The main purpose of the work is to offer a better understanding of the Leibnizean philosophy of space and mature metaphysics, through a pressing confrontation with the problems of geometric foundations. And finally, I am hugely impressed by the expertise he has brought to bear on both the purely formal and the deeply metaphysical sides, each requiring vastly different but equally considerable competences. In sum, this [book] is an extraordinary accomplishment. Arthur, McMaster University I believe that this is an extraordinary [book] which sets new standards for Leibnizean scholarship—and, in particular, for historical and philosophical investigation into the relationship between Leibniz and Kant. Friedman, Stanford University Reviews From the reviews: I find his contribution to the debate on the reality of corporeal substances to be at once original and decisive.

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Physical Monadology The definitive version of this paper will be published in Julian Wuerth, ed. For accepting a professorship offered, Prussian universities required an additional inaugural thesis.

The professorship went to J. Kypke in and passed to J. Buck in PM is a treatise in natural philosophy on the question of the divisibility of matter. Bodies exist in space, are therefore extended, and are thus divisible. If their parts were extended as well, then the divisibility of matter would continue ad infinitum, and bodies could not have simple parts, which seems absurd. But if they did have simple parts, then these parts would not be divisible, hence not be extended, and consequently not constitute bodies, which seems absurd, too.

According to the entry on Zeno by Pierre Bayle in his Dictionnaire historique et critique [], there are three conceivable solutions to this problem, depending on whether matter is assumed to consist of particles, points, or atoms. None of these options is quite satisfactory. Particles have spatial extension, which would make matter infinitely divisible and be devoid of simple elements.

Points are not divisible, which makes them simple elements in space, but since they lack extension, they cannot fill matter. Atoms had been stipulated since antiquity as being indivisible and extended, but this raises the question of how they can take up space without admitting of division. In PM, Kant tries to solve this dilemma by escaping between its horns. On the one hand, he claims in prop.

On the other hand, he admits in prop. Nonetheless, he insists in prop. Not only are these ultimate elements located in space, but they are also actually extended. A monad, Kant argues, can fill space despite its simplicity How is this possible? Physical monads resemble material atoms and geometrical points in being simple and consequently in being indivisible.

But unlike points, they take up space. And unlike atoms, they do not fill a volume by just being there or through some stipulated solidity. Monads are dynamic. Kant suggests in prop. The radiated field he calls sphere of activity sphaera activitatis; 1. In the remainder of PM in prop. Physical monads are points in space.

These points are active as incessant sources of radiation. These force-wells fill space and resist division through the power of impenetrability, which is the dynamic expression of the sphere of activity prop. Essential to the field radiated by the monadic force-wells is its dialectical structure. Instead of being a uniform radiation, the field is braided together by two opposing forces, with countervailing vectors, different initial intensities, and staggered propagation rates.

One aspect of this binary field is a force that is strongly repulsive, and which propagates its intensity at the inverse cube of the distance from the point- source prop. Another aspect is a force that is weakly attractive, and which falls off at the inverse square of the distance from the center ibid. The dialectics of the field explains the constitutive self-organization of matter. Because of the force of repulsion, the physical monad is impenetrable such that contact with others will not obliterate it: the force-well remains stable and the activity-sphere preserves its volume cf.

And because of the force of attraction, the monad accretes with others into the constitutive matrix of material bodies cf. Repulsion, which acts strongly but falls off quickly, allows the activity sphere to hold out against immediate contact with others; attraction, which acts weakly but falls of slowly, allows the activity sphere to grip other force-wells in space to combine into larger material structures.

The interaction of attraction and repulsion is what gives the monad its determinate volume. Since repulsion first overwhelms attraction but then falls off steeply, both forces are equal at some distance from their common source. This equality constitutes dynamically the event horizon and structurally the spatial limit of the activity sphere prop. Ontologically, the constitutive monadology of PM is a linear extension of the dynamic claims of UNH [].

In UNH, Kant develops a cyclic theory of cosmic evolution, from big bang to big crunch, based on the interplay of attraction and repulsion cf. UNH II. A key element of this phoenix of nature :.

This so- called Nebular Hypothesis hinges on a see-saw of attraction and repulsion that allows for the gravitational accretion of material particles to stellar bodies and the arrangement of planetary satellites on an ecliptic plane.

In UNH, attraction and repulsion are invoked as acting upon material particles, for the sake of explaining how interstellar dust coalesces into celestial objects. In PM, attraction and repulsion are shown to act within the particles themselves. The same forces explain natural self-organization on all orders of magnitude, from subatomic to galactic scale. In the conclusion of PM, Kant uses his theory of attractive and repulsive forces to explain inertia and density in Newtonian mechanics.

The account of physical monads entails that all ultimate elements are originally equal in volume prop. Still, bodies can have different masses depending on the inertia they are endowed with prop 11, cor. Mass comes in degrees, which means that matter varies in density.

Varying densities are possible because of the constitution of the activity spheres. Although impenetrable, they are elastic and can be compressed, which packs greater numbers of monads into smaller bodies prop.

Kant believes that PM yields the proof of attractive and repulsive forces cf. The interplay of forces reconciles the divisibility of bodies with the simplicity of elements. This monadology is intended to supply the metaphysical groundwork for Newtonian mechanics. For without repulsion, there could be no solidity; without attraction, there could be no bodies; and without their interplay, there could be no elasticity to explain varying density. In this sense is the physical monadology an example of the value of combining metaphysics and geometry, as the title of the treatise announces.

They radiate forces whose oscillation whips out tiny dimensional bubbles. These bubbles are the ultimate spatial units of matter. Since radiation spawns extension, these units are both indivisible and extended. With physical monads, nature is at least partly capable of creating itself.

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There are no discussion topics on this book yet. Looking for beautiful books? Discourse on Metaphysics, and the Monadology. Related articles in Google Scholar. In sum, this [book] is an extraordinary accomplishment. Table of contents Historical Survey.


Geometry and Monadology






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