Sunday, 7 September 2014

Herbart's Philosophy of Nature

This post summarizes Herbart's philosophy of nature. Herbart shared the project of a philosophical understanding of nature distinct though complementary in its aims and method from natural science with his contemporaries Schelling and Hegel. This is not now a common project. We draw for our account on Marcel Mauxion's La Métaphysique de Herbart (1894). The above image is of the Herbartdenkmal in Oldenburg around 1900.

Chapter 5
Philosophy of Nature

This chapter focuses on the concept of continuity, but corresponds closely enough to Hegel’s Objective Logic and the Philosophy of Nature prior to organic life to warrant a more general heading. 

The continuum 

The continuum (das Stetige, die Continuität) is a central concept that combines Herbart’s interest in mathematics and metaphysics. The continuum is union in separation and separation in union. In other words, parts are necessary to quantity, but if there were no union we would be dealing with discrete, not continuous quantity. Hegel places similar observations in his Logic. Continuity is also flow (Fluss). Thus calculus was called by Newton the “method of fluxions”.

In general, mathematics can be instructive for metaphysics. It shows for example that there are continuous series of different densities (1,2,3 as against 1,1.1, 1.2, ...3). Continua are thus not all of the same kind. The concept also contains contradictions. Thus a finite continuous quantity is also infinitely divisible. Yet continuity is given in experience, or at least representation, despite this contradictory nature.

Continuity pertains eminently to the forms of space and time, where we perceive parts, but not boundaries or divisions. In Herbart's view, the concept of continuity is constructed from this aspect of perception by psychic mechanisms (of which more later). These mechanisms are only brought to consciousness by metaphysical analysis. 

Intelligible space 

Intelligible space is spatiality such as would apply to simple beings (see argument of previous chapter: these are something like Leibnizian monads). Herbart presents his view twice, in Hauptpunkte der Metaphysik and Allgemeine Metaphysik. Here we focus on the first; both are rather arbitrary. 

The concept of place (Ort) is the first concept to emerge in the construction. Two elementary beings A and B may exist together (zusammen) whereby each will react to the other, or else they may exist apart. Both provide a place to the other, potential or actual in these cases. Herbart likens this to the idea of a mathematical point (for the beings are simple). As the simple beings do not change, they can serve as reference points.

We then may imagine lines composed of discrete points; then several such lines; then two-dimensional figures; then three-dimensional figures. This construction is developed further in relation to movement. At this point, our intelligible space approximates to sensible space. It has an aspect of continuity. However, it is independent of any idea of absolute space (as found in Newton, not in Leibniz). However, the construction is not independent of the intuition of sensible space to which it approximates. The presence of three dimensions and exclusion of a fourth seems to rely on sensibility for example. Mauxion wonders what Herbart might have made of Gauss’ concept of n-dimensional space. Mauxion thinks it might have driven his thought towards idealism. As it stands though, Herbart’s construction leads him to endorse geometry and thus in a realist direction.

However, Herbart sees contradictions in both sensible and intelligible space. (Note: this corresponds to Kant’s transcendental aesthetic and dialectic; Hegel on the other hand, seems to veer more towards the idea of intelligible space in his Logic and Philosophy of Nature). Thus the Kantian question of whether space is given externally or is internal to the mind is not relevant to this analysis of the content of the representation and the Kantian solution of transcendental idealism is not a solution to Herbart’s problem (or Hegel’s).

Herbart’s intelligible space is conceptual, not intuitive in content.


Matter can be explained on the basis of the ideas that we have seen developed above. The form of matter is space, as intelligibly constructed (see above) and its elements are simple beings. There are four possibilities for two simple beings: they may be:
  1.  at a rational distance from each other (at a determinate point)
  2.  at an irrational distance (between two determinate points)
  3.  interpenetrated completely
  4.  interpenetrated incompletely (with no common measure, as in incommensurable numbers)
The fourth case is relevant to matter. It is fictive because the simple beings do not have parts, but a necessary fiction in order to speak in spatial terms. Herbart thus imagines two simple beings as spheres of equal size. He likens the forces of attraction and repulsion to tendencies to complete interpenetration (owing to absence of parts) and mutual exclusion. In a similar spirit, he invent analogies for the material properties of cohesion and elasticity. Impenetrability he compares to light passing through glass, or chemical combination.

Mauxion regards these constructions as arbitrary. He explains the intellectual project Herbart is engaged in by comparison to Kant’s Metaphysics of Nature and Leibniz’s concept of phenomena bene fundata. These are other instances of the kind of analysis Herbart is attempting.

Movement, Speed and Time

Matter appears to us as subject to change. How then can we conceive motion in terms of our ontology of simple beings. Uniform motion is a product of space and time. Speed, thinks Herbart, is distance traversed in an instant (ein Jetzt) of time. He discusses divisibility. He concludes that 
“Time is the measure of change."
Die Zeit ist die Zahl des Wechsels.
"Chronos arithmos tes kineseos." (Aristotle).
Without change then, there is no time. Hence for the simple beings there is no time, though they remain present.

With time conceived as a series of instants or moments, difficulties arise for the concept of speed. Herbart speaks of space moving through the simple beings.

Herbart’s Realism

Herbart’s realism emerges from these analyses. In contrast, the real phenomena of Kant are just universally subjective. The phenomena for Herbart, do not depend on the subject, or the spectator. As John Stuart Mill spoke of “possibilities of sensation”, so in Herbart equivalent possibilities are claimed.

As in Kant, space and time are conditions of the unity of thought. Space allows independent beings to be conceived together – and this tends to realism. Time allows us to unite real phenomena. In general, there is a passage between the intelligible and sensible worlds in Herbart of a realistic cast. Events in one can be translated into the concepts of the other. For example, sensations are acts of conservation of the subject, not properties of matter. The world of physics is dark and silent; metaphysics carries its analysis beyond the objective appearances of physics.

The simple beings are penetrable, but this is not to be conceived spatially, as the filling of interstices. Only the images of simple beings have form and divisibility. Herbart is realist as regards the simple beings; he thinks matter has a real foundation, but he is idealist as regards space, time and movement, which are pure forms generated by a psychic mechanism. We know relations, but not things in themselves. This is clear when we relate him to Kant (Mauxion does this in another volume).

Evaluation of Herbart’s Natural Philosophy

Herbart develops natural philosophy in ingenious but arbitrary treatments of light, heat, electricity, magnetism, organic life and action at a distance, all in ways dependent on the natural science of his day. Mauxion summarizes:
“In general, the solutions given to particular problems, always more or less closely related to the contemporary state of positive knowledge, only ever present a mediocre interest when the time comes to overthrow the scientific hypotheses on which they are painstakingly built, and from which they momentarily borrow an illusory probability.” (142)
One might say the same for much of Hegel’s philosophy of nature.
The 20th century proved to be a winter for the philosophy of nature.

Other Problems

Some other questions arise from the concepts contained in our idea of nature or derived from our experience of it. Is the world finite in space, eternal or with a beginning in time? Unlike Kant, Herbart treats these questions as distinct in nature. Space has no outer limits, but there is a finite number of simple beings (to suppose otherwise he considers contradictory). As for time though, this is infinite, time being the measure of motion and the idea of an absolute beginning of motion being problematic.

Is matter infinitely divisible? No – for the number of simple beings is finite and these are its elements.

Are there free causes? Is there a first cause of the world? Herbart’s account of causality dictates the answer No. Causality is a relation and perturbation between simple beings.

As regards Hegel’s philosophy of nature, the above description indicates that the intellectual atmosphere in which Hegel lived looked relatively benignly on “metaphysical” analyses in the Leibnizian tradition. However, sceptical arguments were also represented in the literature of the day, both directly and through Kant. The mathematical interest in Hegel’s Logic is also not an isolated production, but one shared by both Kant and Herbart.