DATASUL: DIVIDIR PARA MULTIPLICAR

―The true criterion regarding the objects of the senses is the connection between phenomena, that is to say the linking up of what occurs in

different places and times, and in the experience of different men, who are themselves very important phenomena to one another.‖

Gottfried Wilhelm Leibniz New Essays

Challenged by the speedy transformation of the natural space surrounding them (through the rapidly increasing industrialization of the European mainland, the ensuing transportation

revolution, and the rise of the urban landscape, to only name a few factors that altered the geographical surface of the world), enlightenment thinkers were forced to reevaluate the philosophical foundations of spatial theories. The ensuing debate that was fought with equal vigor by proponents of the philosophical and the mathematical camp, focused primarily on Aristotle‘s twofold theory of nature. Aristotle argued that there are two possible positions on the subject. The first concept posits that nature includes more than matter, in which case there must be a first philosophy of nature. The purpose of this first philosophy of nature then is to deal with

the basic substance that exists in nature besides, or before, matter, while matter itself is examined

by physics. The second concept Aristotle proposes argues that nature only includes matter and consequently physics becomes first philosophy (Garnett 9).

While Aristotle‘s philosophy had dominated the intellectual inquiry into matters of space and nature for centuries, a new generation of enlightenment thinkers perceived the classical model as increasingly unfit to sufficiently explain a world transformed by ground-breaking discoveries such as the laws of planetary motion (Kepler 1609), the infinitesimal calculus (Leibniz, Newton 1675), and the law of universal gravitation (Newton 1687). These scientific innovations,

especially in the context of the radical social and economic changes outlined above, certainly challenged established understandings of the physical universe in general and the

conceptualization of human and natural space in particular. This process of the scientification of early modern society, however, gradually pervaded philosophical discourse and successfully established the scientific method as a valid metaphysical methodology. Specifically, René Descartes‘ publication of The Discourse on Method in 1637 announced the discontent with

traditional philosophy among a growing number of scientifically minded scholars. For Descartes, philosophy and theology, in their present form, had become ineffective because they have ―been studied for many centuries by the most outstanding minds without having produced anything which is not in dispute and consequently doubtful and uncertain‖ (8). Subsequently, Descartes proposed a combination of scientific empiricism and philosophical intuition aiming at

establishing the mathematical rigor and certainty of algebra and geometry at the center of any philosophical inquiry. Although Descartes‘ work did not trigger a univocal scientific revolution of philosophy, it most certainly inspired the development of European rationalism and

Descartes for his lack of scientific rigidity, rationalists such as Spinoza and Leibniz further developed the Cartesian dualism of the mental and physical world.

Among the second generation of rationalists, the German mathematician and philosopher Gottfried Wilhelm Leibniz (1646-1716), along with his English contemporary Isaac Newton, stands out as one of the most influential and innovative guardians of Descartes‘ legacy. While Leibniz‘s philosophy by no means marks a categorical continuation of Descartes‘ Discourse

(many of Leibniz‘s theories, in fact, directly critique Descartes‘ dualistic model), Leibniz is certainly influenced by Descartes‘ concept of space. Specifically, Leibniz was intrigued by the principle of Cartesian extension as it laid the foundation for Leibniz concept of sensed space.

In his Meditations Concerning First Philosophy (1641), Descartes discussed how questioning

all things material and immaterial will lead ―our minds to become independent of the senses‖ (71). This step, he believed was essential to clear the scientific mind from false opinion and uncertain assumptions that had been ―acquired from the senses or by means of the senses‖ (Descartes 76).

Over the course of the Meditations, Descartes develops this initial differentiation between the

mind and the senses into a dualistic system that differentiates two faculties of knowledge: the intellect and the imagination. The intellect, according to Descartes, is concerned with entirely abstract entities, such as reason, doubt, or ideas, and rejects assumptions derived from the senses, as they are mere representations. Further, the intellect considers simple natures, the smallest building block for knowledge that can only be understood directly and intuitively by the intellect. The imagination, on the other hand, projects images of the corporeal world, such as ―the shape of extended things, their quantity, or size and number, and also the place they are, the time that measures their duration, and so forth‖ (Descartes 78).

While Descartes considered the intellect the superior faculty, he also recognized that there is an inherent interdependence between the two. The intellect is capable to interrogate concepts or ideas symbolically represented by the imagination, and thereby relate to the concrete

manifestations offered (faulty or not) by the senses. It is, however, incapable of representing the abstract entities it considers and therefore dependent on the imagination to convert these general, abstract articles into ―specific magnitudes‖ (110). Therefore, as Stephen Gaukroger nicely summarized, the intellect depends on the imagination ―because the intellect by itself has no relation to the world at all. Entities conceived in the intellect are indeterminate. The imagination is required to render them determinate‖ (Gaukroger 110). In his Rules for the Direction on the Mind (written in 1628-29, published in 1701), Descartes further explained the relationship

between the intellect and the imagination by highlighting the principle of extension. Descartes explains:

By ―extension‖ we understand everything which has length, breadth, and depth, without inquiring whether it is really a body or only a space, nor does it seem to need more explanation, since there is nothing more easily perceived by our imagination […] The abstract entities, therefore, such as extension, are never formed in the imagination apart from something which is extended, whatever the intellect believes about the truth of the matter. And because we are to do nothing from this point on without the aid of the imagination, it is useful to distinguish carefully the ideas by which the meaning of the several words are represented to our intellect. For this reason we propose for

consideration these three ways of speaking: ―extension occupies space,‖ ―body has extension,‖ and extension is not body. (Descartes 214-215)

Descartes‘ concept of extension refers to the imaginative perception of an abstract entity through the senses. Thereby, the intellectually formed, indeterminate idea is rendered determinate as a specific magnitude and extends into the sensually perceivable realm of the imagination. Uniquely, Descartes‘ theory of extension bridges the dichotomy between the intellect and the imagination, thereby creating a concept of space that defines geographical space as intellectual

ideas made manifest in a perceivable reality with the help of intuitive imagination. It is this notion of Cartesian extension that would inspire Leibniz to formulate his theory of sensed space.

For Leibniz, as for Descartes, there is no universal space. Both thinkers reject the notion of void space, because it presupposes that bodies are completely at rest or fixed. However, since no body can ever be absolutely at rest there is no such thing as universal space (Garnett 56). By rejecting the notion of a universal, or void, space, Leibniz resolutely opposes Aristotle‘s first concept of nature and thereby effectively excludes philosophy from the discourse of space. Instead, Leibniz identifies mathematics and physics as the only disciplines to adequately frame the question of space (as much as the question of philosophy thereby indirectly acknowledging the philosophical nature of spatial discourse). In his rejection of void space, Leibniz opposes Newton‘s assertion that space can exist without matter.

Although Leibniz and Newton diverge on the question of void space, it is crucial to point out the significance of Newton‘s thought because it adds an important methodological observation to the conceptualization of space. Although space can exist without matter, Newton argues,

material objects require a space in which they are located. Therefore we have to distinguish between absolute and relative space. Newton writes: ―All things are placed in time as to order of succession; and in space as to order of situation‖ (qtd. in Northrop 427). Consequently we can assert that while Leibniz regards space as a subject of mechanical science, Newton acknowledges the possibility of a philosophical discourse of science by emphasizing the laws of contradiction and sufficient reason.

Although it seems, after a first glimpse into Leibniz‘s spatial theory, that the German

mathematician had little interest in the ontological qualities of spatial discourse as far as it relates to nature, a closer look into his work yields surprising results. In ―A New System of Nature and

Communication of Substances, and of the Union of the Soul and Body‖ an anonymously published article in the Journal des Savants (1695), Leibniz explains, unexpectedly, his

conviction that empirically verifiable matter alone proves insufficient as the foundation for a theory of space:

I perceived that it is impossible to find the principles of a true unity in matter alone, or in what is only passive, since everything in it is only a collection or aggregation of parts to infinity…I found then that their nature consists in force, and that from this there follows something analogous to sensation and appetite, so that we must conceive of them on the model of the notion we have of souls. (139)

Surprisingly, Leibniz‘s essay evokes inherently intuitive qualities to describe the interplay of matter and space that echo the principle of Cartesian extension; traits such as ―sensation,‖ ―appetite,‖ and even ―the soul.‖ The unity between matter and space that Leibniz proposes in his transcendental idealism, is thus created through the interplay of empirical data, matter and the intuition, perceived through the senses of the individual and mediated by reason. Leibniz‘s ―intuitive spatial turn‖ then marks a decisive step in the redefinition of space, for it validates the importance of identity, intuition and reason for the spatial discourse of the enlightenment.

Introducing the principles of transcendental idealism to the debate is certainly one of the key achievements of Leibniz‘s spatial thinking. This is, however, not the only innovation Leibniz contributed to the debate at the end of the seventeenth century. In addition, and important for my understanding of space employed in this project, Leibniz insisted on a crucial distinction in the theory of space: the difference between a sensed space, an individually perceived space or nature (a concept of nature that is uniquely private), and an absolute space, a mathematically and

scientifically perceived and absolute space of matter. This distinction is vital to understand, as it is the sensed places of history that are analyzed in this dissertation. If nature is perceived as a sensed space, the perception of space is distinctly individual because it is determined by the

subjective interpretation of an appearance. In this regard, sensed space is the individual

interpretation of material objects in a time-space relation. Consequently, sensed space can neither be scientifically reproduced nor universally generalized. In contrast, the notion of scientifically verifiable, mathematical space is the subject of science, and should not be confused with the object of this inquiry, which is solely focused on the investigation of sensed space and its individualized manifestation in a specific temporal setting. Whereas the distinction between the two is crucial, the tragic fallacy of the epistemology of space is, as Northrop rightfully notes, to explain sensed space as merely the appearance of empirically verifiable, absolute space (445). In a sense, and in contrast to Newton, Leibniz therefore rejects the notion of a mathematically verifiable absolute space in favor of a concept of space that is reliant upon the human consciousness as a formative force. For him space is ―the relatedness of phenomenal matter within the content of consciousness of the individual monad‖ (Northrop 438). This ultimate and inherent bond between space and consciousness does not, however, simply reproduce the Cartesian dualism of mental and physical space. Instead, Leibniz‘s assertion that the production of space is inextricably bound to the human consciousness introduces a new form of space that is concerned less with actual physical reality (actual space) than with the unlimited amount of possible spaces produced by the human consciousness (ideal spaces).

Leibniz‘s assertion of ideal space marks a significant intervention in the increasingly

scientific spatial discourse of the enlightenment, for it asserts that knowledge of and about space is different from the scientific observation of matter. This differentiation between spatial

knowledge and scientific knowledge rests on Leibniz‘s observation that space is observed through the senses and comprehended through the interaction of intuitive perception and rational

assessment.6 In addition to asserting the intuitive component of spatial production, Leibniz identified another characteristic that is crucial for my understanding of space in this study: the fact that space, as a result of the interplay between observable matter and intuitive perception, involves an element of abstraction and is therefore fictitious in nature. Space for Leibniz, Garnett clarifies, ―is universalized place. Both space and places are metaphysically unreal; both are abstract, but space, involving a certain presupposition which contradicts the nature of phenomena, is, in addition, fictitious‖ (Garnett 55).