Simplex Compendium

At last it is time to take stock, at last to embark on our journey of classification! For this, we shall of course draw on the teachings gleaned in each part of this work.

There is a 6-plane continuum covering what is known (the semantic content of knowledge, 4 planes), and what is lived (the phaneral experience of life, 2 planes).
- Sophia (theoretical philosophy): first-order knowledge about things in the world.
- Phronesis (practical philosophy): second-order knowledge, applying sophia to domains from the episteme level.
- Episteme (theoretical science): first-order knowledge about our physico-mental universe.
- Techne (practical science): second-order knowledge, applying episteme to aims borne out of poiesis-level activities.
- Poiesis: human activity.
- Praxis: human experience.
There are 8 storeys from the simplest formal structures at the root of our world, to those able to represent all of our concepts.
- Meta-ontology: the concept of existence.
- Formal ontology: logical, ontological, mathematical foundations.
- Ontology: simple objects from the three realms (physical, mental, abstract).
- Mereology: complex objects from the three realms (physical, mental, abstract).
- Metaphysics: ordinary objects (susbtance, essence, constitution).
- Modality: possible worlds (nomically, metaphysically, logically).
- Semantics: reference, truth and meaning.
- Axiology: reason, norms and value.
There are 13 stages on the Scala Naturae that illuminate the structure of our actual concrete universe. To each we can associate an emerging concept, fundamental elements and a milieu.
- Spacetime: fundamental quanta in the Universe.
- Forces: elementary particles in the 4D Universe.
- Matter: atoms in the transparent Universe.
- Structure: elements in the cosmic foam.
- Systems: molecules in the galaxy.
- Globes: macromolecules in the planetary system.
- Environment: materials in the geosphere.
- Life: cells in the biosphere.
- Mind: animals in the psychosphere.
- Meaning: groups in the semiosphere.
- Language: communities in the koniosphere.
- Law: societies in the themiosphere.
- Culture: civilizations in the noosphere.

Among the six planes, two are about first-order knowledge: sophia and episteme. We have discussed the distinction between philosophy and science in general terms, but as this study reaches its end, we are able to show a clear delineation, and to substantiate it: I propose that the 8 storeys be associated to sophia, and the 13 stages to episteme.

As they’re piled onto each other, the 8 storeys create objects that are more and more reminescent of our "human, all too human" Umwelt: counterfactuals, meanings and norms are the constant denizens of our thoughts. Yet, objects from the foundational layers are still nothing but abstracta, grinded by the implacable algebraic machinery from their formal foundations. "Dog" is a fine example of ordinary object, due to its sheer familiarity; but ordinary objects would still be things in a world without dogs, without humans, without matter, without much at all. The only characterization of the concrete, physico-mental universe in the 8 storeys is that it exists: the "code" predicate \(\kappa\) that traces a line between concrete and abstract objects is axiomatically imposed and is the reason we can tell apart ontology from mathematics; the theory of physics, mind and value \(\mathfrak{ToPMV}\) is just posited to exist, without details. The facts unearthed by this "ultimate science", tied to the actual world in its empirical sources, but untethered from it in its scope, I call sophia.

In contrast, the 13 stages unfold when we let that theory’s mathematical structures bloom into the concrete world’s metaphysical, semantic and axiological structures. "Dog" is not in actual fact just a useful example of ordinary object that can be used to teach more general metaphysics to human minds. It is also a natural sortal whose existence is grounded not only in \(\mathfrak{ToPMV}\)’s existence, but in its most minute aspects. That ur-object, that one mathematical structure from the infinite sea of possibilities, flowers into more and more elaborate assemblages of physical elements. Such objects, endowed with complex physical properties, but still rough phenomenal ones, can ultimately exemplify macro-mental properties, and enable the plucking of "advanced" abstracta, the most remarkable of which can be called: les fleurs de notre monde. All of this, I propose, is the remit of episteme.

Very well. Is our grand classification then to be a disjointed series of three one-dimensional axes: planes, storeys and stages? Not so. Even a common-sense perspective should make apparent the correspondence between the storeys of abstract structures and the stages of physico-mental emergence. One could readily agree that the study of norms and values is more relevant to law-based societies and to cultures than to atoms or molecules; that semantics has more to do with sign-based social exchange or language-using communities than with planets or galaxies. The deeper locus of that intuition can be rigorously identified from our previous musings: the interaction of physical complexity with a singular phenomenal entity which we’ve called the qualium field gives rise to increasingly nimble mental content, capable of plucking more and more complex abstracta.

That simple worldview makes the storey/stage correspondence entirely natural:

Meta-ontology and formal ontology are foundational and beyond this correspondence.
Ontology pervades everything in the concrete universe, which by definition exists. Hence its correspondence starts at Stage 0 and extends to every stage beyond.
Mereology only intervenes in the universe when complex objects as such interact, emerging as a realisation of mereological union. Stage 2, starring nucleons as arguably the first stable form of composite objects, is the onset of the "building-blocks" construction of physical structures as opposed to the previous mode (loss of symmetry).
Metaphysics proper is centered around the concepts of substance, essence and constitution, leading to the crucial idea of ordinary object. Up to Stage 3, ordinary objects were hardly required to apprehend the world though, and could have stayed an unrealized abstract figment. However, galaxies on Stage 4, which we’ve presented as the first systems on a macro scale (as opposed to un-individuated stuff), and molecules, in many ways their micro-analog, are very much inaugurating the reign of the “ordinary” and of the natural kinds. With Stage 4, it can be said that metaphysics is taking over the universe from ontology.
Modality is the study of necessity and possibility. Self-reflective thinking about these concepts obviously does not occur before later stages on the Scala Naturae. But the ability of complex entities, even non-living, to recognize features of their environment and "behave" accordingly, is intimately linked to modality, which we could say accompanies the transition from the physical to the biological.
Semantics starts to manifest concretely with Stage 8 , when the mind emerges. With subjective minds come intentionality and mental content, which in Stage 9 come to be imprinted as physical occurrences and artifacts.
Axiology’s trace in the concrete universe is conspicuously evident in Stages 10 to 12. Reasons to act, feel or believe cannot be disentangled from the emergence of language and of social communities. The concept of norm is naturally evocative of law-based societies. And value, writ large, is the central tenet of any definition of culture.

The triangle of science

How to represent our classification then? The storey/stage correspondance on the one hand, the association of storeys and stages with the sophia and episteme planes on the other, paint a suggestive picture: two axes deployed onto parallel planes, with the horizontal dimension representing storeys and stages, and the vertical axis a progression across the planes of knowledge and experience.

Yet, that is not the final shape of the classification. The episteme plane, I argue, should not be an axis, or even a double axis (micro/mega dichotomy): it is best represented as a triangle. The reasons are intimately tied to a discussion of human sciences and in particular:

The holistic/individual dialectic.
The existence of three values (which in the sophia plane translates into three branches of axiology: ethics, epistemics and aesthetics).

Natural and Human sciences

It is fair to pause here and ask why we would be considering human sciences, which are disciplines, when the definition of episteme is much broader, covering all knowledge, which includes mundane propositions like "it was mostly sunny in London today". If the aim of disciplinary organization is to achieve a rigorous partitioning of knowledge, then is that knowledge bound to be no more than academic fare?

That simplistic concept of disciplines has nary a defender, though. Auguste Comte himself, known for his esprit de système, still insisted that distinct disciplines were simply clusters of knowledge that it was convenient for teachers, administrators, scientists, or other interested parties to use. Besides the nature of the partition itself, its granularity is in question, with little clarity how coarse- or fine-grained the ideal division should be.

My view of disciplines is neither purely realist nor nominalist. Outlining a set of "discipline-sounding" domains of knowledge like "biology" or "economics", is a very convenient way to describe clusters, or "poles of attraction" in the knowledge distribution. As we’ve highlighted in a previous section, the more mundane the knowledge, the more diffuse it is within this classification as well as on the episteme/techne axis itself. Humdrum knowledge from daily life is then "nowhere" in the classification, or to put it another way, it is in too many places, for lack of formal precision or for excessive context-dependence, like dust that has diluted in a liquid. "Scholarly" knowledge, meanwhile, can be handily localized (I’ll use that term in its common understanding, but it is of course not limited to knowledge produced in an academic setting), and is expected to either be entirely concentrated in the neighborhood of one disciplinary pole, or to be clearly decomposed like a vector (embodying interdisciplinarity, multidisciplinarity, transdisciplinarity, cross-disciplinarity and the likes). Although they are convenient clusters rather than fenced topoi, these disciplinary poles are not purely arbitrary conventions. Our universe harbors structures, formal, physical and mental, which ought to be reflected in knowledge distribution, and thus must influence the disciplines’ positions and their relations. As always, we aim to "carve nature at its joints"!

This all might seem like a distinction without a difference, when thinking about the natural sciences (or, to avoid discipline-laden terminology, the knowledge of natural facts). The double axis of stages seems like it should accommodate a perfectly matching double axis of discipline: to the universe, galaxies and planets would correspond cosmology, astronomy and geology; to particles, molecules and cells: elementary physics, chemistry and biology.

Yet we can see that using a "naive" set of disciplines, this doesn’t perfectly apply to further stages. The last stage’s “atom” on the micro axis is a single civilization, and its milieu on the macro axis is the noosphere that encompasses all civilizations (on Earth and beyond). But we would be hard-pressed to argue in favor of a single associated discipline, or even of a couple. The fundamental Science of Man is an elusive Grail that has been displaced by the concept of intermingling "human sciences".

The Unity of Science question

This discrepancy between the two ends of the scala naturae raises questions about the unity of knowledge, which is tied, as we have just seen, with the unity of science. This perennial topic has lots in common with metaphilosophical questions discussed in a much earlier section, which also pertained to the demarcation of natural sciences from the “humanities”. It should not come as a surprise that this study has ancient roots since unity and difference are at the core of all pre-Socratic enquiries, from metaphysics (Heraclitus’ flux and Parmenides’ substance) to natural philosophy (Empedocles’ elements and Democrites’ atoms). Plato asserted that knowledge was one, as did Aristotle, but the latter, in adding that different disciplines can distinguish between different causes, prepared the ground for the important distinction between ontological and epistemic unity: knowledge of different topics can be the same kind of thing, but acquired in different ways.

Medieval and Renaissance thought prolonged the unitary stance, mostly from the ontological perspective, drawing on monotheist tradition to see in the unity of knowledge a manifestation of some mathesis universalis underlying the unity of God’s creation. From Isidore of Seville to Ramon Llull, the sophistication of classifying schemes grew, culminating in Llull’s tree- and forest-like representations, but the tendency to a quasi-mystic monism was sometimes irresistible, devolving in the use of diagrams not unlike those from kabbalistic or esoteric traditions. Humanists like Petrus Ramus brought on a more sober approach, reviving the dichotomic simplicity of Porphyrian trees.

Grounds to support epistemic unity arose as the works of Albertus Magnus, Roger Bacon, Grosseteste, Zarabella and many more, slowly improving on Aristotelian views, were preparing the consecration of the modern scientific method. All these strands found a durable synthesis in the ideas of Francis Bacon on methodology itself, Galileo’s proclamation that God wrote the laws of nature in mathematical language, and Newton’s tremendous success in applying these apophtegms. Rationalist views, although they were in stark contrast with Baconian ones on the epistemic front, shared the confidence in epistemic unity. To Descartes, geometric reasoning was already, more than a language, the very paradigm for the unification of all knowledge. Later, Leibniz explored this idea in a much more profound way, imagining a "general science" based on an ideal language of purely algebraic symbols, a characteristica universalis that would make mathematical demonstration the purest source of knowledge.

Unity

Empiricism & utilitarianism

By that point, the ontological and epistemic unity within "natural philosophy", or what would become the natural sciences, was seldom in question. In awe of the successes of the scientific revolution, the leading thinkers of the time soon made plans to expand that blueprint to moral and political philosophy. Newton himself in his Opticks mused about how the very same analytical method he had been using, if perfected, could "enlarge the bounds of moral philosophy". This idea is what I would call "naturalism about the human sciences", a variation of which we have already encountered as "naturalism about philosophy": the stance that human sciences studying the mind, society, the arts, and other human phenomena, not only produce knowledge of the same nature as their natural brethren, they shall do so by adopting the same methodology.

David Hume, for one, saw Newton’s achievements as fertile ground for a proposed "science of man", upon which would ultimately depend logic, morals, literary criticism, politics, and even "natural religion". In practice, this meant that the mathematical methods favored by natural scientists should be used to subject human phenomena to quantification. The utilitarian movement, largely fueled by the work of self-proclaimed Hume followers, is a notable example of that evolution. Condorcet, who can be seen as the last scion of the French Enlightenment, had been influenced by the thought of atheist empiricists like Helvétius, of legal thinkers like Beccaria, and of Hume himself. Writing about the judicial system or electoral procedures, he not only used basic arithmetic reasoning to human topics, like Scottish empiricist Hutcheson had done in the ethical field, or Beccaria when thinking about legal penalties, but he also applied modern probabilistic thought, a far-reaching move for the yet unborn social sciences. This work was a precursor to utilitarian thought as developed by Jeremy Bentham. Positing that man’s behavior is governed by the pursuit of pleasure and the avoidance of pain, and that the ethics of legal or political decisions must be evaluated on that basis, Bentham opened the way to more sophisticated forms of utilatarian calculus as a "naturalist" basis for the human sciences.

Positivism

However the bulk of the utilitarians’ contribution was still methodological, introducing formal mathematical reasoning to tackle problems typically considered as the remit of philosophy. Another school of thought would more radically make the epistemic point that scientific knowledge about human affairs can and will be acquired through the same means as in earlier sciences. That expression of naturalist belief is called positivism. The doctrine of positive philosophy was developed by Auguste Comte in the 1830s, and as J.S. Mill noted, the French affinity for manichean intellectual debates soon turned it into a wedge issue. Since we’re talking here of the unity of knowledge, we can sum up the positivist articles of faith that relate to the development and classification of the sciences:

all sciences successively find themselves in three historical stages: the theological, the metaphysic and the positive. In the theological stage, humans find explanation for observable phenomena by way supernatural entities (gods, spirits,...). The metaphysical stage is an intermediary one where supernatural beings are replaced by abstract conceits which are articulated together and with the physical world through the exercise of reason. Lastly, the positive stage describes a "Newtonian" science that only relies on empirical observation coupled to the modern scientific method.
sciences can be ordered according to their "advancement" as they rely on each other in an ascending sequence: physics rely on the law of mathematics, chemistry relies on both physics and mathematics, biology relies on all three, etc.
as a corollary to these principles, sciences reach new stages in a pre-ordained chronological progression. For instance, biology could not reach the positive stage before chemistry does, since biology needs to make use of chemical laws (implicitly: a positive biology needs to apply positive chemical laws), before it can complete its real task of isolating the purely biological laws that are independent of any predecessor science.

The law of the three stages wasn’t just an isolated precept in Comte’s system, it was meant as exemplary of the brand new discipline of sociology that Comte viewed as the most "advanced", most complex science in his classification, coming after biology. The idea of "social physics" was not new indeed, but Comte’s ambitions broke new ground, since he hoped both to unify all positive studies of humankind within the study of the social realm (relegating the political and moral philosophies of his time to the theological and metaphysical stages of sociology’s development), and to crown it as the prospective "queen science", which would in turn explain and organize the way all of scientific knowledge is acquired.

I don’t aim to discuss the merits of Comte’s system here, but to explain its deep subsequent influence on all proponents of the unity-of-science idea. Indeed, he introduced two key ideas.

The chronological nature of the three stages introduces teleology (somewhat paradoxically) as a central tenet of positivism. It explains the state of affairs in Comte’s time (the positive stage of sociology having just been started...by himself), while predicting the inevitable outcome of the history of science (the completion of a fully positive sociology, after those of chemistry, astronomy and biology).
The dependency between disciplines according to Comte is a precursor to rigorous inter-level metaphysics that examines reduction, grounding, etc.

These have played a powerful role in the rise of a modern narrative which, as I’ve underlined elsewhere, lumps in positivism together with physicalism, reductionism and other related, but distinct positions. Comte makes it clear that every discipline’s role is to delineate the body of knowledge that cannot be deduced from its grounding disciplines (for instance laws of biology that don’t proceed from chemistry nor physics). As long as such residual, non-reducible knowledge exists, reductionism ought to be false. Physicalism also does not proceed from positivism, even though Comte himself, despite falling short of a full endorsement, appears very close to that stance. In his sequence of six basic sciences, he places biology directly before sociology, with no intermediary. J.S. Mill deplored Comte’s rejection of psychology as a future positive science, and expressed understandable dismay at Comte’s suggestion that phrenology (the study of scalp morphology’s relation to brain function and mental states) be a possible link. To be fair, Comte did not always reject psychology wholecloth, but he considered that human traits would be illuminated by the discoveries of sociology, and that physiology would set the bridge with the rest of nature. Although there is no clear physicalist credo there, Comte’s work seems of a piece with that idea.

All of this contributes to a convincing case of unity as continuity. If reductionism and physicalism, these modern stalwarts, are accepted as true, then any fact about humanity could be re-expressed by an omniscient being, or a powerful enough machine, as an incredibly complex assemblage of physical facts. Ontological unity is directly entailed, and though it is not clear that the way to acquire such knowledge should be the same in practice (which we may call "strong epistemic unity"), it would seem to be at least possible that an omniscient, all-powerful entity use the same scientific method, since they would only be proving physical facts and their connections (let’s call this "weak epistemic unity"). Comte’s insistence that sociological laws (and subsequent positivists’ yearning for "laws of History") certainly revealed a deep-seated belief in strong epistemic unity.

Now, this case is made incredibly tantalizing by the success of modern natural science, which has successfully established physicalism and reductionism in a vast natural realm covering four of Comte’s five sciences (setting mathematics aside): chemistry, astronomy, biology are all fully grounded in physics, and even reducible to it, albeit the exact form (eliminativist, "classic" or functional) is debatable. This generated a powerful undercurrent of "physics envy" amongst scientists, who promptly sought to emulate their colleague’s achievements by adopting the same methods in a frenzy of mathematization, and sociologists were certainly not immune.

As we mentioned, although Comte’s leanings were plausibly physicalist, his doctrine is not incompatible with some form of emergentism: Comtean sociology needs to rely on the laws of biology, but the discipline’s primary role is to study the social facts and laws that cannot be reduced to physiological findings. This is the origin of the kind of full-blooded methodological holism that Durkheim would later expound: "determining cause of a social fact should be sought among the social facts preceding it and not among the states of the individual consciousness."

Mill’s moral sciences

John Stuart Mill, whose correspondence with Comte nourished his enthusiasm for a law-based historical sociology, departed from positivism in some key points. His Logic of the moral sciences represented a much more thorough examination of the scientific method and its possible application to human topics.

First of all, Mill put Comte’s system on its head by installing psychology as the foundational science. Comte stubbornly rejected subjective psychology and the role of introspection to generate knowledge about the mind. Mental facts could be evidenced at the nexus of social and physiological studies, thus rendering psychology a derivative discipline. Mill, however, took up the brand of associationist psychology that his father James had worked on and surmised that the experimental method and minute observations typical of the natural sciences could be used to evidence the laws of Mind. Mill was cautious to steer clear of metaphysical speculation about the nature of mind vis-à-vis matter, and simply explained that causal chains between body and mind would belong to physiology while the causal links between mental facts would be the subject of psychology.

In Mill’s system, psychology was to serve as the basis for the derivative science of ethology, which studies human character, and in turn of a science of society. Contra Comte, Mill then insisted that social statics and dynamics could only be grounded in the rigorous study of human character or "human nature", which in turn would be derived from the elementary laws of mind developed by psychology.

Although this programme could never be developed by its designer, it proved to be influential and gives us a suggestive picture of modern scientific unity. Mill’s avoidance of metaphysics makes his views agnostic towards both reductionism and physicalism. The jump from biology to psychology is then crossing a potential rift from a metaphysical perspective, but doesn’t jeopardize the unity project: Mill believed that the natural sciences’ methods are best placed to help us understand the laws of mind and human nature. In giving these fields of study the impulsion to progress from their "backward state", Mill laid out the foundations of what he called the "moral sciences".

The term itself is far from innocent, a homage to Condorcet’s sciences morales et politiques, which on the one hand makes official a break with Comtean orthodoxy, and on the other sounds like a challenge to the traditional strand of British empiricism epitomized by Whewell, which sees a priori moral values as the ultimate ground for human action. J.S. Mill brings together his father’s associationist psychology (itself modeled after physics), the Benthamites’ utilitarianism, and a constructive version of Comte’s historical sociology to build his own worldview.

Mill’s logic would serve as the archetype of neo-positivist views about science, and its attitude would be endorsed by the gathering variously known as the Vienna circle, the "logical positivits" or "logical empiricists". We have seen already how members of the group took an intransigently deflationist view of philosophy. Otto Neurath, the main representative within the group of what was mostly called by then the social sciences firmly rejected any attempt at a demarcation between the natural sciences and others, even mocking the tendency of social scientists to focus on methodology, when complete unity with the physical sciences, their methods and their language should be the objective.

The ultimate consequence of positivism and its conceptual neighbors is a restriction of what is considered as "science", in the sense of a body of organized, systematically acquired knowledge pertaining to clearly identified entities. All positivist approaches have had to take stock of some disappointing attempts at forcing certain academic disciplines into their positive phase. The insistence on unfettered unity within science has then inevitably led to excluding large swathes of knowledge from that realm. Social sciences is now the term of the art for those moral sciences who have been admitted to the club, whilst the studies of art, culture, literature or law are set apart as humanities.

I’ve insisted at length that the domains of episteme and techne that I’m aiming to organize are a collection of all knowledge and not limited to formal disciplines, so how helpful is that long digression into scientific methodology and its unity?

The point is that disciplines (sciences, in this instance) are attraction poles in the knowledge continuum. Adopting the positivist stance would be to recognize that knowledge belonging to the "humanities" does not have any pole to coalesce around, and will be diluted into a morass on both the classification of sciences axis and the theoretical/practical axis (the term "liberal arts" as a frequent synonym for the humanities and its practical connotations is a good indicator of that commingling).

Division

Nomothetic vs idiographic methods

Mill’s work proved to be the element that would trigger the modern expression of the competing view, rejecting the unity of science, that was sometimes known as anti-naturalism, interpretivism, autonomism or anti-positivism.

Historiographically speaking, one should remember the context in which those views came to be developed in nineteenth-century Germany. The dominant force in academic philosophy at the time was still Hegelianism, whose idealism considered the natural sciences and their methods as inferior to those with psychological foundations. As Hegel viewed it, "the knowledge of Mind is the highest and hardest, just because it is the most ‘concrete’ of sciences", and the lack of a subjective, self-reflecting component in the Baconian scientific method confirmed its lower status as a use of reason.

The re-birth of earlier strands of French materialism as positivism, and the subsequent maturation of Millian thought that we’ve described, can of course be seen as a reaction against idealism, buoyed by the spectacular success of the natural sciences which rendered radical Hegelian conceits untenable. Post-Kantians and later neo-Kantians from the second half of the nineteenth century joined Mill in his criticism of the idealist school, but found in his work the seeds of a reaction against that reaction (ironically, a textbook case of Hegelian dialectic movement).

That attitude can be traced back to Helmholtz, who not only acknowledged the triumphs of the "physical sciences", but also observed that the opposition with the human sciences had become less and less marked over time. Nevertheless, he added that while the logical induction characteristic of the natural sciences had made headways in the human sciences, it must always be accompanied with artistic induction. Helmholtz may not have believed like Hegel that all sciences must be unified under the banner of Spirit, but he also did not subscribe to Mill’s proposed acculturation of all sciences to the natural mold, which to Mill was a consequence of using the "laws of psychology" as the central ground for all moral sciences. Helmholtz denied that nomological psychology was even possible, judging the web of influences that determines human character to be so extraordinarily intricate as to make it irreducible to any law. To make sense of the countless and "fuzzy" determinants of individual and collective behavior, Helmholtz though one must use a special "tact" or an "intuition", irreducible to universal precepts. Such is that "artistic" induction that seemingly combines the British empiricism which Mill personifies with the German romantic heritage.

Unity of science henceforth stayed a theme for heated debate within German academic circles in the post-Kantian filiation. In one camp, Wilhelm Windelband, from the "Baden school" of Neo-Kantian philosophy, introduced the distinction between nomothetic disciplines (whose efforts are focused on the discovery of laws and regularities) and idiographic ones (whose method is centered around individual cases). In the first category, we find physics, chemistry, astronomy... in short, the natural sciences. In the latter we have first and foremost history, as well as any science of society or study of culture. To Windelband, historians cannot work with generalities but have to contend with individual persons or events. Even more, they must paint a picture of specific people or specific times. "Therein", he said, "roots the affinity of the historical creation with the aesthetic creation and the affinity of the historical disciplines with the belles lettres." This dichotomy would find a later avatar in the more prosaic distinction between methodological holism and individualism. The focus in holism on abstract generalizations (social institutions, artistic movements, etc.) is hardly compatible with the idiographic approach, which would rather use such concepts as convenient shorthands for amoprhous collections of individual beings or events, whose structure emerges from the study of "atomic members" rather than from some immanent substance.

This position is then clearly one of epistemic disunity, with the line of demarcation being explicitly drawn from the perspective of the type of knowledge and how to acquire it. In the specific context of the time, Windelband’s aim was largely to set up a cordon sanitaire that would shield the humanities from the nomological psychology which Mill and others were confident would soon thrive. Indeed, a more traditional, ontological sort of demarcation would simply distinguish between the objects of different disciplines, and therefore between Natur and Geist. Psychology, being the study of the human mind, would naturally fall within the Geisteswissenschaften. But Windelband (unlike Hegelian idealists) does not consider the gulf between Natur and Geist to be fundamental, and thus does not see it as the hinge point for the distinction between different areas of knowledge. He also largely agreed with Mill that psychology could be searching for laws. Unlike Mill though, he refused to see that new and improved psychology as the stepping stone towards a genuinely scientific "ethology" (in the Millian sense) or sociology. The clear separation of the human sciences on the grounds that they are wholly idiographic (and the relegation of psychology from the most fundamental of humand sciences to the most derivative of the natural sciences) could then help keep reductionist temptations at bay.

Erklären vs Verstehen modes of knowing

Wilhelm Dilthey is generally not considered part of the Neo-Kantian group (a loose, post facto assemblage anyway), but was also part of Kant’s closest inheritor in the philosophical world of this time. Dilthey is often distinguished as the man who popularized the term Geisteswissenschaften which to this day, in the German-speaking world, denotes a group of disciplines that encompasses both the social sciences and the humanities. In fact, the term ironically originates with translations of Mill’s Logic. The English phrase moral sciences was first translated as Sozialwissenschaften, but the second edition replaced it with Geisteswissenschaften ("sciences of spirit"). Helmholtz was the first one to use that term in his own work, but it is Dilthey’s thoughtful advocacy that made it a staple in the philosophy of science, though he didn’t settle on that term right away.

Early on in his notes, he talks of Wissenschaften vom handelnden Menschen ("sciences of human action") and of Wissenschaften der praktischen Welt ("sciences of the practical world"). He also considered Moralische-politische Wissenschaften, a direct translation of Condorcet’s sciences morales et politiques which is also closer to Mill’s version. Interestingly, he also toyed with Humanwissenschaften, which would never become widespread in German-speaking culture, while the French equivalent of the Geisteswissenschaften would in fact turn out to be the sciences humaines.

Ultimately, Dilthey made his case that all these designations, as well as Gesellschaftswissenchaften ("sciences of society"), Kulturwissenschaften ("sciences of culture"), Geschichtlicheswissenschaften ("historical sciences"), "suffer from the same fault of being too narrow relative to their subject matter. And the name chosen here has at least the advantage of appropriately characterizing the central sphere of facts in terms of which the unity of these disciplines was actually perceived, their scope outlined, and their demarcation from the natural sciences established, no matter how imperfectly."

Regarding the demarcation itself, Dilthey found himself butting heads with Windelband and rejecting his methodological distinction. Armed with concrete examples, Dilthey showed that many natural sciences have idiographic elements, while human sciences can also adopt a nomothetic approach. Moreover, he argues that historical or philological data about individuals could only be meaningful in the context of regularities, adding that "what is most characteristic of the systematic human sciences is the connection of the general and the individual".

The distinction that Dilthey adopts instead is between modes of knowing, which he calls Erklären (explaining) and Verstehen (understanding). This distinction can thus be seen as questioning both epistemic and ontological unity.

The Verstehen concept can be traced back to Dilthey’s study of Schleiermacher’s hermeneutics. That tradition of interpretive analysis had played an important role in a variety of disciplines like philology, history, jurisprudence, religious studies, medicine... But Dilthey was enthused about the novelty of Schleiermacher’s ideas, and his treatment of interpretation as having universal validity rather than mere subjective import.

Besides a distinction between meaning and truth that prefigures modern semantics, Schleiermacher’s work is notable for the concept of the hermeneutic circle: a text, or any other meaning-laden medium is created by a human mind, but also interpreted by another. To the traditional linguistic approach to interpretation, a psychological side must then be adjoined. The goal of the interpreter is not to explicate a text (that would be linguist’s job), nor to apply it (like lawyers, doctors, writers, believers...), nor to translate it; it is to understand its meaning.

Schleiermacher also insisted on the universality of hermeneutics, which shouldn’t be limited to a specific medium, language, or era. From his intimate knowledge of Schleiermacher’s life and work, Dilthey derived two striking propositions:

The rules-guided approaches of the best interpreters have been preserved into "laws" with universal validity that have developed like the natural sciences. Understanding of inner life is the fundamental procedure that enables interpretation.
The universality of hermeneutical understanding is such that it can, and must, serve as a basis for the human sciences, which can then be seen as a generalization of the interpretive disciplines of yore.

That approach, Dilthey claimed, is the only one by which the Geisteswissenschaften can bloom, for it allows a synthesis between the positivists’ "generalizing rage" (Dilthey’s words), and the Romantic-influenced historical and philological schools that continued the hermeneutical tradition. Those schools have used the Verstehen approach to achieve "sympathetic immersion" into specific historical and cultural contexts and, in Dilthey’s opinion, have correctly surmised that spiritual life and social organization both should be approached historically, not the other way around.

However, their efforts are doomed, in modern times, by a failure to bridge "understanding" with psychological or epistemological facts. In the end, the followers of traditional hermeneutics, as innovative as they were in their idiographic analysis, were left defenseless against positivism for lack of a systematic explanatory method.

Speaking of the "Historical school", Dilthey sharply cut to the chase: "Historical vision and comparative procedures by themselves are incapable of establishing an autonomous system of the human sciences or of exerting any influence on life. When Comte, John Stuart Mill, and Buckle made a new attempt to solve the riddle of the historical world by borrowing principles and methods from the natural sciences, the Historical School could only protest ineffectually against their impoverished, superficial, but analytically refined results by appealing to a more vital and profound intuition which, however, it was unable either to develop or to ground."

Note that Dilthey scolded the humanities of his time not only for failing to develop a rigorous system of justification and a healthy link to epistemology, he also regretted they could not "influence life". Like so many of his fellow thinkers of human sciences, Dilthey saw their normative role as essential. He made explicit that the human sciences consisted of three classes of statements:

one class that describes the facts of empirical reality, which we could assimilate to the goal of idiographic disciplines.
one that identifies uniformities valid for parts of that reality ("theorems"), which sounds like nomothetic ambitions.
one that expresses evaluations and prescribes rules, which covers the normative stakes in the human sciences.

This shows that Dilthey was not denying, as Windelband had seemed to do, the human sciences’ capacity to be nomothetic. Further than that, he did not even deny them the use of the same explanatory procedures as the natural sciences (in short, Erklären). To him, that is a given, since the object of the Geisteswissenschaften, human beings, are not discarnate spirits, but "psychophysical units. That said, the combination of the hermeneutic circle (humans studying humans), and the entanglement with subjectivity, self-consciousness, meaning, values, actions, aims... in short, with the mental-axiological-normative segment of our ontology, must make for a different concept of justification, and thus for a different concept of knowledge (true belief with justification) altogether, which Verstehen epitomizes. As Max Weber, who adopted the concept of understanding put it, "man is an animal suspended in a web of significance of his own making".

Coda

Ultimately, I would argue that Dilthey’s position is then, if not one of full ontological pluralism about knowledge, at least one of ontological disunity about justification, which has its roots in the physical/mental distinction, and is itself a root of the partial methodological pluralism between the natural sciences and the human sciences (partial, because the methodologies are not orthogonal, but overlap: the methods from the natural-scientific method is a proper part of the human-scientific method).

Jürgen Habermas once deplored that “the once lively discussion initiated by Neo-Kantianism concerning the methodological distinctions between natural-scientific and social-scientific inquiry has been forgotten; the problems that gave rise to it no longer seem to be of contemporary relevance." Indeed, as I am prone to harp on, the indisputable successes of the natural sciences have led to an often implicit prevalence of a neo-positivist mindset that unjustly commingles materialism, reductionism and naturalism while expanding the remit of the natural sciences to psychology or sociology. At the same time, the interpretivist tradition goes on, unabashed, in its own faculties and its own circles. This separation, which Snow characterised as between "Two Cultures", and which is also reflected by the hundred-year old schism between "analytic" and "continental" philosophies. could benefit from a revival of neo-Kantianism or of its philosophical brethren, and in my view, Dilthey’s philosophy of science offers a robust scaffold for my classificatory effort.

Circling back to the shape of the episteme plane, this endorsement of partial scientific pluralism helps justify the choice of a triangle instead of an axis. We have pointed out that the positivist outlook could accommodate a "double axis" representation that would map onto the scala naturae: double because of the micro/mega distinction, an axis because of the linearity of the grounding chain and the conceptual "flattening" of possible disciplines at a given level of organization into a single coherent discipline (like Comte though that economics or politics would be derivative of sociology, or like Mill envisaged the psychology/ethology/sociology chain).

The cohabitation of different modes of justification (Erklären/Verstehen), of different types of statements (nomothetic/idiographic) and relatedly of different levels of analysis (holistic/individual), lastly the axiological disparity between good, truth and beauty, all prevent this type of compression within a level. There cannot be a single science studying "culture" or "civilization" because all these dichotomies combine into a fresco of structures that rely on very different epistemological bases and thus must crystallize into different disciplines. Those may seem porous, and they are, as shown by the rich cross-disciplinarity, but their hard cores are autonomous.

The tripartition

Six sciences of nature

Six sciences of society & history

Six sciences of mind & culture

One formal science

Another question that may arise is the place of mathematics amongst episteme fields. Its place among scientific topics has been a subject of some debate in the ninteenth century, with empiricist-minded practitioners heeding the direct use of mathematics in physical sciences and the related academic closeness between disciplines to make it a clear ’science’, albeit a peculiar one in many respects, while humanities writers would be more likely to bundle this decidedly non-experimental endeavour with philosophy, a position made all the more intellectually attractive by the rise of logicism in the foundation of mathematics. We will perform somewhat of a sidestep and remind the reader of our choice to make episteme akin to Wissenschaft rather than science in its most naturalistic sense, and consider this should allow us to elude controversy on the topic.