Avijit Lahiri

The critical brain hypothesis is briefly introduced, and a number of implications regarding the functioning of the brain and the human mind are pointed out. After a brief overview of how the mind emerges from an evolving assembly of neuronal networks of various size-groups in the brain, we include a summary outline of a nontechnical nature relating to a few aspects of dynamical systems, based on which we introduce the idea of critical states, again avoiding technical discourse. Criticality in complex systems involves a close proximity between regular dynamics with an admixture of low dimensional chaos, on the one hand, and relatively high dimensional chaos on the other. The brain is supposed to operate in a dynamic state close to criticality, referred to as one 'at the edge of chaos', where it is driven toward such a state in a process of self-organized complexity, which makes possible an adaptive evolution of the neuronal networks, in response to an uncertain and continuously evolving environment. This process of self-organized complexity culminating in a near-critical state is referred to as self-organized criticality, in which there occasionally takes place a crossing through the critical state with an avalanche-like burst of neuronal activity, when the system return to the near-critical state. Correspondingly, the human mind also operates ‘at the edge of chaos’, which results in a phenomenal robustness and flexibility of the mind, both making it a highly adaptive entity in a constantly changing environment. In particular, the near-criticality of the mind is likely to be of enormous significance in inferential processes like creativity where there occurs an unconstrained exploration of the conceptual space, generating links between remote concepts, thereby resulting in a significant change in our view of the world. Criticality endows our mind with a certain universality in the manner in which we respond to significant changes in our environment---the hall-mark of such near-universal response being a characteristic slowness referred to as critical slowing down. This contrasts with the way we routinely engage in myriads of mental activities in our interactions with the world that are marked by enormous variability between individuals and a much shorter characteristic time of response. Near-criticality of the brain is of great relevance in the setting up of large scale neuronal networks by means of spontaneous neuronal activity---in particular, the default mode network, supposed to be the link between the self and non-self aspects of the mind, is likely to be a result of the spontaneous near-critical dynamics of the brain. Finally, the critical brain hypothesis is supposed to shed much light on the way the mind occasionally loses its coherence, with the resulting emergence of aberrant mental behavior. It needs to be mentioned, however, that the critical brain hypothesis is not a firmly entrenched theoretical idea in neuropsychology and is rooted more in the physical sciences than in neuroscience. However, it is certainly suggestive of fruitful insights that can illuminate large areas of neuropsychology in days to come.

The idea of truth is not a simple one. While truth can be understood in precise terms in the world of mathematics, it appears to be a highly entangled concept when considered in the context of complex systems in the real world. A complex system, interacting with other complex systems in its environment, can be looked at from various perspectives, with reference to which truth appears to have multiple faces. The principle of excluded middle is assumed to hold in the mathematical world, though it engenders a number of foundational issues. But the dichotomous view of the excluded middle, is too simplistic for the real world, in consequence of which the idea of truth becomes an irreducibly complex one. Our perception and interpretation of the world is based on the explicit approach of reason and, at the same time, on the implicit approach of affect, where the two are almost mystically intertwined in the making of inferences and decisions that are supposed to lead us to truth. It is the inscrutable interaction between the two that makes the idea of truth so elusive. The question as to whether truth is absolute or relative has two aspects to it---the one relating to whether it is dependent on the mindset of individuals and the other to whether it depends on the context of our inquiry into reality. Generally speaking, truth always depends on the context though, ideally, it has to be socially shared, i.e., independent of idiosyncrasies of individuals. Here, however, one has to draw a sharp distinction between truths of science and those pertaining to our social life. While truths arrived at in scientific investigations are generally socially accepted ones, most truths relating to our social interactions are affect-laden and imprinted with the mindset of individuals, because these are based on how people perceive one another's mind. The mind is certainly a part of reality, but the way the myriads of human interactions emerge incessantly in that reality is elusive and mostly indeterminate. Only some of those lend themselves to reasoned perception and interpretation, based on which we seek out truth in our social existence on rare occasions when it gains social acceptance. In the midst of all this complexity shrouding the idea of truth, a steadfast adherence to the path of truth is more a moral principle---one of paramount value in our social life---than a reasoned act that can be defended on grounds of social acceptance. What is more, the ultimate standard of truth resides in our own selves and is of enormous value in our human existence.

Ideas and insights of Darwin, Mendel, and their contemporaries culminated in the Modern Synthesis (MS) that can be said to have caused a great upheaval in the minds of men. However, the extra-scientific role that the MS was set to play against the viewpoint of creationism turned it into a frozen dogma. It did not recognize the inherent complexity of the process of biological evolution, which is essentially linked with that of organismic development. The subsequent emergence of the viewpoint of 'evo-devo', that led to what has been referred to as an extended evolutionary synthesis (EES) was initially not recognized as a viable extension of the MS, mainly because it did not yet have a molecular basis. A vastly extended scenario was, however, opened up on the basis of ideas relating to gene regulation and networks of regulatory elements distributed throughout the genome, where these play an essential role in development. Notably, the genome as a whole, with its networks of regulatory elements, is heritable and gets altered across generations by means of mutations, just like the genes within its folds. This leads to the fundamental idea that biological evolution is a consequence of the modification of the developmental process across generations, where the entire genome passes through a complex progression of structural and functional alterations on a time scale large compared to that of organismic development. The resulting theory of regulatory evolution (TRE) is truly a remarkable extension of the MS. In this essay we examine the emergence of the TRE from within the womb of the MS in the light of a number of fundamental aspects of the evolutionary dynamics of complex systems.

The vast number of neurons in the brain are ceaselessly engaged in spontaneously generated activity in virtue of interactions between those. It is in the background of this intrinsic activity that the brain responds to signals from the environment and from endogenous signals received by way of active mental processes. This spontaneous activity persists in the `resting state' and is modulated by evoked signals resulting from task-induced activity. The two together generate an ongoing process of self-organization in the brain whereby dynamic excitation patterns are set up and correlated with one another in neuronal aggregates of diverse population size in an intricately nested hierarchy. These correlated patterns constitute distributed models of reality, based on which the brain generates expectations, plans, and predictions relating to the dynamically evolving world that we all are embedded in. The process of neuronal self-organization provides the basis for the emergence of a structured mind exhibiting an exquisite functional complexity. Generally speaking, mental (and, in particular, psychological) processes are based on large scale (`macroscopic') neuronal networks, while microscopic and mesoscopic neuronal populations constitute the `substratum' of the mind, where elementary and tiny bits of experience are represented so as to act as atomic ingredients in the more complex processing of compositely constituted information involved in mental activities. Processes in the microscopic and mesoscopic neuronal aggregates occur on relatively short spatial and temporal scales while those in macroscopic networks are slower and distributed across brain regions. The large scale networks operate near the `edge of instability', which means that these networks, taken together, form a system close to criticality---this is what makes the mind possessed of its remarkable fluidity. The neuronal aggregates themselves are in a constant state of flux, with groups of neurons constantly entering and leaving larger aggregates, and with neurons being simultaneously operative in the functioning of more than one aggregates at a time. In the backdrop of this enormous complexity, the operations of the mind constitute a complementary description of the brain-mind complex to those of the neuronal populations---neither of the two is reducible to the other. In other words, the functioning of the mind is not determinable in terms of the activities of the neuronal populations. The `substratum of the mind', made up of microscopic and mesoscopic populations of neurons, in addition to providing the hinterland in which latent operations supporting all mental processes are enacted, is involved more directly with representations of elementary concepts, with distributed memory (in a broad sense), and with heuristics of an elementary and atomic nature that help us in making vast numbers of `decisions' of a similarly elementary nature.

In this essay we focus on our vast web of beliefs that serves us as a rough and ready map of reality, generated more to give us comfort and confidence in an intimidating world than to be accurate. Maps of reality can never be accurate in any ultimate sense since reality itself is a convoluted entity that can only be accessed in never- ending layers. Our repertoire of beliefs, generated compulsively in the mind, span a huge spectrum in respect of ties to affect and emotions on the one hand and of their credibility in depicting reality on the other. The interaction between our affect-based psychological needs, our need for having a sound comprehension of reality, and the infinitely tangled reality itself, leads to the generation of a large diversity of types of beliefs, where these get revised under the impact of reality by overcoming the restrain- ing effect of emotions in diverse ways and over diverse time scales—interestingly, the ‘reality’ includes the complex repertoire of affect and emotions itself that may, in cer- tain cases, generate the impact for our beliefs to change. Beliefs represented by small clusters in our belief network (see below) are commonly prone to frequent revision in a more or less random manner, though there are beliefs acquired in early life that are intransigent to change because of overriding ties to emotions. Beliefs represented by larger clusters are comparatively durable, and their revision has a systematic aspect to it because of a greater role of evidence-based factors—however,the evidence may, once again, be tied with emotions and beliefs oriented away from reason. Finally, there are prepotent beliefs that are resistant to change even over a lifetime. Often, these beliefs get revised only if we engage with our own selves, looking at conflicting forces within ourselves. In this context, we refer to narratives that are self-reinforcing and exercise almost a mesmerizing influence on us. In all this, there is a dual role of ‘rationality’ that needs being attended to in describing and explaining belief revision—rationality is not exclusively based on evidence and reason, but includes the implicit operation of affect and emotions too.

This monograph focuses on two major themes of current interest---those of complexity and emergence. Neither of the two concepts is, in the very nature of things, precisely defined or easily comprehended. Complexity is all around us while the sciences often analyze entities and events by making simplifications. But the fault lines in the latter get exposed over larger spans of space and time. Complexity entails emergence that involves discontinuity and novelty in the evolution of complex systems, based on the appearance of distinctive spatial and temporal structures. Underlying an occurrence of emergence is an instability involving the transition from one stable regime to another, where distinct space-time scales acquire relevance across the transition. The structures on the two sides of the transition are characterized by distinct sets of state variables where, on one side of the transition, collective variables make their appearance. Complexity and emergence are viewed in this book in the context of the Kantian noumenal-phenomenal divide. The noumenal reality is the repository of all the complexity that there is, while the phenomenal reality emerges from the noumenal in the process of our perception, interpretation, and inference. The noumenal exists in itself as a self-determined whole, and reveals itself to us in fragmentary patches as skewed projections that we assemble to form our phenomenal world that keeps on emerging ceaselessly. Our own biological evolution and the evolution of our phenomenal world occurs in a mutually consistent process, that can be referred to as co-evolution. We seek regularities in the phenomenal world by means of our scientific theories which are often successful, but that success is fragile as, over larger spans of space and time, anomalies make their appearance, giving a lie to the simplicity and regularity previously presumed to have been unearthed. Simplicity, regularity, and harmony are only fleetingly located in the phenomenal world by means of our theories as these keep on being revised endlessly and often radically, thereby generating a mosaic of theories that becomes ever more complex, indicating a pervasive complexity of the noumenal world from which the phenomenal emerges by way of strictly limited projections. The foundational metaphysics on which this book is based tells us that reality is fundamentally complex, while tiny islands of simplicity, regularity, and harmony are embedded in it in isolated space-time domains.

[A revised and updated version of an earlier article 'Understanding Creativity: Affect Decision and Inference' (unpublished), posted at PhilArchive in 2021.] This book looks at the creative process in the human mind. Creativity involves a major restructuring of the conceptual space where a sustained inferential process eventually links remote conceptual domains, thereby opening up the possibility of a large number of new correlations between remote concepts by a cascading process. Since the process of inductive inference depends crucially on decisions at critical junctures of the inferential chain, it becomes necessary to examine the basic mechanism underlying the making of decisions. In the framework that we attempt to build up for the understanding of scientific creativity, this role of decision making in the inferential process assumes central relevance. Referring to the process of inferential exploration of the conceptual space that generates the possibility of correlations being established between remote conceptual domains, such exploration is guided and steered at every stage by the affect system, While the affect system plays a guiding role in the exploration of the conceptual space, the process of exploration itself consists of the establishment of correlations between concepts by means of beliefs and heuristics, the self-linked ones among the latter having a special role in making possible the inferential journey along alternative routes whenever the shared rules of inference become inadequate. Representing the conceptual space in the form of a complex network, the overall process can be likened to one of self-organised criticality commonly observed in the dynamical evolution of complex systems. An instance of self-organised criticality is found in the avalanche set up in a slowly growing sand-pile.

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal world is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold.

This book looks at the affective-cognitive roots of how the human mind inquires into the workings of nature and, more generally, how the mind confronts reality. Reality is an infinitely complex system, in virtue of which the mind can comprehend it only in bits and pieces, by making up interpretations of the myriads of signals received from the world by way of integrating those with information stored from the past. This constitutes a piecemeal interpretation by which we assemble our phenomenal reality. In perceiving the complex world and responding to it, the mind invokes the logic of affect and the logic of reason, the former mostly innate and implicit, and the latter generated consciously in explicit terms with reference to mind-independent relations between entities in nature. It is a strange combination of affect and reason that enables us to make decisions and inferences, --- the latter mostly of the inductive type --- thereby making possible the development of theories. Theories are our tool-kits for explaining and predicting phenomena, guiding us along in our journey in life. Theories, however, are defeasible, and need to be constantly updated, at times even radically. In this, the self and the soul are of enormous relevance. The former is the affect-based psychological engine driving all our mental processes, while the latter is the capacity of the conscious mind to examine and reconstruct the self by modulating repressed conflicts. If the soul remains inoperative, all our theories become misdirected and a rot spreads inexorably all around us.

In this essay we collect and put together a number of ideas relevant to the under- standing of the phenomenon of creativity, confining our considerations mostly to the domain of cognitive psychology while we will, on a few occasions, hint at neuropsy- chological underpinnings as well. In this, we will mostly focus on creativity in science, since creativity in other domains of human endeavor have common links with scientific creativity while differing in numerous other specific respects. We begin by briefly introducing a few basic notions relating to cognition, among which the notion of ‘concepts’ is of basic relevance. The myriads of concepts lodged in our mind constitute a ‘conceptual space’ of an enormously complex structure, where con- cepts are correlated by beliefs that are themselves made up of concepts and are as- sociated with emotions. The conceptual space, moreover, is perpetually in a state of dynamic evolution that is once again of a complex nature. A major component of the dynamic evolution is made up of incessant acts of inference, where an inference occurs essentially by means of a succession of correlations among concepts set up with beliefs and heuristics, the latter being beliefs of a special kind, namely, ones relatively free of emotional associations and possessed of a relatively greater degree of justification. Beliefs, along with heuristics, have been described as the ‘mind’s software’, and con- stitute important cognitive components of the self-linked psychological resources of an individual. The self is the psychological engine driving all our mental and physical activity, and is in a state of ceaseless dynamics resulting from one’s most intimate ex- periences of the world accumulating in the course of one’s journey through life. Many of our psychological resources are of a dual character, having both a self-linked and a shared character, the latter being held in common with larger groups of people and imbibed from cultural inputs. We focus on the privately held self-linked beliefs of an individual, since these are presumably of central relevance in making possible inductive inferences – ones in which there arises a fundamental need of adopting a choice or making a decision. Beliefs, decisions, and inferences, all have the common link to the self of an individual and, in this, are fundamentally analogous to free will, where all of these have an aspect of non-determinism inherent in them. Creativity involves a major restructuring of the conceptual space where a sustained inferential process eventually links remote conceptual domains, thereby opening up the possibility of a large number of new correlations between remote concepts by a cascading process. Since the process of inductive inference depends crucially on de- cisions at critical junctures of the inferential chain, it becomes necessary to examine the basic mechanism underlying the making of decisions. In the framework that we attempt to build up for the understanding of scientific creativity, this role of decision making in the inferential process assumes central relevance. With this background in place, we briefly sketch the affect theory of decisions. Affect is an innate system of response to perceptual inputs received either from the exter- nal world or from the internal physiological and psychological environment whereby a positive or negative valence gets associated with a perceptual input. Almost every sit- uation faced by an individual, even one experienced tacitly, i.e., without overt aware-ness, elicits an affective response from him, carrying a positive or negative valence that underlies all sorts of decision making, including ones carried out unconsciously in inferential processes. Referring to the process of inferential exploration of the conceptual space that gener- ates the possibility of correlations being established between remote conceptual do- mains, such exploration is guided and steered at every stage by the affect system, analogous to the way a complex computer program proceeds through junctures where the program ascertains whether specified conditions are met with by way of generating appropriate numerical values – for instance, the program takes different routes, depending on whether some particular numerical value turns out to be positive or negative. The valence generated by the affect system in the process of adoption of a choice plays a similar role which therefore is of crucial relevance in inferential processes, especially in the exploration of the conceptual space where remote domains need to be linked up – the affect system produces a response along a single value dimension, resembling a number with a sign and a magnitude. While the affect system plays a guiding role in the exploration of the conceptual space, the process of exploration itself consists of the establishment of correlations between concepts by means of beliefs and heuristics, the self-linked ones among the latter having a special role in making possible the inferential journey along alternative routes whenever the shared rules of inference become inadequate. A successful access to a remote conceptual domain, necessary for the creative solution of a standing problem or anomaly – one that could not be solved within the limited domain hitherto accessed – requires a phase of relatively slow cumulative search and then, at some stage, a rapid cascading process when a solution is in sight. Representing the conceptual space in the form of a complex network, the overall process can be likened to one of self-organized criticality commonly observed in the dynamical evolution of complex systems. In order that inferential access to remote domains may actually be possible, it is necessary that restrictions on the exploration process – necessary for setting the context in ordinary instances of inductive inference – be relaxed and a relatively free exploration in a larger conceptual terrain be made possible. This is achieved by the mind going into the default mode, where external constraints – ones imposed by shared beliefs and modes of exploration – are made inoperative. While explaining all these various aspects of the creative process, we underline the supremely important role that analogy plays in it. Broadly speaking, analogy is in the nature of a heuristic, establishing correlations between concepts. However, analo- gies are very special in that these are particularly effective in establishing correlations among remote concepts, since analogy works without regard to the contiguity of the concepts in the conceptual space. In establishing links between concepts, analogies have the power to light up entire terrains in the conceptual space when a rapid cas- cading of fresh correlations becomes possible. The creative process occurs within the mind of a single individual or of a few closely collaborating individuals, but is then continued by an entire epistemic community, eventually resulting in a conceptual revolution. Such conceptual revolutions make pos- sible the radical revision of scientific theories whereby the scope of an extant theory is broadened and a new theoretical framework makes its appearance. The emerging theory is characterized by a certain degree of incommensurability when compared with the earlier one – a feature that may appear strange at first sight. But incommen- surability does not mean incompatibility and the apparently contrary features of the relation between the successive theories may be traced to the multi-layered structureof the conceptual space where concepts are correlated not by means of single links but by multiple ones, thereby generating multiple layers of correlation, among which some are retained and some created afresh in a conceptual restructuring. We conclude with the observation that creativity occurs on all scales. Analogous to correlations being set up across domains in the conceptual space and new domains being generated, processes with similar features can occur within the confines of a domain where a new layer of inferential links may be generated, connecting up sub- domains. In this context, insight can be looked upon as an instance of creativity within the confines of a domain of a relatively limited extent.

We introduce the notion of complexity, first at an intuitive level and then in relatively more concrete terms, explaining the various characteristic features of complex systems with examples. There exists a vast literature on complexity, and our exposition is intended to be an elementary introduction, meant for a broad audience. Briefly, a complex system is one whose description involves a hierarchy of levels, where each level is made of a large number of components interacting among themselves. The time evolution of such a system is of a complex nature, depending on the interactions among subsystems in the next level below the one under consideration and, at the same time, conditioned by the level above, where the latter sets the context for the evolution. Generally speaking, the interactions among the constituents of the various levels lead to a dynamics characterized by numerous characteristic scales, each level having its own set of scales. What is more, a level commonly exhibits ‘emergent properties’ that cannot be derived from considerations relating to its component systems taken in isolation or to those in a different contextual setting. In the dynamic evolution of some particular level, there occurs a self-organized emergence of a higher level and the process is repeated at still higher levels. The interaction and self-organization of the components of a complex system follow the principle commonly expressed by saying that the ‘whole is different from the sum of the parts’. In the case of systems whose behavior can be expressed mathematically in terms of differential equations this means that the interactions are nonlinear in nature. While all of the above features are not universally exhibited by complex systems, these are nevertheless indicative of a broad commonness relative to which individual systems can be described and analyzed. There exist measures of complexity which, once again, are not of universal applicability, being more heuristic than exact. The present state of knowledge and understanding of complex systems is itself an emerging one. Still, a large number of results on various systems can be related to their complex character, making complexity an immensely fertile concept in the study of natural, biological, and social phenomena. All this puts a very definite limitation on the complete description of a complex system as a whole since such a system can be precisely described only contextually, relative to some particular level, where emergent properties rule out an exact description of more than one levels within a common framework. We discuss the implications of these observations in the context of our conception of the so-called noumenal reality that has a mind-independent existence and is perceived by us in the form of the phenomenal reality. The latter is derived from the former by means of our perceptions and interpretations, and our efforts at sorting out and making sense of the bewildering complexity of reality takes the form of incessant processes of inference that lead to theories. Strictly speaking, theories apply to models that are constructed as idealized versions of parts of reality, within which inferences and abstractions can be carried out meaningfully, enabling us to construct the theories. There exists a correspondence between the phenomenal and the noumenal realities in terms of events and their correlations, where these are experienced as the complex behavior of systems or entities of various descriptions. The infinite diversity of behavior of systems in the phenomenal world are explained within specified contexts by theories. The latter are constructs generated in our ceaseless attempts at interpreting the world, and the question arises as to whether these are reflections of `laws of nature' residing in the noumenal world. This is a fundamental concern of scientific realism, within the fold of which there exists a trend towards the assumption that theories express truths about the noumenal reality. We examine this assumption (referred to as a ‘point of view’ in the present essay) closely and indicate that an alternative point of view is also consistent within the broad framework of scientific realism. This is the view that theories are domain-specific and contextual, and that these are arrived at by independent processes of inference and abstractions in the various domains of experience. Theories in contiguous domains of experience dovetail and interpenetrate with one another, and bear the responsibility of correctly explaining our observations within these domains. With accumulating experience, theories get revised and the network of our theories of the world acquires a complex structure, exhibiting a complex evolution. There exists a tendency within the fold of scientific realism of interpreting this complex evolution in rather simple terms, where one assumes (this, again, is a point of view) that theories tend more and more closely to truths about Nature and, what is more, progress towards an all-embracing ‘ultimate theory’ -- a foundational one in respect of all our inquiries into nature. We examine this point of view closely and outline the alternative view -- one broadly consistent with scientific realism -- that there is no ‘ultimate’ law of nature, that theories do not correspond to truths inherent in reality, and that successive revisions in theory do not lead monotonically to some ultimate truth. Instead, the theories generated in succession are incommensurate with each other, testifying to the fact that a theory gives us a perspective view of some part of reality, arrived at contextually. Instead of resembling a monotonically converging series successive theories are analogous to asymptotic series. Before we summarize all the above considerations, we briefly address the issue of the complexity of the {\it human mind} -- one as pervasive as the complexity of Nature at large. The complexity of the mind is related to the complexity of the underlying neuronal organization in the brain, which operates within a larger biological context, its activities being modulated by other physiological systems, notably the one involving a host of chemical messengers. The mind, with no materiality of its own, is nevertheless emergent from the activity of interacting neuronal assemblies in the brain. As in the case of reality at large, there can be no ultimate theory of the mind, from which one can explain and predict the entire spectrum of human behavior, which is an infinitely rich and diverse one.

This essay presents a point of view for looking at `free will', with the purpose of interpreting where exactly the freedom lies. For, freedom is what we mean by it. It compares the exercise of free will with the making of inferences, which usually is predominantly inductive in nature. The making of inference and the exercise of free will, both draw upon psychological resources that define our ‘selves’. I examine the constitution of the self of an individual, especially the involvement of personal beliefs, personal memories, affects, emotions, and the hugely important psychological value-system, all of which distinguish the self of one individual from that of another. The foundational position that adopted in this essay is that all psychological processes are correlated with corresponding ones involving large scale neural aggregates in the brain, communicating with one another through wavelike modes of excitation and de-excitation. Of central relevance is the value-network around which the affect system is organized, the latter, in turn, being the axis around which is assembled the self, with all its emotional correlates. The self is a complex system. I include a brief outline of what complexity consists of. In reality all systems are complex, for complexity is ubiquitous, and certain parts of nature appear to us to be ‘simple’ only in certain specific contexts. It is in this background that the issue of determinism is viewed in this essay. Instead of looking at determinism as a grand principle entrenched in nature independent of our interpretation of it, I look at our ability to explain and to predict events and phenomena around us, which is made possible by the existence of causal links running in a complex course that set up correlations between diverse parts of nature, in this way putting the stamp of necessity on these events. However, the complexity of systems limits our ability to explain and to predict to within certain horizons defined by contexts. Our ability to explain and predict in matters relating to acts of free will is similarly limited by the operations of the self that remain hidden from our own awareness. The aspects of necessity and determinism appear to us in the form of reason and rationality that explain and predict only within a limited horizon, while the rest depends on the complex operation of self-linked psychological resources, where the latter appear as contingent in the context of the exercise of free will. The hallmark of complex systems is the existence of amplifying factors that operate as destabilizing ones, along with inhibiting or stabilizing factors as well that generally limit the destabilizing influences to local occurrences, while preserving the global integrity of a system. This complex interplay of destabilizing and stabilizing influences lead to the possibility of an enormous number of distinct modes of behavior that appear as emergent phenomena in complex systems. Looking at the particular case of the self of an individual that guide her actions and thoughts, it is the operation of our emotions, built around the psychological value-system, that provide for the amplifying and inhibiting factors mentioned above. The operation of these self-linked factors stamps our actions and thoughts as contingent ones that do not fit with our concepts of reason and rationality. And this is what provides the basis of our idea of free will. Free will is not ‘free’ in virtue of exemption from causal links running through all our self-based processes - ones that remain hidden from our awareness, but is free of what is perceived to be ‘reason and rationality’ based on knowledge and the common pool of beliefs and principles associated with a shared world-view. When we speak of the choice involved in an act of exercise of free will what we actually refer to is the commonly observed fact that various different individuals of a similar disposition respond differently when placed under similar circumstances. In other words, free will is ‘free’ precisely because it is not subject to constraints of a commonly accepted and shared set of principles, beliefs, and values. While it is possible that, in an exercise of free will, the self-linked psychological resources are brought into action when a number of alternatives are presented to the self by the operation of the ingredients of a commonly shared world-view, it seems likely that, that set of alternatives is not of primary relevance in the final response that the mind produces, since the latter is primarily a product of the operation of the self-based psychological resources. What is of greater relevance here is the operation of emotion-driven processes, guided by the psychological value-system based on the activity of the so-called reward-punishment network in the brain. These processes lead the individual to a response that appears to be free from the shackles of determinism precisely because their mechanisms, which are hidden from us, do not conform to commonly accepted and shared rules and principles. In contrast, inductive inference is a process that is based on the ‘cognitive face’ of self, where the self-based psychological resources play a supportive role to the commonly shared world-view of an individual. There is never any freedom from the all-pervading causal links representing correlations among all objects, entities, and events in nature. In the midst of all this, the closest thing to freedom that we can have in our life comes with self-examination and self-improvement. The possibility of self-examination appears in the form of specific conjunctions between our complex self-processes and the ceaseless changes of scenario in our external world. This actually makes the emergent phenomenon of self-examination a matter of chance, but one that keeps on appearing again and again in our life. Once realized, self examination creates possibilities that would not be there in the absence of it, and these possibilities include the enhancement of further self-enrichment and further diversity in the exercise of our free will.

This monograph is an in-depth and engaging discourse on the deeply cognitive roots of human scientific quest. The process of making scientific inferences is continuous with the day-to-day inferential activity of individuals, and is predominantly inductive in nature. Inductive inference, which is fallible, exploratory, and open-ended, is of essential relevance in our incessant efforts at making sense of a complex and uncertain world around us, and covers a vast range of cognitive activities, among which scientific exploration constitutes the pinnacle. Inductive inference has a personal aspect to it, being rooted in the cognitive unconscious of individuals, which has recently been found to be of paramount importance in a wide range of complex cognitive processes. One other major aspect of the process of inference making, including the making of scientific inferences, is the role of a vast web of beliefs lodged in the human mind, as also of a huge repertoire of heuristics, that constitute an important component of ‘unconscious intelligence’. Finally, human cognitive activity is dependent in a large measure on emotions and affects, that operate mostly at an unconscious level. Of special importance in scientific inferential activity is the process of hypothesis making, which is examined in this book, along with the above aspects of inductive inference, at considerable depth. The book focuses on the inadequacy of the viewpoint of naive realism in understanding the contextual nature of scientific theories, where a cumulative progress towards an ultimate truth about Nature appears to be too simplistic a generalization. It poses a critique to the commonly perceived image of science which is seen as the last word in logic and objectivity, the latter in the double sense of being independent of individual psychological propensities and, at the same time, approaching a correct understanding of the workings of a mind-independent nature. Adopting the naturalist point of view, it examines the essential tension between the cognitive endeavours of individuals and scientific communities, immersed in belief systems and cultures, on the one hand, and the engagement with a mind-independent reality on the other. In the end, science emerges as an interpretation of nature, which is perceived by us only contextually, as successively emerging cross-sections of limited scope and extent. Successive waves of theory building in science appear as episodic and kaleidoscopic changes in perspective as certain in-built borders are crossed, rather than as a cumulative progress towards some ultimate truth. While written in an informal and conversational style, the book raises a number of deep and intriguing questions located at the interface of cognitive psychology and philosophy of science, meant for both the general lay reader and the specialist. Of particular interest is the way it explores the role of belief (aided by emotions and affects) in making the process of inductive inference possible since belief is a subtle though all-pervasive cognitive factor not adequately investigated in the current literature.

This article, written in Bengali ('Gonit Dorshon' means `philosophy of mathematics' ), briefly reviews a few of the major points of view toward mathematics and the world of mathematical entities, and interprets the philosophy of mathematics as an interaction between these. The existence of these different points of view is indicative that mathematics, in spite of being of universal validity, can nevertheless accommodate alternatives. In particular, I review the alternative viewpoints of Platonism and Intuitionism and present the case that in spite of their great differences, they are not mutually exclusive - that both can be accommodated within the infinite edifice of mathematics. This, in turn, is argued to be consistent with the viewpoint of Category Theory that holds the promise of an entirely new interpretation of the world of mathematics and the relation of that world to the world of our concepts and ideas: mathematics is a human enterprise and mathematical logic is a reflection of how our ideas and concepts are formed and combined with one another. I venture that this, perhaps, is the view of mathematics that Ludwig Wittgenstein would espouse.