The Integration of Knowledge

Halfway between the amplitude of an essay and the rigor of a monograph, I have attempted to follow a plausible logical course in the exposition of the principal themes and arguments. Indeed, I have been guided by the conviction that the way in which the contents are ordered is itself a philosophical thesis.

Reflecting on the nature and limits of human knowledge represents one of the main tasks of philosophy. What is generally called “epistemology,” or “theory of knowledge” (Erkenntnistheorie in the German philosophical tradition), aims to address the problem of knowledge, that is, the question about how we acquire valid knowledge from sensory experience and rational thinking. Thus, an alternative formulation to this inquiry may be posed as follows: what features of the human mind (and, more specifically, of the way in which rational thinking works) make scientific knowledge possible in its most relevant manifestations, from logic, mathematics and physics to neuroscience and the social disciplines? Of the great challenges confronted by philosophical speculation, we shall probably not find one in which such profound and universal aspects converge. And, certainly, in the act of posing the question about the nature of knowledge, it is essential to examine concomitant problems, true touchstones for human reason, such as the nature of the world and the mind (sources from which we extract all possible knowledge), as well as, in more general terms, the nature of the human being, who undertakes the ambitious project of transcending the specific situation in which he finds himself, his spatiotemporal context, in such a way as to obtain knowledge of universal validity, suitable for revealing the most elusive and recondite details of the universe.

Thus, this work tries to systematize the basic conceptual tools of an ontology and an epistemology capable of adequately integrating knowledge, both in the natural sciences and in the disciplines that study the human world. Therefore, the following chapters can be seen as an attempt to explore the fundamental categories of reason in an effort to organize the results of the different branches of knowledge, inserting them in a broader framework.

From a philosophical perspective, it would be legitimate to argue that this project has the purpose of testifying to the continuity that exists between all levels of reality and knowledge. Without pretending in any way to impose philosophical apriorisms on scientific research (which does not need any metaphysical endorsement in order to expand the cognitive heritage of humanity; indeed, philosophy is not the arbiter of science), our method can be conceived from a formal point of view and from a material angle. In the first case, it consists in identifying those notions endowed with greater explanatory power for each area of knowledge and thought; in the second, it appears as a vast logical and causal mechanism, which aspires to look for explanatory itineraries capable of manifesting the links of continuity between the different areas of nature. To use an analogy inspired by integral calculus, it can be said that the project of integration of knowledge can be visualized as a limiting procedure that approximates the whole “area” of human knowledge by summing over a potentially infinite number of explanatory elements, which nonetheless converge into a finite, and usually small, set of fundamental concepts or categories of explanation. Through them it should be possible to establish meaningful relations that enable to form an articulated system of knowledge, where all concepts, extracted from a diverse array of disciplines, can nonetheless be understood in a unified manner. Thus, if in its most elementary historical formulation a mathematical integral was the conceptual tool that allowed for computing the area described by a function, to integrate knowledge would entail the identification of the area (or space) of concepts that form a unified conceptual system. Hence, by understanding the implications of the truly fundamental concepts of each discipline it should be possible to draw its entire explanatory domain, or the space of concepts of varying degrees of extension and intension that it covers. Then, the goal would be to understand the whole space of spaces, or system of conceptual systems.

So, we shall start from the mind (in its formalizing dimension) to return to the mind (in its condition of natural and historical object).

Regarding the material elements with which human knowledge is concerned, we have adopted an evolutionary and gradualist point of view. The goal is to link the simplest entities (the physical and chemical realm) with the most complex ones (the biological sphere and the human world, as a subset of the previous one), in such a way as to highlight the profound intertwining of all levels of nature.

This work is philosophical in nature, but our epoch questions the need for philosophical reflection. For many, the ancient metaphysical disquisitions played a precursory role towards the full development of rational thought, as initial gateways to the flourishing of a truly scientific worldview. However, according to this updated version of Comte’s law of three stages, at present the human mind could completely dispense with philosophical speculations, limiting itself to collecting empirical data and to harmonizing them in increasingly sophisticated theoretical models.

Indeed, no one can deny the intimate historical link between the natural sciences and philosophy. Not only did Newton include the term “philosophy” in the title of his opus magnum, Philosophiae Naturalis Principia Mathematica, of 1687, but also John Dalton, whose A new system of chemical philosophy, first published in 1809, paved the way for a revolution in chemical thinking through the elaboration of the modern atomic hypothesis. So did Jean-Baptiste Lamarck in his Philosophie zoologique (1809), which, beyond its biological mistakes, represents the first great landmark in applying evolutionary thought to natural history.

Nevertheless, the question refers not so much to such a distinguished history of interlacing premonitions and achievements between science and philosophy, as to the possible meaning of the philosophical enterprise for our days. For, what can philosophy mean today? What can it offer to the human pursuit of knowledge? Has it been entirely replaced by the children that it brought to life and initially nurtured, or does it still enjoy a certain degree of epistemological autonomy?

Thus, the very notion of a “philosophical problem” will raise many suspicions. Are not these supposed philosophical problems pseudo-questions, which can be approached from a logical and scientific point of view? What is the object of study of philosophy? Its hypothetical difficulties, do they not actually respond to linguistic confusions or to conceptually incorrect perspectives? How should one explain the small progress made in the path towards its resolution?

With the probable exception of ethical problems, where the need for philosophical reflection seems incontestable (since it has not yet been possible to reduce the traditional philosophical examination to a procedure similar to that used by the natural sciences), a great majority of questions so far investigated by philosophy tend to be susceptible of a logical and scientific analysis. Discussing the nature of space, time and the mind—to mention some illustrious examples—is no longer the exclusive domain of philosophy. Sciences like physics and neuroscience have contributed more to the clarification of these mysteries than the countless philosophical speculations devoted to understanding them.

In this sense, there are no exclusively philosophical problems, just as there is no method monopolized by philosophy. The convergence of creative rationality and empirical selection continues to be, as in the natural sciences, the quintessential strategy towards a reliable understanding of reality. Nevertheless, philosophy does not only aspire to understand, but to edify; it is therefore in understanding the meaning of scientific results for human life and the possibilities which they offer for improving the world where an important dimension of philosophical activity resides. It is, in short, in the totality of human experience where a genuinely philosophical interest shines that, far from being satisfied with contemplating, as separate parts, the different realms of world and history, pretends (naïvely or heroically) to provide an integrating synthesis.

Hence, and although I am fully aware of the deep and painful crisis that philosophy is experiencing, I believe that one of the most pressing responsibilities of what has traditionally been called “love of wisdom” is that of contributing to the synthesis of knowledge. Our knowledge is vast, but we do not always know how to integrate such an extraordinary wealth of knowledge; nor how to extract the appropriate consequences so as to build a more just and humane world. Indeed, I dare to say that this necessity of distilling the really essential elements from an overabundance of information, thereby promoting a spirit of synthesis in parallel to analytic progress, defines one of the major challenges of our age. And a philosophy capable of addressing this challenge will not only capture the spirit of its time, but it will also shape the spirit of the future, by setting a constant goal of exchanging and nurturing ideas and perspectives beyond academic disciplines and cultural traditions.

For the sake of simplicity, references to plausible manifestations of abstract reasoning and symbolic intelligence in other species of genus Homo shall not be the object of our discussion. Certainly, over the recent decades there has been a significant debate about the existence of these faculties (which seem for us, members of the human species, one of our most eminent characteristics) in Homo neanderthalensis. For example, some expressions of paintings in caves of Spain and Portugal might confirm the hypothesis that Homo sapiens has not been the only species with highly developed cognitive abilities, like the capacity for elaborating abstract representations. Only future research and the accumulation of new evidence will shed light on this intriguing—and indeed fascinating—possibility. Thus, the primary focus of this and the following sections will be rationality in its formal dimension, as it currently appears in a biological structure like the human brain or in a computational device. In any case, the analysis of the relationship with the way in which nature is organized shall also be present in this book. Moreover, it is important to remark that the terms “presupposition,” “assumption,” “postulate” and “premise” will be taken as synonyms for “initial tenets in a chain of reasoning.” The noun “axiom,” however, will be reserved for those initial truths that are universally taken as self-evident to a first approximation (even if a deeper analysis may show that they may be subject to a petitio principii, like Euclid’s fifth axiom).

At least to a first approximation, the optimization of a utility function—either in economic terms or in a purely logical sense—stands as a key element to any attempt at identifying a universal definition of rationality that may be valid for all domains of human activity.

Hence, rationality can be regarded as the general process of thought in which presuppositions, seen as primitive and irreducible tenets for reasoning, are taken to a minimal value. Or, in other words, rationality may be seen as a form of intellectual symmetry within a system of categories, understanding by symmetry an operation in which presuppositions are organized with the highest degree of efficiency, and no element is left to chance or arbitrariness. Thus, the number of presuppositions is drastically reduced with the goal of finding the optimal correspondence between the elements of information that need to be modeled and the minimal possible number of categories that must constitute the model.

Following this line of reasoning, an enlightening analogy can be unveiled between some basic propositions of thermodynamics and the process that we have just sketched. Inspired by this heuristic analogy, a further analytical inquiry into rationality can be proposed, from which some interesting results emerge.

If the basic thermodynamic identity discovered by Boltzmann establishes that the entropy (metaphorically, a measure of the number of “useless assumptions”) of a thermodynamic process is proportional to the number of possible states that the system can adopt, it may be argued that rationality implies the minimization of the entropy of “an intellectual system,” or the prevalence of one state—that in which the number of presuppositions is minimized—over the others.