0.00 — Introduction: Language and Science
1.00 — Science in Classical Antiquity
2.00 — Science in Medieval Christendom
3.00 — Science in Secular Modernity
4.00 — The Future of Parsimony in Scientific Rigor
5.00 — Epilogue: Macrohistorical Periodizations of Science
0.00 Introduction: Language and Science
0.01 Three ages of science correspond to three ages of language, as the use and the ability of language to express distinct aspects of human experience has developed through a range of media.
0.02 The three ages of language, according to the present author, are the poetic, the prosodic, and the formulaic.
0.03 The earliest efflorescence of language was in poetry, including the poetry of mythology. Next, language entered its prosodic stage, which eventually culminated in the prose novel. Lastly, language approached the formulaic in the full formalization of rigorous logic and mathematics.
0.04 Even theoretical works began in poetry, with Parmenides, the beautifully poetic dialogues of Plato, and Lucretius’ rendering of Epicurus’ philosophy in poetry. Then came the age of the prose treatise, and treatises of some considerable length were penned, not least the Summas of medieval Christendom. Now, the dominant paradigm is to be able to formalize scientific ideas, the better to approximate theoretical rigor. This perhaps began in science, as the scientific revolution coincided with the expression of the laws of nature in mathematical form.
0.05 Science — or, before science, the scientific impulse — must be expressed in language — science is an essential element of human collective learning, and as such it serves as a record of human experience. The means by which the scientific record is preserved is language. Thus the development of science parallels the development of language.
1.00 Science in Classical Antiquity
1.01 Before mathematicization, science was given its exposition in natural language; science, like history, was a narrative.
1.011 Even before science was conducted in narrative prose, science has its earliest beginnings in the philosophical poetry of Parmenides and the poetic prose of Plato. This was the poetic Age of Science.
1.02 Even early mathematics was given its exposition in natural language. Euclidean axiomatics is implemented in natural language and supplemented by illustrations.
1.03 From the point of view of empirical science, mathematics is an aid to the exposition of science that would be expressed at greater length and somewhat less elegance in natural language. It is the world itself from which elegance flows, and not from the contingent form given the thought.
1.04 From the point of view of mathematics, the various special sciences are special cases of mathematics — mathematics to which additional, empirical assumptions have been superadded above and beyond the non-empirical assumptions required for mathematics when mathematics is not employed in the exposition of the sciences.
1.05 What are the non-empirical assumptions required for the development of mathematics? The assumption of mathematics is that we should assume nothing. But we must begin somewhere, so we cut the Gordian knot, positing axioms, and beyond these we assume nothing.
1.06 Mathematics, as the simplest science incorporating the fewest presuppositions, is the science that is entailed by the principle of parsimony.
1.07 That is to say, as logic was once thought to be a consequence of the principles of identity, non-contradiction, and excluded middle (as was formerly said of it), then mathematics is a consequence of the principle of parsimony.
1.08 In classical antiquity mathematics was the model of demonstrative science. This was science in the Platonic-Aristotelian sense: apodictic, certain, eternal, and unchanging. Even the empirically-minded Aristotle was also the Father of Logic, and Aristotle’s Posterior Analytics, which gives his philosophy of science and mathematics, is as categorical as any Platonic Form.
1.09 In the Platonic tradition, time was unreal; the conception of an eternal order underlying the fleeting shadows of this world would not allow for the reality of time. Plato called time the moving image of eternity. In this poetically conceived universe, given its mature scientific formulation in the works of Aristotle, Ptolemy, and Euclid, the convergence upon consensus meant a recognized regime of truth, and a recognized regime of truth meant institutional ossification that was the mirror of the eternal, unchanging order of this Platonic-Aristotelian synthesis.
1.10 The synthesis of Platonic and Aristotelian thought that emerged in Late Antiquity and which dominated the thought the Middle Ages has been the object of intense scholarly study, and famous monographs like The Great Chain of Being and The Elizabethan World Picture have detailed the features of this comprehensive and rigidly hierarchical conception of nature. The Breakup of this edifice in recounted in Koyre’s equally notable study, From the Closed World to the Infinite Universe.
2.00 Science in Medieval Christendom
2.01 Medieval science was a function of ancient science re-conceived under the aspect of institutionalized Christianity as the central fact of institutional and intellectual life. This is an intellectual life of derivative truths; the certainties of classical antiquity were repeated verbatim with a Christian gloss.
2.011 The language of medieval science was the summa, a vast treatise encyclopedic in conception and almost anti-poetic in execution. This was a prosodic science, but not yet having achieved (or even maintaining as an ideal) a seamless narrative exposition, as is to be expected from this transitional form of science from a transitional age between classical antiquity and secular modernity.
2.02 Already in late classical antiquity philosophical thought turned largely sterile and primarily became a matter of reconciling and commenting upon the ancient authorities, of whom Aristotle, Euclid, and Ptolemy were the central sources of the science of antiquity.
2.03 Medieval theologians who were scientists only secondarily constructed a backward-looking science on the presumption that truth was to be found in its pristine state only at its origins, in the past. To find the fons et origo was to find the undisputed truth.
2.04 Even as an inaccessible ideal of past truth was institutionalized as an aspiration, the actual conception of the past was naïve to the point of absurdity. Science suffered because history was occluded by an eschatologically-conceived cosmology in which evidence was secondary to the certainty and impassibility prized by the ancient sources of thought.
2.05 It was not until after medieval thought had already fully matured and entered into a period of dissolution in which the ideal it set before itself was more distant than ever that this mode of thought produced profound and transformative ideas that would, in the long term, culminate in the emergence of modern science.
2.06 Decadence was the conditio sine qua non of medieval theoretical innovation. It was, in Huizinga’s memorable phrase, the autumn of the middle ages that produced the intellectual axialization of the era.
2.07 Ockham’s Razor, formulated midway between Platonic antiquity and scientific modernity, is the point of transition between medievalism and modernity, between the old and the new, between looking backward and looking forward, between principled stagnation and unthinking iconoclasm.
2.08 It was only at this late point in time that the theoretical principles of Greek science were given explicit expression and formulated as a principle. The idea had already been employed in practice, but the idea of the idea was lacking. In other words, formal reflexivity was lacking. This is the first intimation of the formulaic mode of thought, of rigor for its own sake.
2.09 This idea of the idea of formal reason Ockham supplied, and in so formulating the principle of parsimony, superseded Euclidean axiomatics in its own sphere of formal consciousness of assumptions. Now there was a principled imperative to minimize assumptions, and not merely to state them explicitly at the outset.
2.10 It is the progressively more rigorous implementation of principle of parsimony that eventually yields the minimalist scientific reason of later ages. The spirit of parsimony continued to be expressed in the logical empiricism of the twentieth century, and today in post-positivist modes of thought.
2.11 After Ockham, skepticism in the service of fideism reached a level of radical extrapolation (again, a consequence of logical rigor, like minimalist scientific reason) that was not to be understood again until long after the gains of the scientific revolution were consolidated in social and economic form by the industrial revolution. Here the idealistic superstructure long preceded the formation of the economic base.
3.00 Science in Secular Modernity
3.01 In contemporary modernity, mathematics has once again become the model of science, but it is mathematics unlike that of antiquity. The categorical assumptions of the Platonic-Aristotelian synthesis have evaporated, dissipated by the very Ockhamist rigor intended to secure the ossified and institutionalized experience originally given shape in classical antiquity, and then, through descent with modification, transformed into something unrecognizable under medieval Christendom.
3.02 The organic assumptions of agrarian-ecclesiastical civilization, tied so closely to the soil by the manorial system, gave way to mechanistic assumptions that almost seemed purposefully formed in order to contradict that vision of the world that preceded it.
3.03 The mechanistic conception of nature and the Newtonian clockwork universe might be understood as having its origins in the Aristotelian conception of nature, though mechanism only truly came of age with the scientific revolution (coming after the lapse of Aristotelian cosmology had already taken place), which sought to explain all natural phenomena according to fixed and universal laws of nature.
3.04 Even as socioeconomic institutions experienced a gradual and continuous transformation that makes it difficult to identify the exact point of origin of modernity, the intellectual discontinuity was nearly complete, so that formerly medieval peoples suddenly found themselves to be modern men living in a medieval world that they were compelled to violently reform in order to bring the world into conformity with their conception of themselves. This is humanism.
3.05 The mathematicization of the sciences in the wake of the scientific revolution has transformed the sciences from prose into formulae, though even in the time of Darwin, science could still be given an exposition in prose narrative form. Evolutionary biology was not to be given mathematical form until the twentieth century, but this is arguably due to the radical nature of the Darwinian conception of nature.
3.06 In the modern tradition, sciences are marked by their recognition of the temporality of all levels of nature. Darwin made this possible; Darwin was the prophet of time. It was Darwin, himself indebted to geologists such as Hutton and Lyell, who made time respectable in science and banished essentialism without abandoning realism.
3.07 The Platonic-Aristotelian synthesis is now no longer merely abandoned, but overturned, utterly defeated, and science still today is engaged in the root-and-branch reconceptualization of the world sub specie temporalis. The eternal and unchanging universe of Plato has been replaced by a changing world continually in the process of self-transcendence.
3.071 It was only in the second half of the twentieth century that this temporal understanding of the world came to the Earth sciences, and the understanding of Earth as static and unchanging was replaced by an understanding of Earth in terms of a natural history punctuated by dramatic and even violent events.
3.072 Even more recently, the emergence of mineral evolution has transformed formerly physics-oriented minerology into an historic science that asks when and how minerals first formed. One should not underestimate the profundity of this paradigm shift from producing catalogs of properties to placing the development of minerals into a comprehensive conception of an evolving universe.
3.08 To be objective now in the age of empirical science is no longer to be certain and apoditic, but to be implicated in the restless and relentless change that has come to define the world. If objectivity is understood to be mundane impassibility, the objective is necessarily insulated from (or cut off from) the world, but empirical confirmation constitutes the negation of independence from the world.
3.09 The transcendence we know today has nothing whatsoever to do with neoplatonic freeing of the soul from a fallen world, launched in splendid isolation into the realm of the mind. Transcendence today is change that remains within the world, transforming the world from the inside until the world is no longer what it was, but remains the descendant of a past that no longer exists. Transcendence is now constrained by the world, and is the passage from one immanent state to another immanent state.
3.10 In an inscrutable parallelism, the development of the scientific impulse over time has also been utterly transformed from within, so that the latter realization of science that we know today is only with difficulty identified with the origins of science in the distant past. Science itself, then, mirrors what we understand to be the structure of the world.
4.00 The Future of Parsimony in Scientific Rigor
4.01 The progressive rigorization of science from antiquity to the present day has frequently taken the form of a progressively rigorous application of the principle of parsimony. But this begs a question. Why should we prefer a simpler theory to a more complex theory? This is the same as to ask why the principle parsimony should have any role to play in the future of scientific thought.
4.02 Given two (or more) empirically equivalent theories with the same observational predictions, is there any reason to prefer the simpler theory other than its theoretical elegance? Is parsimony merely an aesthetic requirement of a theory?
4.021 Does parsimony confer any predictive power, i.e., does it confer a privileged relationship to empirical empirical truth, or is parsimony merely an artifact of our perceptions that says nothing about the world beyond what it says about our taste? Is there, or can there be, any objective principle of theory choice?
4.03 Questions parallel to those above regarding simplicity can be formulated regarding the mathematization of a scientific theory. Why should we prefer a theory formulated in mathematical terms to a non-mathematicized theory?
4.031 Why should mathematics have such a central role to play in scientific theory? Does mathematics have any predictive power, or is it simply an artifact of our cognition that says nothing about the world beyond what it says about our brains?
4.04 There is a relationship between simplicity (i.e., parsimony) and mathematics: mathematics is, in a sense, the simplest science.
4.05 Mathematics is the simplest science because it begins with the least empirical content, which is none at all. All the sciences presuppose mathematics, except mathematics, which only need presuppose itself, and nothing at all about the world. Mathematics is the science of nothingness.
4.06 Why should it be significant that there is a relationship between simplicity and mathematics, and what relevance has this relationship to the practice of science? Simplicity and mathematics both serve to exhibit the symmetries present in a theory that is formulated with an eye to simplicity and to mathematical exposition.
4.07 If symmetries are naturally present in nature, then any method that exhibits symmetry will better serve as a method for the exposition of nature, i.e., will make for a better science.
4.08 If nature is symmetrical, and simplicity and mathematics both are able to exhibit symmetries in their formulations, then simplicity and mathematics are both intrinsically suited for the exposition of nature. Thus, again, science mirrors what we understand to be the structure of the world.
4.09 Nature need not even always be symmetrical; any method that exhibits symmetries will be disproportionately effective merely if nature is symmetrical more often than it is asymmetrical. The efficacy is stochastically dependable.
5.00 Epilogue: Macrohistorical Periodizations of Science
5.01 In the above I have divided the three ages of science according to the classic division of western historiography into ancient, medieval, and modern. This makes sense as an exposition of how science developed in western civilization, but a more radical perspective would be a tripartite breakdown of three ages of science according to the partition of human history into hunter-gatherer nomadism, agrarian-ecclesiastical civilization, and industrial-technological civilization.
5.02 In such a schematic treatment of the development of science, hunter-gatherer nomadism could be little more than a mute predecessor of the scientific thought that would, after a fashion, emerge in the settled, literate civilizations of the agrarian-ecclesiastical paradigm, and the scientific revolution itself would not occur until late in agrarian-ecclesiastical civilization. It is only with the slow maturation of science after the scientific revolution that science eventually comes into its own as the source of the STEM cycle that lies at the foundation of industrial-technological civilization.
5.03 The macrohistorical division of human history here outlined is itself but a fragment of big history. The periodizations suggested by big history do not always coincide with those periodizations that stand out in human history, and the periodizations of the whole of human history do not always coincide with the periodizations that strike us at a more parochial historico-temporal order of magnitude.
5.04 There is a precedent for nested periodizations, each highlighting distinct features of history, in the geological reckoning of time, which must take into account the whole of geology and biology (and now, in the anthropocene, humanity also) that shapes the Earth.
5.05 The most comprehensive division of geological time, that of aeons, divides the whole of terrestrial time into four aeons, the Hadean, the Archean, the Proterozoic, and the Phanerozoic. This schema, while quadripartite, may also be taken as a simple before and after periodization, as the latter division between the Proterozoic and the Phanerozoic marks the division between the uncomplicated life that inhabited Earth for billions of years prior to the Cambrian explosion, reaching back into the Archean, and all complex life after the Cambrian explosion.
5.051 An even more comprehensive division of time is that formulated by Fred Adams and Greg Laughlin, whose cosmological periodization distinguishes the Primodial Era, the Stelliferous Era, the Degenerate Era, the Black Hole Era, and the Dark Era. The whole of our vast geological time scale of Earth and its development is but a moment within the Stelliferous Era, constituting another nested periodization.
5.06 The whole of the Phanerozoic, following the Cambrian explosion, can be decomposed into three periodizations that reflect the dominant life of the planet, punctuated by mass extinctions that cleared most ecological niches for new species: the Paleozoic, the Mesozoic, and the Cenozoic — the ancient, medieval, and modern eras of terrestrial life. Just so, once we have a macrohistorical decomposition of the whole of history, further decompositions can be made within each periodization.
5.07 Geologists today are considering the possibility of naming a new period in geological time, and that is, of course, the Anthropocene — a geological age defined by the impact that human beings, as intelligent and purposive agents, have had, are having, and will continue to have upon our homeworld.
5.071 The christening of the Anthropocene provides a conceptual framework with which we can begin to project the geological scale of time into the future, and this begins the extension of a scientific conception of time to a truly comprehensive conception of the world — the kind of understanding that was once the province of metaphysics in pre-modern history.
5.08 The systematic and rigorous application of science to the world on ever-larger scales expands the scope and scale of science. The enlargement of science may yet converge upon a formal historiography that is the mathematicized expression of conceptions of time emerging from big history and the refinement and extrapolation of geological time scales. Eventually this may also be reflexively applied to civilization.
5.09 The ultimate inversion of the Platonic conception of the world — the denial of the reality of time in the interest of mathematical certainty — will be, at the same time, be the ultimate affirmation of Plato’s conception of the world, with a mathematization of time more rigorous than any conceived in classical antiquity. Until this happens, the scientific revolution remains incomplete. When the scientific revolution is complete, the way will be clear for a fourth age of science.