."

This is the real challenge not only for the behavioral and cognitive sciences but for multi-agent systems and Social AI, and computer-supported societies: *Reconciling Emergence with Cognition.* Emergence and cognition are not incompatible with one another; neither are they two alternative approaches to intelligence and cooperation.

On the one hand, cognition has to be conceived as a level of emergence (from sub-symbolic to symbolic; from objective to subjective; from implicit to explicit).

On the other side, emergent and unaware functional social phenomena (ex. emergent cooperation, and swarm intelligence) should not be modeled only among sub-cognitive agents (Steels, 1990; Mataric, 1992), but also among intelligent agents. In fact, for a theory of cooperation and society among intelligent agents – as we said – *mind is not enough,* and cognition cannot dominate and exhaust social complexity (on that Hayek is right; Hayek, 1967).

This is why a crucial revolution in the behavioral sciences is and will be "computational modeling," with its radical "operational" approach. There is no alternative to this, especially if one has to model at the same time the process at a given micro-layer and the processes at the macro-layer, and also the emergent (bottom-up) and the immergent (top-down) feedbacks, and how all this works.

We need a computational modeling of cognitive representations and manipulation (processing; Cognitive Mechanisms Producing and Controlling Our Behavior) and a computational modeling of their neural implementation and of brain very complex dynamics (The Neural Implementation of Psychological Representations and Processes). The same holds at the social level.

### **THE** *THEORETICAL* **MISSION OF SOCIAL SIMULATION**

Agent-based computer simulation of social phenomena is the crucial (revolutionary) challenge for the future of behavioral sciences. But why is it so?

As we said, the micro-macro link is the *foundational* issue of the behavioral sciences: they should investigate the relation between cognition and individual behavior, on the one hand, and social self-organizing phenomena or complex structures, organizations, and institutional actions and entities5 on the other hand. This is the main mission of the social sciences, what they have to"explain," diachronically and synchronically.

No approaches or models for studying this complex phenomenon and eventually understanding its (causal) mechanisms are better than agent-based computer simulation. It is the only approach able to model *at the same time* different layers of processing and their top-down and bottom-up feedbacks and circularity. We can model more or less complex minds (with goals, beliefs, reasoning, decisions, etc., but also emotions, reactions, biases, and perception, learning, etc.) and interaction, dependence networks, group activity, organization, cooperation and competition, norms, roles. And we can observe the internal and external dynamics.

Moreover computer implementation of models provide us a formal validation of the theory predictions, and new experimental data (by simulation).

# **CONCLUDING REMARKS**

What is the correct relation between social and collective human behaviors and the individual mind, and between mind and brain? The answer is: *a well-conceived reductionism,* preserving different (interconnected) ontological layers with their vocabulary (like in chemistry for the notion of "valence" or of "acid").

#### **A LAYERED SCIENCE FOR A LAYERED WORLD**

Nature (and, in nature, society) has *different levels of complexity and organization*, with the emergence of macro-level entities,

5The two faces of "social order": the "spontaneous" one and the organized or at least institutionalized one.

phenomena and laws, grounded on the entities, properties and mechanisms of the lower layer (micro).

"Reductionism" should not be the "elimination" of the entities, notions, dynamics of a given macro level, considered superfluous once it is explained in terms of their micro-entities. "Reductionism" should be "re-conduction": bringing back and grounding the macro-dynamics on the underlying ones. The theories of the macro layer should be not only *compatible* (non contradictory) with the laws of the micro one; they have to be grounded and derivable. Otherwise they are wrong.

Consider for simplicity the following layers of complexity: let's ground all on physics (particles, atoms, forces, etc.); on top of physics, let's put chemistry, then biology grounded on organic chemistry, then neuroscience, then psychology, then social sciences (economics, sociology, anthropology, politics).

Biology has to be explained in biochemical terms, but we cannot eliminate the notion of "cells" with their new properties and laws, although we have to biochemically know how they "work"6.

In the same vein, social and collective behavior is due to the conduct of individual actors; but individual action is due to mental representations and processes; therefore the principles of social sciences should be grounded in the underlying mental and behavioral phenomena and laws. However after such a re-conduction is made, we cannot do without such notions as crowd, market, inflation, government, etc.

Science has for example re-conducted chemical "valence" (introduced much before atomic modeling) to atomic properties: particles, their electric charge, etc. To have explained "valence" and how it works doesn't make this notion useless; and we couldn't put aside notions like "acid," "basis," "chemical bonds" although we have a full grounding and understanding of them in atomic terms. The Phlogiston theory has been eliminated, because there was no possible confirmation of the hypothesized processes at the supporting/implementing layer.

Exactly in the same way we have to re-conduct mental representations, functions, and processing to the body and its neural mechanisms and structures; they are just material, informational entities7; emergent *functions* of their ground, described in informational/functional terms. If it is not possible to bring them back to their sub-stratum, they are inexistent (like phlogiston); but if they are brought back to their underlying micro-processes, they will not be redundant and eliminable. The psychological notions should be preserved for understanding and explaining "what the brain is *doing*": perceiving, memorizing, retrieving, deciding, pursuing, and so on; at its macro-functional level of activity.

Neural correlates cannot be the right *vocabulary* for explaining human behaviors, just because they are at a micro-level and do not still represent and discriminate the complex "patterns" and their properties and functions (not of their sub-components) at the cognitive and motivational macro-level of working. When we will have the real neural representation of a complex object like a "motivating goal," or an "altruistic intention," or of real "trust attitude" (The Neural Implementation of Psychological Representations and Processes), or a "complex emotion with its appraisal components" like envy, we will have a quasi-complete explanation of it (see previous note), but we will not renounce to that psychological vocabulary; since it holds and works at the functional/informational macro layer. Also because, there are other properties of that entity that are due not to its microimplementation and mental representation, but to its functions and relations at the macro anthropological, sociological, economic level. A table is a "table," functionally and practically speaking, although it is just a cluster of molecules of a given substance; however, at certain level of use its analysis in physical and material terms is fully irrelevant.

More in general: there are no alternatives to the need for*reading* and *understanding* body in terms of functions, not just in terms of "simple" matter and its physico-chemical processes description.

We look at the kidney as a "filter," at glands in terms of "secretion." Otherwise we do not understand what they do, that is, what they are; which is the sense of the physico-chemical processes that we are describing.

The same obviously holds for our brain (just a body organ). Brain anatomy must be a "political geography," not a "geography" of physical objects/structure: it has to localize the areas of given psychological functions. And brain physiology (activity) – to be understood – requires to be read in terms of active psychic processes. "Mind" is just a functional notion: the high level function of neural activity and patterns; and given its *emergent, functional, informational, semiotic-representational* (and even *institutional*) nature is not "reducible" to brain processes, that just provide its material implementation.

We need a micro-macro theory, a specification of the underlying entities and processes producing given phenomena at the superordinate layer. This is what we call – in strict sense – *Science of "mechanisms."*

### **THE NEED FOR COMPUTATIONAL MODELING**

I claim that there is no alternative to computer modeling. We have to provide not just mathematical or formal models but computational ones, if we want to model the proximate causes of a given phenomenon, and its superficial dynamics; the *underlying "mechanisms" that determine those behaviors*. We also need "synthetic" modeling, that is, the material construction of the modeled entity to show how it actually produces the predicted behaviors/effects in interaction with the environment.

As rightly pointed out by Shieber (2004): "The whole thinking process is still rather mysterious to us, but I believe the attempt to make a thinking machine *will help us greatly in finding out how we think ourselves*."

*Computational/synthetic modeling* will be pervasive. It will model any hidden mechanism and "dynamics": from chemical reactions, to DNA, from evolution to psychological mechanisms, to social, economic, historical phenomena. This is the message and the *gift* that ICT and in particular AI has to give to science.

Computational modeling will provide not only "models" and conceptual instruments for the theory, but also *experimental platforms*, new empirical data obtained through simulation, and new hypotheses and predictions. Some experiments will be made possible, which are impossible in "nature," either for practical, social, historical, or moral reasons (demography, urbanistic, etc.)

6To say nothing of the "evolutionary theory": a completely new foundation. 7However, see note 13.

or for the natural inseparability of some distinguishable mechanisms (for example motivational and emotional mechanisms). This will be crucial both for modeling both proximate causes and diachronic, evolutionary causes.

Computer simulation of neural, cognitive, social mechanisms and dynamics, obviously *is not the only method* for identifying the proximate causes, but the most promising method for (i) their fully *procedural* and *formal* characterization (ii) with the additional advantage of "running" the postulated dynamics and seeing their results (conform or not to predictions), and (iii) to conduct a new precious kind of experiments, in particular useful for complexity and emergent effects. The most promising method/tool, especially for modeling "processes" not just static features (physiology not just anatomy) (iv) at different layers, but interacting; including also the bottom-up and the top-down effects, and the resulting dynamics. It is the only approach able to deal in an integrated way with all these mechanisms.

Moreover, computers are a fundamental device for intelligently *collecting and analyzing relevant data* [from the web, for example "Big Data," and from human behavior in natural conditions (traffic, investments, migration, etc.)]. Also in the sense that major scientific discoveries will be made by computers (able to manage Big Data, to demonstrate theorems, to interpret the laws and mechanisms of that data), but also in the sense of "human" traditional science supported by computational instruments.

In sum, in a few years, science will be "computational"; otherwise it will not be.

#### **"MORE GEOMETRICO DEMOSTRATA"**

To be more explicit about psychology status: It is unbelievable that after more than half a century the critical remarks of Wittgenstein on psychology be still valid: "*The confusion and barrenness of psychology* is not to be explained by calling it a "young science"; its state is not comparable with that of physics, for instance, in its beginnings. (...) For *in psychology there are experimental methods and conceptual confusion*. (...) The existence of the experimental method makes us think we have the means of solving the problems that trouble us; though problem and method pass one another by" (Ludwig Wittgenstein *Investigations* PII p. 232).

In my view, Psychology is one of the few sciences that do not officially have a clearly separated theoretical domain, with its university chairs, conferences, curriculum, ... likefor physics, biology, economics, ... without any direct experimental activity (in case taking into account and *explaining* the result of their "experimental" discipline; and anticipating of half a century the empirical results, like for Einstein theories).

Psychology – probably because of its "guilty" origin from philosophy, and the consequent inferiority complex to the "hard sciences" – has repressed its theoretical and analytical impulses.

Philosophy is in a sense a party to this somewhat phobic attitude of psychology, because it considers the analytical, formal, theoretical work as a prerogative of its own. However, philosophical contributions, though welcome, cannot replace the theoretical and analytical work that must be internal to psychology.

It is not a matter of "experimental philosophy," it is a matter of "theoretical psychology" (Cognitive Science sometime plays such a role).

We need to have psychological states "more geometrico demostrata."

#### **JUST STATISTICAL LAWS AND CONSTRUCTS, AND PROBABILITY?**

However, let us conclude with a query about next future, by following not just optimism of will but pessimism of reason:

Will this analytical and "cognitive mediated" view of social phenomena and dynamics, and of computational Agent-based modeling (we hope for) win?

Not so sure at all: we will attend a short cut of statistics, the impressive power of Big Data, correlations, probability, ... An already very robust trend. The title of Mayer-Schonberger & Cikier' book is "Big Data: A Revolution That Will Transform How We Live, Work, and Think" and I think that they are absolutely right; but this revolution will be insufficient and even deviating if it will just empower our "predition" capabilities, and will not ground new *theoretical understanding* of the mechanisms and causal processes underlying society and cognition. I worry about Anderson's profecy: "The End of Theory: The Data Deluge Makes the Scientific Method Obsolete"; prophecy that of course begin to be based on Big Data! And I care more about scientific aim and frame than about scientific "methods" (See also Anderson, 2008; Harford, 2014).

We are witnessing a growing trend of *predicting without understanding*, without modeling the proximate causes.

Does God play dice?

#### **REFERENCES**

**Conflict of Interest Statement:** The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 30 January 2014; accepted: 14 May 2014; published online: 03 June 2014. Citation: Castelfranchi C (2014) For a science of layered mechanisms: beyond laws, statistics, and correlations. Front. Psychol. 5:536. doi: 10.3389/fpsyg.2014.00536 This article was submitted to Theoretical and Philosophical Psychology, a section of the*

*journal Frontiers in Psychology.*

*Copyright © 2014 Castelfranchi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

# Multi-leveled objects: color as a case study

# *Liliana Albertazzi 1 and Roberto Poli 2 \**

*1 Center for Mind/Brain Sciences and Department of Humanities, University of Trento, Trento, Italy*

*2 Department of Sociology and Social Research, University of Trento, Trento, Italy*

# *Edited by:*

*Roberto Cordeschi, Sapienza University of Rome, Italy*

# *Reviewed by:*

*Kent Johnson, University of California Irvine, USA Frederic Fol Leymarie, Goldsmiths, University of London, UK*

*\*Correspondence:*

*Roberto Poli, Department of Sociology and Social Research, University of Trento, 26 Verdi street, 38122 Trento, Italy e-mail<EMAIL_ADDRESS>
The paper presents color as a case study for the analysis of phenomena that pertain to several levels of reality and are typically framed by different sciences and disciplines. Color, in fact, is studied by physics, biology, phenomenology, and esthetics, among others. Our thesis is that color is a different entity for each level of reality, and that for this reason color generates different observables in the epistemologies of the different sciences. By analyzing color as a paradigmatic case of an entity naturally spreading over different levels of reality, the paper raises the question as to whether making explicit the usually implicit ontological assumptions embedded within the different observables exploited by the different sciences may eventually clarify some of the difficulties of developing a comprehensive theory of color.

**Keywords: color appearances, color models, color systems, levels of reality, phenomenology**

# **INTRODUCTION**

What is color? Is it a quality of the phenomenal (subjective) appearance or a property of the physical object? Or both? How are the phenomenal quality and the physical property related to each other? As well known, widely different answers have been provided. Among them are the following: color realism based on the reflectance of light by surfaces, that is, physics; phenomenal objectivism based on sensory-motor contingencies; color subjectivism based on qualia, i.e., atomic color experiences; color as brain product based on the effects of objects within us, from the point of view of the nervous system; and color dispositionalism based on the effects of objects within us, from the point of view of our experiential states (on the different epistemological stances see Byrne and Hilbert, 1997).

Consequently, theories on these various matters have analyzed aspects concerning the nature of stimuli, the workings of the neurons, sensory response, the eminently qualitative nature of phenomenal vision, or aesthetic yield. But on establishing correlations among events at these various levels, one should be careful to avoid epistemologically collapsing their relations of ontological dependence into reductions to either the physical or the neuronal level (Albertazzi, 2006, 2013). In fact, as Köhler wrote

If someone states that things seen must first be experienced as if they were in the brain, he has not realized that the first part of his statement refers to the visual field as a fact of experience, whilst in the second part, where he uses the expression "the brain," he is speaking of a physical object in physical space. This means that he expects to see parts of visual space localized in relation to parts of physical space, and this notion is entirely impossible.

(Köhler, 1947, p. 213)

The discussion on color continues to suffer from the same shortcomings as denounced by Köhler. It still lacks, for example:

• A categorical classification of the differences among the physical, the neuronal, and the properly psychic (mental) marking the onset of color perceptions.

The thesis put forward in this study is that *only the framework provided by a properly developed theory of levels of reality can handle the complexity of color perception and color spaces*. The assumption, however, is that the different color observables are not totally independent from one another, in the sense that they are connected by a network of dependencies arising from the different levels of reality.

As a step toward understanding and clarifying the nature of color, this paper suggests verifying whether at least some of the controversial aspects of color understanding depend on different ontological (not epistemological) assumptions. Otherwise stated, we propose to bracket the models' epistemological assumptions as far as is possible in order to better grasp the possible presence of underlying ontological differences.

Color perception is characterized by the presence of different theories based on conflicting primitives (wavelength, neural correlates, color appearances), and parameters (hue, saturation, chroma, brightness, lightness, to mention but a few). Furthermore, a variety of color solids have been proposed as models of the space of colors, including cylindrical, conic, pyramidal, and spherical ones (Billmeyer, 1987). Moreover, even when the different theories adopt the same categories, they define them in different and often conflicting ways.

To make matters worse, even the identification of colors raises major problems: to wit, the color matching procedure, on which most colorimetry is based (Boynton, 1979; Brainard, 1995; Koenderink and van Doorn,2003;Koenderink,2010), exploits a severely restricted use of color terms and does not consider what the viewer actually perceives, with the exception of the viewpoint of color differences. The phenomenological aspects of observed colors (Stumpf, 1917; Hering, 1920, 1964; Gelb, 1929; Katz, 1935) remain hidden behind the yes/no responses to just noticeable differences (*jnd* – the units of psychophysical analysis).

The question also arises as how to relate natural language color terms for perceived dimensions of color, i.e., relatively to what kinds of concepts are encoded or not encoded by languages, what are the ontological referents, in what universal and linguistic (or culture-specific) meanings consist, etc. The so-called nature/nurture debate in the field of colors is particularly difficult to address, given the tangled development of the taxonomy of colors over time and in the different languages (Williams, 1976; Dedrick, 1998; Paramei, 2007; Jameson and Komarova, 2009; Rakhilina and Paramei, 2011), the terminology adopted by scientific theories that may define colors according to metrical parameters or differently shaped color spaces, and the question of how the subjective perception of color relates to cross-cultural color naming (Jameson, 2005). Furthermore, many more colors exist perceptively than can be linguistically named (Kuehni, 2007, 2010). The problem is that there are not enough terms to qualify color appearances in simple, precise, and exhaustive terms, if necessary.

Scientific nomenclatures usually adopt severely constrained sets of basic terms and qualifiers. While this may be appropriate for specific uses, such as industrial ones, it is too coarse to capture distinctions that people spontaneously make.

Color nomenclatures usually apply to isolated, uniform patches, or the very simplest configurations of color mondrians. Moreover, special color nomenclatures refer to colors pertaining to particular areas of the entire space of colors. A color nomenclature typically relies on a highly simplified framework based on a small number of qualifiers and their combinations (for instance, "red," "deep red," "dark red," "light red," etc.). These labels are the linguistic translations of numerical expressions. That is, they are operational definitions that do not consider the correlation between perception of color and the linguistic expression that best matches the perception. Perception, depending on different settings, including the physical and the mental, often leads to color terms that do not fit into acknowledged standards.

#### **COLORS AND COLOR TERMS**

The CIE (Commission Internationale de l'Eclairage, International Commission of Illumination) definition of color runs as follows: Color (perceived) is the "characteristic of visual perception that can be described by attributes of hue, brightness (or lightness) and colourfulness (or saturation or chroma; see International Lighting Vocabulary [ILV], 2011; Standard CIE S 017/E:2011). A series of notes (http://cie.co.at/index.php?i\_ca\_id=827) clarify that: "when necessary, to avoid confusion between other meanings of the word, the term "perceived color" may be used (note 1); that "perceived color depends on the spectral distribution of the color stimulus, on the size, shape, structure, and surround of the stimulus area, on the state of adaptation of the observer's visual system, and on the observer's experience of the prevailing and similar situations of observation" (note 2); and that "perceived color may appear

in several modes of color appearance. The names for various modes of appearance are intended to distinguish among qualitative and geometric differences of color perceptions. Some of the more important terms of the modes of color appearance are given in 'object color,' 'surface color,' and 'aperture color.' Other modes of color appearance include film color, volume color, illuminant color, body color, and Ganzfeld color. Each of these modes of color appearance may be further qualified by adjectives to describe combinations of color or their spatial and temporal relationships. Other terms that relate to qualitative differences among colors perceived in various modes of color appearance are given in'luminous color', 'non-luminous color,''related colour,' and 'unrelated color"' (note 4).

However, color *terms* can only be linguistic labels of perceived *appearances* of colors, not of physical stimuli because we do not perceive physical stimuli as such. If anything, we perceive colors as a consequence of physical stimulation. Also in this respect, however, the relation between physical stimuli and color appearances is less direct than one might think, or can be taken for granted, given the strong contextual dependence of color appearances (Chevreul, 1839; Albers, 1963). It is our suggestion that grounding color nomenclature on the perceptual experience of subjects provides models more robust than those based on an automatic translation of numerical expressions or geometrical positions in a color space. From this emerges the need to arrive at a robust perceptual definition of color terms.

Natural languages use different types of color terms (Biggam, 2012). Since Berlin and Kay's (1977) seminal book, the literature has drawn on a variety of different methodologies ranging from purely linguistic analyses (Wierzbicka, 2006), to anthropological field researches (MacLaury et al., 2007), mainly with the subministration of Munsell chips1 (Berlin and Kay, 1977; MacLaury, 1992; Davidoff et al., 1999), and Osgood's semantic differential (Madden et al., 2000). More recently, results from the neurosciences have begun to be used (Kay and McDaniel, 1978; Wuerger et al., 2005). For an extensive review of the different universalist and relativist positions see Da Pos and Albertazzi (2007).

Specifically, as regards basic color terms2, natural languages segment color appearances according to identifiable patterns. Most languages broadly agree on the prototypicality of linguistic categories for so-called focal colors (Rosch, 1973; Rosch et al., 1976). However, agreement on what aspects are the proper referents of color terms in natural languages is still lacking, because different models refer to different parameters or different aspects of color. Most of the dispute between universalists and relativists on color terms, for example, arises because the exponents of each perspective use concepts of color referring to *different* realities, including stimuli, neural correlates, and color appearances. The usual recourse in these cases to qualifiers such as "'unique," "pure,""primary,""elementary,""basic,""focal," and "prototypical" is widely insufficient, because these qualifiers are themselves far from being univocal. A more systematic framework is needed.

1That is, the hues presented in his *Notation* book, see Munsell (1905).

2That is, universal color categories assumed to be present in most languages, and in a highly constrained order; (see Berlin and Kay, 1977; Kay and McDaniel, 1978; Kay and Regier, 2006, 2007).

To present one of the customary confusions in addressing colors, it is enlightening to consider the difference between hue and color. Unique (also known as unitary or psychologically primary) colors (Hering, 1920) are colors which do not resemble any other colors, whilst binary, or psychologically mixed colors resemble at least two others. The definition is based on the visual similarity which a color shows, or does not show, with other colors, obtained by pure phenomenological observation. The system of color notation closest to the perception of colors based on their visual similarity is the Natural Color System (NCS, Sivik, 1991). In the NCS, reference to unique hues amounts to reference to yellow, red, blue, and green, while reference to unique colors includes also the achromatic white and black; in fact, from a phenomenological viewpoint, black and white are also perceived as colors. The categories of color and hue are not easily definable, however. Prima facie we might define color as everything that is directly seen, i.e., as the color appearance – defined in CIE as the "aspect of visual perception by which things are recognized by their color" – while hue is the aspect possessed by many colors and which makes them chromatic, distinguishing them from non-chromatic colors. A specific hue is more or less visible in a particular color, in the sense that two colors can be of the same hue: one can see the presence of more red in a highly chromatic color of red hue than in a scantily chromatic color of the same hue (for instance in a whitish pink), although the hue of both is simply red. On the other hand, one can also say that the color most representative of redness is a highly chromatic red. In linguistic terms, talk of a focal color as the most representative color of a category ("the best cues of the category," according to Rosch's prototypical classification; Rosch, 1973; Rosch et al., 1976) makes reference to the color with which the word "red" fits best. In fact, focal color is the color in which one sees what one considers the best red, not a color which belongs to the red hue, which is reddest because it is less blue and less yellow. It is worth noting that the "best" red, differently form "unique" red, can bear cultural connotations as well.

Highly chromatic colors belonging to a bipolar scale between two consecutive hues show different degrees of similarity with the extreme colors of that interval. For instance, the interval defined by the extremes "most chromatic yellow" and "most chromatic red" in which mixed colors appear more or less yellowish or more or less reddish – i.e., are similar to one or the other color in different ways – show different degrees of similarity with the extreme colors of that interval. Linguistically, these intermediate colors can be expressed, for example, in terms of "red and yellow," "saffron,""pumpkin,""orange,""carrot," etc. Not necessarily, however, do these color terms have the same referent, and some may also overlap. For example, a color may appear more or less red either because it is pink or because it is orange: in the former case, the hue is maximally red but little visible (the color is only slightly chromatic); in the latter case, the hue is not very red and the color may be highly chromatic. Consequently, one assesses pink as "very red" because it is only slightly or not at all yellow or blue; and likewise one assesses orange as only slightly red because the "hue" is not very red. However, it seems that one can also make an absolute assessment of how much a color is red, so that orange and pink might be treated equivalently, i.e., the extent to which red (not hue) is visible in them.

The perceptual similarity of the mixed hues to the extremes "red" and "yellow" can be quantified (for instance, halfway in the interval (50–50); or more yellowish than reddish (say, 70–30); and so on. Needless to say, different similarity metrics can be developed.

The problem of the perceptual identification and denomination of colors is particularly complex in the case of mixed colors, such as orange. To be noted is that Berlin and Kay's (1977; see also Kay and Maffi, 1999) eleven basic color terms include both unique colors such as white, black, red, yellow, green, and blue (the first six colors in their list), and mixed colors such as orange. According to Sternheim and Boynton (1966), however, when the orange response category is available in a judgment experiment on the color continuum together with the response categories for red, yellow, and green, orange is used with the lowest reliability, i.e., randomly. When the orange response category is omitted, the hues otherwise associated with orange are completely dispersed into the red and the yellow, though with peaks in either red or yellow. Sternheim and Boynton (1966) therefore conclude that orange is some combination of red and yellow, and that the hues associated with the long wavelength part of the spectrum3 can be described without the category of orange, and making use of two already known color terms (yellow and red). The superfluous nature of the category "orange" was questioned by Boyton himself in a later study. He interviewed Japanese subjects, who were required to express their degree of agreement on the existence of specific categories related to Berlin and Kay's basic color terms. For 90% of the subjects, the category of orange was well categorized as a salient color, and the category was linguistically expressed by mono-lexemic typical terms different from red and yellow (Uchikawa and Boynton, 1987).

This would imply that, phenomenologically, "orange" lies *exactly midway* between the two pure colors of red and yellow (on the status of "orange" from the point of view of painters, see Garau, 1993). Whenever orange varies from the mid-point between red and yellow, the resulting color is described as yellowish red or reddish yellow, as are the other mixed hues of the same range.

# **NOMENCLATURES**

One of the problems raised by the relationship between color perception and color terms is whether perceptual categorization requires linguistic categories at all. That is: do perceptual categories depend on language, learning and higher cognition, or are they independent from them? Munsell chips are definitely too poor a tool with which to verify this issue experimentally (Lucy and Shweder, 1979; Wierzbicka, 1996, 2006; Lucy, 1997). Testing the possible influence of language on color perception requires a more sophisticated experimental setting, such as having several words available for, say, red, in order to signal different environmental conditions (Green-Armytage, 2006; Winawer et al., 2007). In fact, as we have already noted, there is an indefinite number of color appearances, more than any natural language may encode. Therefore, the question arises as to how to relate natural

3The expression in Sternheim and Boynton's paper is unfortunate, because the study refers to "perceived" colors.

language terms for perceived colors and the terminology adopted by scientific theories.

Scientific nomenclatures usually adopt severely constrained sets of basic terms and qualifiers. Four different spaces should be taken into account: (1) The space of colorimetry (to be noted, however, is that there are colorimetric spaces, such as CIELAB and CIECAM (respectively Lab Color Space and Color Appearance Model both published by CIE), that (do not perfectly) represent perceived colors, (2) the physiological space LMS (color space based on human cone cells – LMS stands for L- M- and S-cones) and its derivate DKL (Derrington–Krauskopf–Lennie color space), (3) the space of the linguistic representation of colors, and (4) the space of the subjective perception of colors.

To be noted is that the phenomenological perspective under (4), thus far rarely adopted, is starting to attract attention (Sivik, 1974, 1997; Albertazzi et al., 2012).

For each of these spaces, different theories are customarily developed. Each space requires specific groups of observables. The main issue is that most of the contemporary literature fails to distinguish them as clearly as needed, and therefore has difficulties in addressing the problem of their relations. Since colors, whatever they are, are also, and we would say primarily, a question of perception, one may wonder whether starting from real (i.e., subjective) perceptual experience of color provides information that may escape or remain hidden if one instead starts from other frameworks.

# **COLOR PRIMITIVES**

Color theories use different primitives – and even when they use the same terms, they may define them differently. It is consequently mandatory to be clear about the different terminologies and the ways in which different theories use any given term.

It is generally assumed that color can be described according to the parameters of hue, brightness and saturation (Kuehni, 2003; on measurement see Krantz et al., 1989)4. These properties make explicit reference to the relation between a given stimulus (hue correlated with wavelength, brightness correlated with luminance, saturation correlated with purity) and the subsequent subjective experience of a perceiver. On the other hand (see above), it is also often taken for granted that hue, brightness, and saturation are attributes of the color *as perceived*; also taken for granted is what they are correlated with, and what they correspond to; and that they form a 3D space where each of them represents a distinct dimension. These parameters result from innumerable experiments on the physical stimuli, i.e., light spectra, or the power at each wavelength. As it happens, light spectra can be readily measured and characterized by three numbers (the so-called tristimulus values of light). However, the shift is constantly made from properties of light spectra (as measured by the tristimulus values) to properties of the surfaces of seen objects (Wyszecki and Stiles, 1982; Hurlbert, 2013). It is customarily claimed that the tristimulus values specify the response of the standard human eye to the color spectrum. This standard response, however, is far from providing a *general* answer to the ways in which human eyes perceive colors, because the determination of the tristimulus values requires highly specific and severely constrained conditions, i.e., generally isolated colors. To provide an example, visual perception in complex environments where phenomena of contrast and assimilation regularly occur is purposely never taken into consideration: in fact, one of the major self-imposed limits adopted by colorimetric analysis is that it should consider only isolated colors, without taking colors combined with other colors into account (Boynton, 1979).

The problems are compounded because the literature on color defines hue, brightness, and saturation in different, often mutually incompatible, ways. Furthermore, although the distinction among hue, saturation and brightness is correct as far as the properties of light are concerned, it is far from being a "natural" – i.e., "phenomenological" – distinction from the point of view of the perceiver (Stumpf, 1917, p. 8; Katz, 1935). Saturation, for example, is a technical term used to characterize decontextualized light stimuli. According to the CIE definition of saturation, it is "the colourfulness of an area judged in proportion to its brightness" [1136], and in a note it is specified that "For given viewing conditions and at luminance levels within the range of photopic vision, a colour stimulus of a given chromaticity exhibits approximately constant saturation for all luminance levels, except when the brightness is very high." Originally introduced by Helmholtz (1867) – explicitly aware of its arbitrariness from a perceptual point of view – the property of saturation should measure the degree of chromatic content in proportion to the brightness of a color. However, Wyszecki and Stiles (1982) note that the concept of saturation (together with the concept of chroma) is perhaps the most controversial concept in the literature on color appearance. In fact, different systems of color representation differ as to their primitives: for example, one finds chroma in Munsell and Sättigung in Deutsches Institut für Normung (DIN)5. Since the definition of saturation changes relatively to the color model adopted, the "'usual" definition of saturation as the "colorfulness" (Hunt, 1986) of a color in relation to its "brightness," or the degree of departure from the gray with the same lightness (all grays having zero saturation), is of little help (Mausfeld, 2003).

Finally, the different meanings of "saturation" or "chroma" are not limited to the different color systems in which they appear. Saturation, in fact, is confused with another phenomenological aspect of color, its insistence or forcefulness, i.e., the fact that a color appears more vivid or brighter in the field (Katz,1935). These qualities of color carry emotional and affordance-type information like the difference between cold and warm colors (Ou et al., 2004a,b; Xin et al., 2004; Da Pos and Green-Armytage, 2007; Da Pos and Valenti, 2007) and the difference between light and heavy, large and small colors (Arnheim et al., 1954/1974; Itten, 1961), and they concern the theory of the harmonic dimensions of color (Burchett, 2007).

4Alternative names for "saturation" are "colorfulness," "intensity," and "purity." Munsell uses instead a different primitive, namely "chroma"; "chromaticness" in NCS. See below for a brief reconstruction of their meaning.

5DIN is based on a circle of 24 color-hues, a saturation scale, and a darkness scale as a special parameter for establishing the relative brightness of non-selfilluminating colors (i.e., colors that are illuminated by an external source). See http://www.colorsystem.com/?page\_id=948&lang=en.

In past years, "brightness" was sometimes even used as synonymous with "lightness," which fortunately is no longer the case. From a perceptual point of view, "brightness" is an attribute of the light that reaches the eye from a surface, while "lightness" refers to the colors of an object, i.e., it is an attribute of a surface. Lightness is an observable referring to white, understood as the color with the highest lightness (100%). It follows that the lightness of chromatic colors and grays is always less than 100%. Lightness then corresponds to the reflectance of a surface, a property of distal stimulus **–** that is, a phenomenologically inaccessible property. Using brightness and lightness as synonymous would therefore merge two different observables: an observable of light and an observable of surface. To further compound the confusion, "brightness" may be also used for surfaces, thereby indicating the more or less strong illumination (i.e., *light*) to which they are subject. In this latter case, many technicians prefer to use "luminance" (thereby not referring to the corresponding perception, i.e., brightness). Luminance, in fact, is a psychophysical property pertaining to the stimulus, and not perceivable as such by a perceiver.

Finally, "brightness" is also used for the correlation between the impression of lightness and luminance, where under the same luminance colors of higher saturation appear brighter than colors of low saturation (for example, the Helmholtz, Kohlrausch, and Boswell illusion; see Kaiser, 1985).

### **FRAMEWORKS OF ANALYSIS**

The foregoing discussion has shown how tangled the "scientific" analysis of colors is, and we have provided some evidence about how different some of the presently most widely used theories and approaches are. Some of their differences are due to pragmatic factors such as the needs of the communities using them: for instance, technicians requiring colorimetric data prefer to use either the DIN, the Munsell, the CIELAB or CIECAM02 systems (nowadays with a preference for the last). In one way or another, all the systems need to take account of four different natural systems: physical radiation, physiological elaboration, perception, and language. They differ as to where the focus falls, and therefore in which other system(s) should be kept under control in order to obtain the information they deem relevant. Munsell, NCS, and also OSA-UCS (Optical Society of America, Uniform Color Scale), for example, have a phenomenological base, none of them is primarily focused on physical radiation. Munsell, however, accepting the Fechnerian psychometric law adopts a two-sided understanding of perception, while the NCS adopts and develops a properly phenomenological stance (perception as connected to what appears to awareness), though ruled by psychometric principles.

The Munsell system constrains both psychological and linguistic information: the former by showing individual chips, that is by avoiding contextual influences on color, and the latter by admitting only yes/no answers by the perceiver.

On the other hand, the NCS constrains the neurophysiological base of perception and considers both the source and the neuronal elaboration of the stimuli to be irrelevant. This is not to imply that opponency has no neuronal correlates (Jameson and Hurvich, 1955; MacLeod and van der Twer, 2003; MacLeod, 2010). The problem, however, is that anatomo-physiological substrates cannot explain the phenomenological *qualities* of opponent colors

(Valberg, 2001; Kuehni, 2004). As a matter of fact, stimuli for the NCS may arise from any source whatsoever (either "external" or "internal"), and there may be different kinds of them.

By not constraining its phenomenological base, NCS seems to better exploit the richness of both perceptual experience and its linguistic formulation: for example, the relation between warm and cold colors and its linguistic expression (Hård and Sivik, 1981; Da Pos and Valenti, 2007). The very existence of NCS shows that phenomenological observables can produce scientifically exploitable models of color.

The problem remains of making sense of the variety of models. As said, some models are explicitly tailored to the needs of specific communities of users, whilst others are more general in nature. The question however is that all the major models succeed in capturing aspects of the enormously complex problem of color perception. Finding a way to better codify the specific points of view embedded in the various models and systematically coordinate their outcomes may greatly deepen our understanding of colors. Since the discussion has already shown not only that the different models focus on different types of information, but that these types pertain to different sciences (physics, biology, psychology, linguistics – what in a more explicit philosophical parlance becomes the different levels of reality characterizing physical waves, neurophysiological activities, perception, and language **–** the question arises naturally whether a theory of the levels of reality will indeed be able to clarify and connect, at least to some degree, the different models.

# **APPROACHING LEVELS OF REALITY**

Before presenting some aspects of the theory of levels of reality and their relevance to our topic, some preliminary clarifications on the nature of ontological categories are needed. Needless to say, these clarifications are far from being anything like the presentation of a full-fledged, ontological framework. The economy of the paper forces us to skip issues that a purely philosophical paper would have to address. With these limitations, these clarifications may provide the required anchor points to an ontological framework sufficiently general to clarify scientific models.

We distinguish between categories on the one hand, and individuals on the other, as the entities to which categories refer. Only individuals pertain to the furniture of the world. Categories are not new entities added to the furniture of the world; they are instead principles (or determinations) of the individuals that they categorize. Individuals may be subdivided between *concreta* and *abstracta*, and their categories between real and ideal categories. *Concreta* and real categories pertain to the ontology of real being, *abstracta* and ideal categories to the ontology of ideal (or abstract) being. Universal categories comprise both *concreta* and *abstracta*, real and ideal being. The partial ontology that we are presenting in this paper deals with some aspects of real being only, namely colors.

Moreover, the difference between the nature of categories as principles and the often cumbersome process of their discovery and refinement should never be forgotten. The following quotation aptly summarizes our own understanding of ontological categories:

"the categories with which ... ontology deals are won neither by a definition of the universal nor through derivation from a formal table of judgment. They are rather gleaned step by step from an observation of existing realities. And since, of course, this method of their discovery does not allow for an absolute criterion of truth, here no more than in any other field of knowledge, it must be added that the procedure of finding and rechecking is a laborious and cumbersome one. Under the limited conditions of human research it requires manifold detours, demands constant corrections, and, like all genuine scholarly work, never comes to an end"

#### (Hartmann, 1975, p. 13–14).

One of the most difficult problems faced by any ontology is the answer to the following question "What are the individuals to which ontological categories refer?" Two main positions compete; one according to which ontological individuals are only atomic entities, and one which accepts both atomic and molar entities. The former position sees ontological categories as referring to the most elementary components of the universe of discourse (e.g., colors as captured by colorimetry), from which all the other components should derive by composition or other suitable procedures. This is obviously the classic reductionist credo. The alternative vision is more flexible in the sense that it admits a variety of ontological individuals, some of which may work at molar levels of reality (e.g., colors as they appear in the environment, according to phenomena of assimilation and contrast). The main problem facing this alternative vision is that no generally accepted set of intermediate levels arise as the natural candidates from which to start. To compound the difficulty, the various sciences are such that a number of different levels present themselves as "natural" starting points. Selecting any one of them rather than any other is entirely arbitrary. Therefore, there is no saying that the former position is much simpler and (apparently) more effective than the latter. Notwithstanding all the difficulties encountered by the reductionist strategy, many see the reduction to atoms or basic individuals as a perhaps awkward but unavoidable TINA (There Is No Alternative) position. The underlying belief is that the difficulties arising from the reduction to atoms will eventually be solved by more refined strategies, such as new forms of composition. The possibility is usually overcome that even if some individual problem can be reductionistically analyzed, this does not necessarily imply that a generic (that is universal) reductionist strategy is available. Anyway, no patent decision procedure exists to help seriously puzzled scholars to choose between the former and the latter strategy. The unavailability of a proper decision procedure means that in the end the decision depends on a choice that the community of scholars has to take.

Our take on the issue is that the constraint forcing ontological categories to refer to atoms only impoverishes reality in the sense that information is lost and in the end authentic aspects of reality are missed. Instead, an ontological framework acknowledging both atomic and molar categories is both *more general*, in the sense of being able to categorize a wider spectrum of real phenomena, and *more complex*, in the sense of having to address many more problems, such as the ontological nature of the relations between different levels of reality.

This ontological framework systematically distinguishes between "pure" (i.e., "general" or "universal") categories and "domain" (or "level") categories. Keeping in mind this distinction will avert misunderstandings, especially when categories like those of space, time, and causation are introduced.

# **LEVELS OF REALITY**

Today, levels of reality are mostly discussed under the rubrics of "emergence" and "parts and wholes6." In fact, the two most obvious strategies with which to approach levels are to divide the world into hierarchies of entities (such as atom–molecule–cell, etc.) or groups of properties (physical, biological, etc.). Not surprisingly, the main distinction among theories of levels of reality closely replicates the divide between entity-based and property-based theories. It is also not surprising that the entity-based theory of levels comes close to part-whole theories, and the property-based theory of levels comes close to type theories. Their merits and demerits notwithstanding, it is worth taking immediate note of an underlying problem: in the above lists of entities/properties, the exact meaning of the concluding "etc." is unclear. Consider the entity-based framework: let us suppose that the series "atom– molecule–cell" will be at some point enlarged by the addition of new entities such as "mind" or "society" (or suitable alternatives). While there are *prima facie* plausible candidates for the relation connecting the items "atom,""molecule," and "cell" (e.g., a part–whole relation), the candidate relations for the new items are remarkably less easy to detect. Similarly, the connections between the properties characterizing "physical" and "biological" types are much simpler (e.g., a subset-set inclusion) than the connections between the properties characterizing the group comprising also "psychological" and "social" types7.

Of the two main ontological acceptations of entity-based or type-based theories of levels, the former, as said, comes close to the theory of parts and wholes, and the latter to the theory of ontological types. Let us adopt the latter option and understand a level of reality as a group of (ontological) categories (Poli, 2001).

The next step is to distinguish universal categories, those that pertain to the whole of reality, from level categories, those that pertain to one or more levels, but not to all of them. The distinction among physical, biological, psychological, and social types follows naturally. The subsequent step is to specify the relations connecting the levels to each other. Contemporary theories of levels of reality customarily exploit only *one* inter-level relation (e.g., in the form of supervenience). As far as color is concerned, for instance, its phenomenic appearance would be a supervenient product over its physical basis. One of the reasons for rehabilitating Hartmann's theory of levels (see note 6) is that his theory uses *two* different inter-level relations and is therefore able to better distinguish the differences between the physical and the biological levels, on the one hand, and the biological and the psychological levels on the other (Poli, 2006a,b,c, 2007). Provided that the

6In the English-speaking world, both strands of analysis have been stimulated by influential papers by Hilary Putnam – notably Oppenheim and Putnam (1958) and Putnam (1961). Since them, an enormous discussion has developed, which cannot be summarized here (for an old but still valuable survey, see Blitz, 1992). However, as important as the discussion in English has been, it is worth noting that some major pre-WWII contributions have never been taken into account, notably those by Nicolai Hartmann. See Hartmann (1940, 1975),Werkmeister (1990), Poli (2012). 7Furthermore, beyond or above the distinction between entity-based and type-

based theories of levels of reality, other acceptations of levels often intrude, such as notions of levels of organization, complexity or representation.

theory is fully developed and updated to contemporary knowledge, the two relations cover the connections between the physical and the biological levels, on the one hand, and among the biological, psychological, and social (including language and culture) levels on the other (Birren, 1969; Bornstein, 1973). With reference to colors, the two mentioned relations respectively cover stimuli (wavelengths) and their neuro-physiological elaboration (neural correlates), on the one hand, and perceptual modes of appearances of colors (Katz, 1935) and the relations among color terms in natural languages on the other.

As said, the original theory of levels developed by Hartmann is based on *two* different inter-level relations. Leaving universal categories aside, the following two main categorical situations can be distinguished: (a) Beings A and B are categorically different because the categories upon which the former is founded are partially different from the categories upon which the latter is founded, in the sense that the latter is founded on new categories (which implies that the latter includes at least a *novum*, a new category not present in the former); (b) Beings A and B are categorically different because the categories upon which the former is founded and those upon which the latter is founded form two entirely different (disjoint) groups of categories. Following Hartmann, the two relations can be termed respectively relations of super-formation (*Überformung*) and super-position (*Überbauung*; Hartmann, 1940).

Super-formation [the type (a) form of dependence] is weaker than super-position because it includes already actualized categories, those of the level below. Suffice it to consider the super-formation between molecules and cells, i.e., between the physical and the biological levels of reality. In this regard, one can mention that even if organisms are unquestionably more complex than mechanisms, the behavior of organisms complies with the laws of mechanics. On the other hand, the psychological and social levels are different because they are characterized by an interruption in the categorical series and by the onset of new categorical series (relative respectively to the psychological and social levels). The relation between the biological level and the psychological level, on the one hand, and the relation between the psychological level and the social one, on the other, are both relations of superposition. By way of example, the group of categories embedded in psychological entities is different from the group of categories embedded in biological entities. Similarly, the group of categories embedded in social entities is differentfrom the group of categories embedded in biological entities.

When the connecting relation is a relation of super-formation, some categories of the lower level recur in the higher one. Recurring categories interact with the categories of the higher level and are, so to speak, contaminated by them; some of their moments become different. Higher levels are never characterized by recurring categories, however. Each level has its *novum*, the category or group of categories that distinguishes the level from the lower ones. The *novum* does not derive either from the elements of the level or from their synthesis.

Two aspects characterize super-position relations: first, the categories embedded in the entities of the connected levels are different (they are all *nova*); second, a relation of existential dependence links the higher level to the lower one. Most details

of the links connecting together the various levels of reality are still unknown, because the various sciences have worked mainly on causal links internal to their regional phenomena8.

As an observable, color has ramifications into all these different levels of reality and as we have seen the properties of color are different in the different levels.

This is the main reason for at least some of the differences among the different color models.  While two different levels related by a relation of super-formation may indeed present the same category, the internal determinants of this category are nevertheless partially different because the category pertains to two different categorical groups: that is to say, it interacts with two different groups of categories. One may say that the category seems to presents an intrinsic ambiguity. We say "seems" because the ambiguity is not embedded in intrinsic features of the category but depends entirely on the observer's shift between different levels of reality (connected by a relation of super-formation). Reading a physical category (the three stimulus codification of a light wave) as a biological category (the three stimulus codification of a neural network) is a case in point.

On the other hand, levels of reality connected by a *superposition* relation present a remarkably different situation. In this latter case – and leaving universal categories aside – the categories defining the two levels are different. In this sense, no ambiguity is likely to arise. Moreover, the two levels are connected by a relation of existential dependence, meaning that the higher level requires the lower one as its existential bearer. Examples from the field of colors are provided by the difference between warm and cold, light and heavy, large and small colors (see Color Primitives above). None of these properties is present in the space of physical radiation. They are authentically phenomenological categories, present only at *that* level of reality. On the other hand, the phenomenological level requires suitable existential bearers – and more than one as a matter of fact: not only the brain as the bearer of the mind, but also the body (because the brain is not an autonomous whole)9, and the external environment. All of them are required, and all of them are sources of possible perceptual stimulation.

## **CONCLUSION**

As we have seen, color perception is paradigmatic for its complexity, including its ramifications into the physical, the neurophysiological, the linguistic (and cultural) and the phenomenological

8The lack of a theory of levels of reality has possibly been the main obstruction against development of the theories needed. Proposals concerning the architecture of levels and their links will improve our understanding of the world and its many dependencies. To mention but one case, the theory of levels paves the way to the claim that there may be different families of times and spaces, each with its own structure. We shall argue that there are numerous types of real times and spaces endowed with structures that may differ greatly from each other. The qualifier *real* is mandatory, since the problem is not the trivial one that different abstract theories of space and time can eventually be, and have been, constructed. We shall treat the general problem of space and time as a problem of chronotopoids (understood jointly, or separated into chronoids and topoids). The guiding intuition is that each stratum of reality comes equipped with its own family of chronotopoids (Poli, 2007; for further details on the theory of levels of reality, see Poli, 1998, 2001, 2006a,b,c, 2009, 2010a,b, 2011a,b, 2012).

9Here is where the connection with the theory of levels from the perspective point of the theory of wholes becomes visible.

Albertazzi and Poli Multi-leveled objects: color as a case study

domains. Some of these ramifications are simpler than others. Not surprisingly, the phenomenological one is the most complex because phenomenic color exists only in the way in which it appears and therefore is a primarily contextual entity deeply influenced by interaction and assimilation (Katz, 1935) and language. The higher complexity of color perception may partly explain the preference shown by many experts for other points of view.

The research hypothesis that we have presented is that the theory of levels may clarify some of these intricacies in the sense of making explicit the ontological references of the various aspects of color, and it may therefore contribute to explaining the concepts of color used in science, phenomenology, and natural language conceptualization.

The analysis has shown that the different models explain color perception by encoding qualities pertaining to different levels of reality, which implies that strictly speaking they model different realities. However, since phenomenic color is essentially a contextual entity, the NCS system seems to be the model closer to color appearances. Further studies may provide additional evidence about whether the explicit connection between a model and the level of reality that it encodes is indeed able to clarify the relations among models themselves (an issue that may be called "ontology as a framework for clarifying science").

#### **ACKNOWLEDGMENT**

The authors thank Osvaldo Da Pos for his comments.

#### **REFERENCES**

Albers, J. (1963). *Interaction of Color*. New Haven: Yale University Press.

Hunt, R. W. G. (1986). *Measuring Colour*. Chicester: Ellis Horwood.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 26 January 2014; accepted: 27 May 2014; published online: 02 July 2014. Citation: Albertazzi L and Poli R (2014) Multi-leveled objects: color as a case study. Front. Psychol. 5:592. doi: 10.3389/fpsyg.2014.00592*

*This article was submitted to Theoretical and Philosophical Psychology, a section of the journal Frontiers in Psychology.*

*Copyright © 2014 Albertazzi and Poli. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

# On agent-based modeling and computational social science

# *Rosaria Conte and Mario Paolucci\**

*Laboratory of Agent Based Simulation, Institute of Cognitive Science and Technologies, CNR, Rome, Italy*

#### *Edited by:*

*Roberto Cordeschi, Sapienza University of Rome, Italy*

#### *Reviewed by:*

*Pietro Terna, University of Torino, Italy Stefano Balietti, ETH Zurich, Switzerland*

#### *\*Correspondence:*

*Mario Paolucci, Laboratory of Agent Based Simulation, Institute of Cognitive Science and Technologies, CNR, via Palestro 32, Rome 00185, Italy*

*e-mail<EMAIL_ADDRESS>
In the first part of the paper, the field of agent-based modeling (ABM) is discussed focusing on the role of generative theories, aiming at explaining phenomena by growing them. After a brief analysis of the major strengths of the field some crucial weaknesses are analyzed. In particular, the generative power of ABM is found to have been underexploited, as the pressure for simple recipes has prevailed and shadowed the application of rich cognitive models. In the second part of the paper, the renewal of interest for Computational Social Science (CSS) is focused upon, and several of its variants, such as deductive, generative, and complex CSS, are identified and described. In the concluding remarks, an interdisciplinary variant, which takes after ABM, reconciling it with the quantitative one, is proposed as a fundamental requirement for a new program of the CSS.

**Keywords: agent-based modeling, computational social science, agent-based simulation, interdisciplinarity, multi-realizability, model building**

# **1. INTRODUCTION**

The two decades around the turn of the millennium have seen the rapid advent, and perhaps the premature decline, of a paradigmatic shift in science, represented by agent-based modeling (ABM) and simulation. In this section, after shortly defining what we mean with ABM, we present a short account of its history.

### **1.1. WHAT AGENT-BASED MODELING IS**

What is meant by Agent Based Modeling? Often, this is defined in opposition to Equation-Based Modeling (see for example Dyke Parunak et al., 1998; Cecconi et al., 2010). More specifically, ABM arises at the intersection between agent theory, systems, and architectures, on one hand, and the social sciences, on the other hand. Agents are usually defined (see Conte, 2009) as autonomous systems that operate transitions between states of the world, based on mechanisms and representations somehow incorporated into them.

Under this general definition, the field of agents shows a tremendous variability. Agents vary indeed on several dimensions, which include whether and to what extent they are autonomous, self-interested, sociable, and capable to learn from experience and/or observation. Agents also differ in their level of complexity: according to a classic distinction introduced by Wooldridge and Jennings in their influential work (Wooldridge and Jennings, 1995), agents in a "strong" sense are capable to manipulate and reason upon mental representations; otherwise they are considered agents in a "weak" sense.  Sub-symbolic representations are unaware, implicit, based for example on network-like configurations representing the structure of relationships among neurons in cerebral areas, and not liable to purposive manipulation on the side of the agent. Finally, agents vary according to the philosophical or metatheoretical view their description is based upon. One example is the attempt to model agents on the basis of a personal utility function, on which much work on agents has been done over the past 30–40 years or so, and that has also been criticized as for its micro plausibility (Antunes and Coelho, 2004).

The practice of ABM however did represent a substantial under-exploitation of such wide spectrum of possibilities. De facto, much of the agent models worked out and simulated are totally *ad-hoc*, based on very simple local rules (Epstein, 2006), more or less arbitrarily implemented on a program running on a computer (Gilbert and Troitzsch, 2005). When the program is run, macroscopic effects of the local rules can be observed on the screen, and then be stored, analyzed and possibly visualized in search for emergent phenomena. We will return to the problem of *ad-hoc* rules in section 2.3 below. Such a practice of modeling lends itself well to observe and experiment upon multi-agent worlds or agent societies. These are meant to either reproduce some real-world setting or phenomenon [a typical example is the Anasazi culture simulation (Axtell et al., 2002)], or to build up and observe would-be worlds (Casti, 1997). Such models allow novel theories about abstract social phenomena to be formulated, operationalized, and tested. Examples of this application of ABM abound and are among the best cited works so far worked out in this field.

# **1.2. AGENT-BASED MODELING IN A HISTORICAL PERSPECTIVE**

Conference proceedings, dedicated to the new methodology of ABM and its multiple applications within the social and behavioral areas of science, started to appear in Europe since the early nineties (Gilbert and Doran, 1994; Gilbert and Conte, 1995; Conte et al., 1997). Agent-based models of social phenomena trace back to as early as 1971, when the famous (Schelling, 1971) model of segregation was published in the Journal of Mathematical Sociology. In 2002, the field obtained a major institutional acknowledgment, when the proceedings of a Sackler Colloqium of the National Academy of Sciences, under the title "Adaptive Agents, Intelligence, and Emergent Human Organization: Capturing Complexity through Agent-Based Modeling," held in October 2001, were published on PNAS (Bonabeau, 2002). In that circumstance, ABM was proclaimed as the leading field—we might say the flagship to use a trendy tag - in the renewal of the social, behavioral, and complexity science, which was expected to take place in the years to come. Consecrated by the US scientific institutions, the field was already intensely practiced also, if not primarily, in Europe, where ABM had given rise to a new journal, the Journal of Artificial Societies and Social Simulation (JASSS, founded in 1998), to the first scientific association (ESSA, The European Social Simulation Association, created in 2003), and was at the center of a variety of promotional activities. Soon enough its range of influence extended beyond the two sides of the Atlantic, reaching out to the Pacific area, and giving rise to the PAAA association. At the same time, the NAACSOS association was founded in the US. After some years of fruitful competition, the associations joined in the first World Conference on Social Simulation held in Kyoto in 2006.

At the end of the first decade, however, the ABM leadership seems to be challenged if not decisively weakened by the (re)appearance of a more sober, more encompassing, and less innovative tag, that of Computational Social Science (CSS), of which ABM is a component (see Bankes et al., 2002) for an early insight), and which now candidates itself to replace ABM in the same leading position for the next decade. Evidence of a change of leadership and of a possible coming era for bare CSS, rather than for the more inspiring Generative Social Science proposed by Epstein in 2006, can easily be found in some position papers (e.g., Lazer et al., 2009; Cioffi-Revilla, 2010), books recently appeared (Gilbert, 2010), a new regional association—the CSS Society of the Americas, born on the ashes of the short-lived NAACSOS, and the relative conference held in 2011—and, finally, the objectives of the unsuccessful but groundbreaking EU FET flagship pilot FuturIct (www*.*futurict*.*eu).

If history is instructive, the study of signaling is fun. In the era of information overflow, distributed content production, collaborative filtering, crowd sourcing, and so on, emblems are decisive. Tags have a far-reaching but short life. Under the tyranny of PageRank, contents compete in terms of lookups, and these most certainly depend on familiarity, and possibly also on tags appeal. Science makes no difference. It is somewhat surprising when a paradigm shift is signaled by a flat combination of two traditional scientific areas: social sciences and computational science. What is the meaning conveyed by this signal? Does the new label correspond to a new paradigm shift in the social and behavioral sciences, or does it simply meet a kind of marketing need for periodical renewal of names?

This paper presents an attempt to weigh up the impact of ABM and answer the question whether this field is undergoing or not a real decline; whether or not his replacement was timely, necessary, and effective. Next, some current variants of CSS will be compared. Finally, some important requirements for achieving real progresses in the computational study of social phenomena will be identified and discussed.

# **2. AGENT-BASED MODELING: A BALANCE**

Rather than a detailed survey of ABM (for a good example, see Helbing and Balietti, 2011a) this paper presents an attempt to draw a balance of this field, pointing to its main weaknesses and strengths.

#### **2.1. STRENGTH OF AGENT-BASED MODELING**

One may wonder what ABM is good for and what are its major strong points. The tricky questions as to when ABM is really needed, whether agent-based models can or cannot be converted into an analytical, equation-based model and to what extent this can be done has been debated at length elsewhere (see for example Epstein, 2006; Cecconi et al., 2010). Nonetheless, ABM remains the only known approach apt to model and reproduce sets of heterogeneous agents interacting and communicating in different ways.

Of course, ABM can only provide a sufficient explanation of the phenomenon of interest, not a necessary one. This feature, which (Epstein, 2006) extensively clarifies and discusses, is also known as *multi-realizability* (Sawyer, 2005), and it is an outstanding property of multilevel systems. A macro-level phenomenon in whatever domain social, natural, mental, etc. of reality, is multirealizable when it can be implemented in different ways on the lower levels. Inevitably, ABM generates the higher-level effect by following one of the possible generating paths. Even if as many models as generating paths were actually implemented, it would still be difficult, if not impossible, to assess which one among them is effectively implemented in the real world. But, interestingly, this is true also of the target phenomena: an organization can perform its mission independently of the internal structure (consider as an example a project-based structure against a functional one). Social conformity is achieved through a variety of internal mechanisms, e.g., imitation or norm compliance. It is still unclear how disapproval works as a sanction, whether it affects people's decision-making because it activates an expected associated material punishment, or violates the goal of a good (self) esteem. Actually, multi-realizability is a property not only of ABM but also of the real world. In this sense, multi-realizability differs from the more general issue of model underdetermination, as it connects it directly with possible generative paths in reality, an analogy that makes ABM particularly apt to study the equivalence, or possible lack thereof, of structure and mechanisms inside intermediate levels, in the sense of the examples above.

To implement sets of heterogeneous agents in interaction brings about a series of second order advantages: agent societies are (1) operational platforms where theories get converted into falsifiable hypotheses; (2) experimental laboratories where theories get gradually and thoroughly controlled; (3) multilevel worlds where the level of individual units, the agent, is clearly distinct from the macro-level, the system level and unforeseen effects and emergent properties of interaction can be observed.

In short, ABM is an *in nuce* society, which unfolds and actualizes when the model is implemented on a computer program and this runs. In some cases, the effects observed in the computer could not be predicted while modeling and implementing the single units, the individual agents. Hence, the effects of such behavioral units on the whole agent society or parts of it can be observed and investigated. Otherwise stated, ABM allows the interplay between different levels of a social system to be modeled and observed. As shall be seen later, this important property of real-world societies has been insufficiently exploited. The main dynamic investigated by ABM is the way-up of the interaction among the micro and the macro-level. The complementary process, the way-down from the macro-level to the micro-level, has been poorly explored. Closing the loop, however, may require a high level of ABM complexity. Theory-driven, non-*ad-hoc* models of phenomena generated by intelligent behavior may be relatively difficult to calibrate (Heckbert et al., 2010). Difficulties usually increase with the model's level of scale and the number of parameters. One may perceive a trade-off between vertical scaling, i.e., agent complexity, and horizontal scaling, i.e., scenario complexity. Such a trade-off is probably one of the keys for ABM development and leads us straightforward to one of the weak points in the field.

# **2.2. WEAKNESS OF AGENT-BASED MODELING**

Some problems and difficulties in the field of ABM and simulation have been perceived from within the scientific community since long, while others have only recently come to our attention. Since the field's early days, a serious concern of Agent Based modelers and simulators is how to design large-scale agent-based simulations. In its initial applications, agent-based models did not care much about the problem of scale, as they were applied to observe the emergence of patterns from interaction at the microscopic level in artificial scenarios sharing some crucial features of the real-world, but not really aimed to reproduce its details. As soon as the potential of agent-based models became apparent revealing a great occasion for observing and manipulating *in silico* models of target phenomena in order to acquire a better control, and possibly to optimize intervention—upgrading their level of scale of several orders of magnitude proved necessary. You cannot optimize a system of traffic if you do not manipulate parameters in populations of several millions of agents.

Under the pressure of complex systems science, which is gaining ground in the study of social phenomena (Helbing and Balietti, 2011b), agent-based simulation is increasingly expected to meet a further, and connected, important requirement, i.e., to be fed by massive data in real-time. To answer the problems of scale and real-time simulation, a variety of ICT solutions (parallel and supercomputing infrastructures) are being designed and tested. To deal with this challenge, agent-based simulations were bent to applications needs, such as policy modeling and traffic optimization (Grether et al., 2010), distributed communication over the Internet (Chen, 2009), electricity market (Guerci et al., 2010), financial crisis (Sornette, 2003), epidemics (Pastor-Satorras and Vespignani, 2001). This is not the forum for discussing sophisticated technical solutions (but for a review of techniques to that purpose, the reader might be referred to Paolucci et al., 2013) to the problem of making ABM more apt to the requirements of BigData science. We will instead touch briefly on the question of model equivalence across disciplines and applications.

# *2.2.1. Equivalence of models*

Unlike laws of nature, Agent Based models of socio-economic phenomena are countless and not always consistent (see Alfi et al., 2009). Think of the various heuristics and rules of thumb applied in defining microscopic rules for ABM. Most of them generate results at the macroscopic level, which are applied more or less the same narratives or metaphors. Hence, cooperation in Prisoner's Dilemma is found to emerge from a set of heterogeneous strategies, from TIT-FOR-TAT (Axelrod, 1997) to strong reciprocity (Boyd et al., 2003), from image-scoring (Nowak and Sigmund, 1998) to reputation-building (Pinyol et al., 2012), and finally group selection (Di Tosto et al., 2007); social control is found to emerge from ostracism (Xenitidou and Elsenbroich, 2010), but also from partner selection, and finally from gossip (Giardini and Conte, 2012); norms emerge from punishment (Galán and Izquierdo, 2005), which in turn is but a TIT-FOR-TAT strategy, but can also emerge from conditioned preferences (Bicchieri, 2006), and from habituation (Epstein, 2008). Is models' equivalence a major shortcoming of the field, or something social scientists can put up with? What does it depend upon? Is it a necessary or a contingent feature of ABM?

We believe the variety of equivalent agent models in part depends on a property inherent to multi-level systems as complex social systems are. The property in question is the multirealizability that we have mentioned above. In part, we believe it to be a consequence of the shaky foundations, the poor theoretical justification at the basis of many agent models. This is not equal to finding poorly realistic the model of agent often proposed by current modelers, and asking to improve it toward psychological, cognitive, or sociological plausibility - toward a *seemingly human* agent. What is wrong, in our view, is the procedure for model building and the role of behavioral rules. Let us examine both points with some detail in the next two sections.

#### **2.3. THE ABM RECIPE FOR MODEL BUILDING**

A consensus seems to have emerged in ABM on a minimality procedure; that is, models are built by setting up the rules that are minimally required to obtain the macroscopic effect to be described. While minimality might sound obviously inspired by the success of hard sciences, the substantial failure to apply such a minimality procedure to social science is testified by centuries of failed attempts, starting from what had been announced as "Social Physics" in the seventeenth century (for an historical perspective, see Ball, 2002). The reasons for consensus on minimality might be better described with the tools of the sociology of science than rooted in the search of theoretically sound and scientific advances. Indeed, the ABM community, being still relatively small, is subject to issues of disciplinary recognition, with the consequent pressure to publish in a limited number of outlets; and it might still be looking for the right dimension of the contribution the ideal paper size, as measured in effort invested and soundness of results, could be very different from the "correct" paper size in terms of publication chances. This discrepancy causes a motivational pressure toward minimal (and publishable) models, and hampers research in the much more interesting issue, why minimality seems to fail in the social sciences. We will get back to our intuition on this matter in the conclusions.

Under the rule of minimality, model building is operated (1) a posteriori, based on backward engineering from the effects obtained to the generating rules; (2) *ad-hoc*, so that rules are suggested by the specific results to be obtained; (3) in a ruleoriented rather than agent-oriented approach: what is achieved is a set of rules, rather than an agent view; (4) inspired by the minimal-conditions logic: modeling consists of finding out a set of microscopic rules minimally required to reproduce a given phenomenon of interest. The minimal approach, thus, strongly reduces the validity of ABMs on two separate accounts. On the one hand, theory-based, agent models are implausible caricatures of agent as prescribed by the rationality theory, with a touch of psychological realism in the best possible case. On the other hand, when agent models are not derived from any pre-existing agent theory or vision, whether computational or not, but only by the behavior they are expected to generate (Epstein, 2006), agent models become arbitrary, poorly comparable, competent in highly specific domains of knowledge and disarmingly inapt in any other. It should not come as a surprise if, as a result, a myriad of rather inconsistent agent-based models have been produced over the past 20–30 years or so. Is it possible to find an escape between implausible models and arbitrary ones, or between *ad-hoc* rules and useless ones? Options exist, but are poorly exploited. Why?

# *2.3.1. From cognitive models...*

One such option is represented by cognitive agent models, which exist since the late nineties. Their wide range of influence is shown by the popularity of BDI architectures (about 32,700 "BDI agents" cites on Google Scholar retrieved on March, 18th 2013) within and beyond the field of agent systems and theories. Simulation of social phenomena with BDI based models also abound in the literature (about 7060 "BDI social simulation" cites on Google Scholar on March, 18th 2013), and usable platforms to implement them are under consolidation, from Jason (Bordini et al., 2007) to Netlogo extensions (Sakellariou et al., 2008). However, works with this approach receive attention mostly from the computer science community, and are rarely published in main social scientific journals.

Although the rich cognitive models tag appeared since the early nineties (for a recent example see Dignum et al., 2010), the amount of models inspired from it remains negligible. Subsymbolic systems and neural nets did not make much better. Although neural nets and social simulation fare better, relative publications again do not appear in major social scientific journals. Why are cognitive theories on agency, whether symbolic or subsymbolic, so poorly applied in ABM? In part, there are problems of inner validity and calibration. While it is difficult to control the inner validity a complex agentbased model (Cioffi-Revilla, 2002; Windrum et al., 2007), to calibrate it and manipulate parameters values so to reflect a real-world system is hard. To gather data on which the agent model is based upon takes more time and more complex empirical methodology. Therefore, the utility of a complex agent model to simulate the real-world system (i.e., showing that the model's results match the real-world data) is questionable (Crooks et al., 2008). Undoubtedly, these difficulties reduce the interest of cognitively grounded models simulators, although the latter's foundations are much firmer than those of most of the models used. The lesson one might draw is that, like it or not, scientific developments are often due to practical utility more than theoretical soundness. However, the little success of cognitively grounded agent-based models is also due to other factors.

First, unlike other theory-grounded agent models, for example the rational models, cognitive models are not prescriptive. Whereas the theory of rationality is a theory of action, cognitive modeling provides theories of the agent. Hence, the rational agent model fits only apparently better the objectives of ABM and simulation, but it does so only because it allows the modeler to get rid of the tricky part of the modeling, that is, how agents form the goals, the motivations, the preferences, that will be implied in the decisions.

## *2.3.2. .. to generative models.*

Secondly, cognitive modeling is a truly generative theory of behavior, accounting for behavior in terms of the mechanisms that are supposed to operate while producing it. A generative explanation of an observed social phenomenon consists of describing it in terms of the external (environmental and social) and internal (behavioral) mechanisms that generate them, rather than by inferring causes from observed co-variations. This is a vital property of explanation, which cannot easily be realized otherwise. When describing agent behavior by means of other formalisms (logic-based or numeric), we describe behavior from the outside, as perceived by an observer, but do not describe the way it is generated. ABM explains behavior from within, in terms of the mechanisms that are supposed to have generated it, that is, the mechanisms that operate in the agent when s/he behaves one way or another.

Of course, behavior can be explained otherwise. For example, the flight of hawks is wonderfully explained by the mathematical property of logarithmic spiral, such that any tangent from the center of the spiral yields an angle of the same width. Thanks to this property, hawks can keep their preys always in their aim while describing a spiral before pouncing on them. But this explanation is not generative, in the sense that it does not tell us what are the internal mechanisms allowing hawks to fly the way they do. For sure, hawks do not fly based on an understanding of the properties of logarithmic spiral. How can they show the corresponding behavior? The often invoked evolutionary explanation offers poor help: it accounts for behavior in terms of its reproductive advantage. As the spiral-like flight proved advantageous for hawks, those who performed it were able to generate more offspring, while the others extinguished. No generative theory here: it tells us not how hawks produce the behavior in question. We could use the mathematical theory to describe their behavior, and incorporate the mathematical explanation into a set of *ad-hoc* behavioral rules for reproducing it. But neither the mathematical explanation, which describes internal causes, nor the set of *ad-hoc* rules are generative.

Now, a fully generative explanation implies a more general theory of how external causes, including fitness-enhancing effects, get converted into internal reasons (what sometimes are called proximate causes of behavior). Agent-based models are often limited in focus, and not easily compatible with the temporal perspective and the theoretical requirements of a fully generative - in the sense here intended - explanation. Do we always need a generative explanation? Not really, as *ad-hoc* rules sometimes are just all that is needed to explain behavior. This is the case of entirely programmed organisms, and it may even be the case of hawks, as far as we know. Sometimes, instead, you need more. Suppose you want a hawk to learn a new trick with respect to the approach behavior. That is, you, or nature, in the form of new environment - perhaps, but we're letting imagination run wild here, in the form of a prey that develops a counterstrategy to the spiral. Then, immediately how the flight is generated becomes important: how much learned, how much hard wired, and where; in a plastic neuronal connection, or in a fixed relative placement of eye and bone? Suddenly, to reproduce their behavior you would need more than a rigid set of rules; you need to know how it is generated.

Cognitive modeling aims at finding the general mechanisms yielding the wide spectrum of behaviors of relatively autonomous systems. Of course, you don't need such mechanisms to simply reproduce behavior. The more specific the target behavior, the lesser you need a cognitive agent-based model. Since ABM is often used to investigate fairly specific phenomena, either mathematical model or a set of *ad-hoc* rule are preferred over cognitive modeling. But together with cognitive modeling, we also dispense away with truly generative modeling.

# **2.4. WHY BOTHER WITH GENERATIVE EXPLANATION**

One might say, who cares after all? Provided we can reproduce behavior, observe it and make artificial experiments to optimize it, why bother with theory-driven generative modeling? There are several reasons. One is that a truly generative explanation is needed to model complex social dynamics. For universal admission, the dynamics of social entities and phenomena is at least bidirectional if not multidirectional. Entities and properties emerge from the bottom up and retro-act on the systems that have generated them. Current agent-based models instead simulate only emergent properties, i.e., the way up of social dynamics. To mention only a few examples, the ABM literature offers countless models of the emergence of segregation, norms, reciprocity, altruism, cooperation, punishment, conventions, institutions, coalitions, leadership, hierarchies, the modern state. Studies of different types and levels of downward causation are much less frequent (to cite some exceptions, see Gilbert, 2002; Conte et al., 2013). However, how to change self- and otherdamaging behaviors (i.e., smoking, over-eating, etc.) was ranked as the fourth most important among the top-ten hard problems the social sciences will have to address in the near future (Giles, 2011).

Agents should not be taken for granted as they change under different types and degrees of social influence. Entities at the macroscopic level affect them and their behavior, and we must understand how this can happen if we want to drive, enforce, or prevent such an influence. This a line of research that presents obvious ethical issues, but at the same time addresses themes so important that social science cannot just leave them alone, or, even worse, desert them to market solutions. For example, at least in some fields, we badly need to know how to reduce or control people's overconfidence, for example in finance, where it so heavily contributed to the last financial crisis (see Akerlof and Shiller, 2010), causing a disruption of global scale; how to change people's bad food habits, which are mainly responsible for highly diffuse diseases as diabetes; how to make low compliant populations to obey the norms, how to increase social trust, reduce hostility toward out-groups, favor communitarian attitudes, and so on. All of these questions might find useful answers based on reality mining. Through Google or Yahoo we may trace people's habits, moods, investment decisions, political views, risk propensity and attitudes toward culture, education and migration. Based on this information, we may drive production, capital movements, business strategies, political decisions, and international cooperation. But we will not be able to suggest effective plans for modifying such behaviors and the underlying mental states, unless we understand the mental dynamics and how this interacts with the social dynamics, and model the cognitive mechanisms that respond to external influence and rule behavioral change. In absence of such theory and model, we will not get to the core of hard problems.

#### **2.5. A MISSED OPPORTUNITY**

ABM is a powerful means for investigating the hinge between different domains of reality, including economy, environment, and society: systems' behavior at different levels of scale. It is necessary to explain phenomena pertaining to any domain of reality that is heavily dependent on the behavior of autonomously interactive systems, as was convincingly argued by Epstein. More, ABM is unique for allowing a generative approach to behavioral systems in the sense here defined, and somewhat different from Epstein's, i.e., to describe phenomena in terms of the external and internal mechanisms that produce them.

However, ABM seems to have fulfilled its mission only in part. Its generative capacity has been deployed to a lesser extent than could have been the case. The practice of ABM missed the opportunity it provided: paradoxically, the same principle that led it to a fast popularity, like the KISS principle—i.e., keep it simple, stupid - introduced by Axelrod (1997), and moreover the procedure to find the minimal required conditions to obtain a given phenomenon, do now sentence ABM to a premature end. The KISS principle still drives most of the simulation work: we have performed a check on a whole year of JASSS, a journal that we consider representative of the files. In 2013, JASSS published 49 papers, of which 38 could be classified as simulations (the rest is composed mostly by theoretical papers). Of those, 30 could be considered as following the KISS advice, which makes about the 80% of published papers.

 Why bother with agents, if one can apply computational tools to reality mining and platforms to large scale real-world data-driven simulations, and aim at even higher orders of magnitude, enabling us to forecast events at aggregate levels, such as epidemics, climate change, and traffic jams? Couldn't it be the case that a mere quantitative use of computational tools be enough to forecast financial crises, social instability, and even human well-being?

It could be the case, indeed. However, centuries of failed attempts (see the "Social Physics" case mentioned above) make us doubtful. But what is maybe more important, by pursuing this quantitative approach alone, science would have lost a wonderful opportunity: to understand the micro-foundations of phenomena at aggregate levels and how the latter (re)generate them.

### **3. COMPUTATIONAL SOCIAL SCIENCE**

Science, like history, is not a linear process. A decade ago, social, and behavioral science dropped the disciplinary label (Conte, 2002) under the influence of an entirely new field, ABM. In the last couple of years a CSS is being re-proposed. But CSS is being practiced since a couple of decades if not earlier. What is new to the current program?

Computational Social Science (from now on CSS) can be meant in at least three different ways, the deductive, the generative, and the complex one; and it should be made clear which one we are referring to. As these are conceptual, rather than empirical, variants, there is no need to have each of them matching a defined historical example of CSS, since concrete examples are often a mix. Let us characterize variants also with reference to existing programs and try to forecast what their consequences might be.

#### **3.1. THE DEDUCTIVE VARIANT**

The second half of the last century is constellated of attempts to apply the theory-building instruments of mathematics and the theory-testing tools of computer science on one side, game theoretic, and logic-based computational models on the other, to describe and explain social phenomena. The latter, in particular, attempted at deducing properties at the macro-level from general assumptions at the micro-level. Expectations á la *homo economicus*, allowed by the theoretical framework, turned out to be wrong, what did not imply that the approach was incorrect, only that it had been based on the wrong assumption, depending on the theoretical and sometimes ideological positions of the authors. What was worse, these position were often left implicit. The deductive variant consists of formulating the mathematical equations that account for the phenomena to be explained. With the support of observation and data gathering, parameters can be assigned their correct values. Although the theoretical framework is often much too simple, the general program scarcely interdisciplinary, and the ambition for social impact mainly based on a rather prescriptive view of micro-level theory, deductive CSS yielded a foundational, general, explanatory theory of social systems. A lesson we should not forget.

#### **3.2. THE GENERATIVE VARIANT**

The decline of the rationality paradigm produced several consequences. One of these was a stronger and more interdisciplinary effort to ground computational models on explicit models of the micro-foundations. This led to the advent of the generative variant of ABM, which derives its explanatory vocation and micro-foundational framework from the deductive variant. Unlike it, generative science aims at modeling operational microscopic rules that generate macroscopic phenomena, rather than formulating mathematical equations from which to deduce them. The explanatory vocation is declined in a radically different way: rather than describing a causal process from the outside, the modeler attempts to show the internal rules that initialize it and follow the unfolding of it all the way up to the observed effects.

As argued in the preceding section, however, ABM fulfilled its mission, provide generative theories, to a lesser extent than was expected. If the deductive variant was found to theorize upon fairly abstract phenomena and has often been criticized for its poor predictive capacity, the generative variant did not prove any better at prediction, partly due to problems of validation and calibration.

#### **3.3. THE COMPLEX VARIANT**

Inductive computational science is certainly not new (Newell and Simon, 1976). The necessity to combine mathematics and logic with learning, probability, and induction is receiving a growing attention since the early nineties in several computational disciplines such as knowledge representation, reasoning about uncertainty, data mining, and machine learning. Nor is new the use of computational instruments for quantitative social science: it suffices to think of the wide application of statistics package for social scientific research, and by the number of repositories and archives of social scientific data (for example, http:// www*.*data-archive*.*ac*.*uk/). However, techniques of data-mining are exercising an even stronger influence on the social sciences. The use of advanced computer technology by social scientists is also shown by sites where freely available web resources are assembled with information on how access social scientific data (see for example, http://guides*.*lib*.*wayne*.*edu/socialsciencesdata), and by funded programs for interfaces between computer and social sciences.

A new impulse to computer-based quantitative social science is coming from the science of complexity, which is now going through a season of deserved popularity. The use of complex systems' methods, models and techniques to economic systems goes back to the nineties (for a rather informative introduction, see Mantegna and Stanley, 2000), and the welcome received by mechanical statistics in the field of economics and finance was such as to encourage its wider application to the rest of the social sciences. The popularity of sociophysics grew even more under the influence of success stories, especially concerning the domain of pedestrians' crowd (Helbing et al., 2000) and that of epidemics (Pastor-Satorras and Vespignani, 2001). In the last few years, a diffuse uncertainty related to globalization, international and cultural conflicts, and the recent financial crisis, led to the necessity to anticipate and manage critical events on the front-stage. Not only stakeholders and policy makers but also, and consequently, research and development funding agencies and evaluators laid emphasis on science as a system of warning, a source of anticipatory information on the performance of aggregate systems, simultaneously triggering and guiding the action of politicians, administrators, and businessmen. But science is more than anticipation. It is first of all explanation. Accurate prediction can do without explaining, especially if it is based on large datasets and sophisticated techniques for extracting knowledge out of them. Science cannot. Of course, explanation may be allowed by statistical analysis. For example, topological properties of complex networks are found among the main factors affecting epidemic dynamics (for a review, see Yang et al., 2007). But this is not always the case. Indeed, this is not the paradigmatic case in those social phenomena in which behavior can be assumed to be irrelevant, or non-influential.

Behavior is irrelevant or non-influential in social dynamics where the implications of the phenomenon in question are social, but its nature is not. To go back to epidemics, the nature of epidemics is biological. The level of reality involved entities belong to does not matter for the observed phenomenon to take place: the nature of entities involved in and target of epidemics matters not. In the spread of epidemics, the difference between human behavior and that of particles in the space does not matter, nor does the difference from carriers and the viruses they carry around. But in other cases, that is, when the nature of behavior matters, accurate statistical analyses of social dynamics can maybe reach predictive power but cannot fully explain what is going on.

As a hypothetical example, suppose we want to know what are the main factors responsible for the dynamics of opinions. Again, current models (Deffuant et al., 2001; Galam, 2002; Hegselmann and Krause, 2002; Castellano et al., 2009), find that the structure of the network of communication affects opinion dynamics. Of course, the source of information also matters; a contrasting source may inhibit the effect of media broadcasting and the process is non-linear: under a given critical level of coverage, the broadcasting message may be inhibited by a "contrarian" opinion spread through word of mouth. Analogously, below a critical level of confidence "contrarian" opinions may reach all agents (Castellano et al., 2009). Social dynamics are often nonlinear and typically smolder at some length under the ashes and only subsequently surface in convergent opinions or behaviors. Suppose one predicts the moment(s) at which this will happen in real-world dynamics thanks to statistical analysis and physical models. The question is why it happens. Of course behavior is irrelevant to predict when convergence will occur. But it matters if, for example, we want to affect the process, by shortening or delaying it, or even prevent it; to educate people to a higher autonomy; to favor info-diversity; finally, to convert opinions in something more solid and resistant, like knowledge, and so on.

People withdrawing support from political leaders is a good example of non-linear opinion dynamics. It is unclear when people change their minds and turn down their leaders. The destiny of a popular (and often populist) figure is often decided upon in a very short time. Today, those who enjoyed the favor of their followers until yesterday, may suddenly lose popularity and fall in disgrace, what is again a matter of threshold: after a certain level of spreading, and perceived spreading, agents are led to modify their opinions, what probably reveals an interesting effect of shared representations about shared opinions on one's confidence level. Possibly, such a lowering confidence leads agents to be more eager to change opinions.