The enlightenment rationalist G. W. Leibniz (1646-1716) was a master at articulating certain general and fundamental principles and applying these principles to various philosophical problems. Principles are statements of basic laws, truths, or rules from which other laws, truths, or rules are derived. In many cases, principles are not the results of demonstration: they are the things we use to demonstrate something. Now, Leibniz is a rationalist philosopher not an empiricist or someone who thinks all knowledge must come directly or indirectly from sense experience. This means he believes there are certain principles we can discover which are innate to our minds, that is, principles which we do not learn from sense experience. Once we are in possession of these principles, we can just think and use logic to see how they relate and how we can construct arguments using them.
In what follows, I present five of Leibniz’s principles and show how they can be applied to the question of whether or not there are atoms or indivisible material substances. These arguments can, perhaps, be used to think more philosophically about the current debate over whether, for example, Quarks can be further divided into point-like Preons (for some insights about this issue go here). I will be paraphrasing from Leibniz’s work Monadology as well as from Nicholas Rescher’s helpful overview of Leibniz’s principles. I will give the respective section number(s) of the Monadology after each principle for reference and some quotations will be from Leibniz’s Discourse on Metaphysics and Other Essays (Hackett Publishing). In future blogs I will cover different principles and topics. If you are interested, you can read Leibniz’s Monadology here.
Leibniz’s favorite argument against atoms is based on the Principle of Continuity which asserts that nature never makes any leaps: “a motion never arises immediately from rest nor is it reduced to rest except through a lesser motion” (Discourse, 56). “To judge otherwise is to know little of the immense subtlety of things, which always and everywhere involves an actual infinity” (Discourse, 57). See Monadology 53-58, as well as 13, 61, 67, 72. Here is the argument:
If atoms are indivisible material substances not made of parts then when they collide they would instantaneously change their direction and speed, that is, they would change discontinuously.
But according to the Principle of Continuity no motion “arises immediately from rest nor is it reduced to rest except through a lesser motion”, that is, no motion is discontinuous.
Therefore atoms cannot exist.
Leibniz is saying this: when one thing collides with another and moves another, the movement can only take place continuously if each object has parts that are in turn made of parts, etc. It is the movement of these parts, however subtle and unseen, that allows for the continuous and partially elastic movement that is experienced in the collision. If atoms exist then they have no parts and therefore their movement—whether acceleration of deceleration—would not occur in a gradual, continuous manner as their internal parts shift this way and that; rather, their movement would be an immediate leap from one state to another. But this leap would violate the principle of continuity and thus atoms cannot exist. Go here for a ten second video that might help make this point about continuity, collision, and elasticity clear.
Of course, one might be willing to accept that nature does makes leaps; certainly quantum mechanics maintains energy can be emitted in discrete, non-continuous packets. But Leibniz would say the acceptance of such leaps in nature is akin to accepting miracles. We would be accepting that there are events that cannot, in principle, be understood since their existence, not being continuous with any past event, would be grounded in nothing. This would violate the Principle of Sufficient Reason which asserts that for every contingent fact (something that could have been different) there is a sufficient reason why the fact is thus and not otherwise (Monadology 32). To violate this principle is to admit there are absurd events occurring out of connection with all other things. And this, for Leibniz, is irrational. John Dewey describes Leibniz’s point well in his 1888 book Leibniz’s New Essays Concerning the Human Understanding:
“It is the very nature of matter to be infinitely divisible: to say this is to deny the existence of any true principle of unity. The world of nature is the world of space and time; and where in space and time shall we find a unity where we may rest? Every point in space, every moment in time, points beyond itself. It refers to the totality of which it is but a part, or, rather, a limitation. If we add resistance, we are not better situated. We have to think of something which resists; and to this something we must attribute extension,–that is to say, difference, plurality. Nor can we find any resistance which is absolute and final. There may be a body which is undivided, and which resists all energy now acting upon it; but we cannot frame an intelligible idea of a body which is absolutely indivisible. To do so is to think of a body out of all relation to existing forces, something absolutely isolated; while the forces of nature are always relative to each other….Nor do we fare better if we attempt to find unity in the world of nature as whole. Nature has its existence as whole in space and time. Indeed, it is only a way of expressing the totality of phenomena of space and time. It is a mere aggregate, a collection.” (pp. 289-290)
A second argument against atoms can be formulated based on Leibniz’s Principle of Agency that asserts everything that exists is active to some degree: if something doesn’t act then it can’t exist (Discourse, 54, 65 and Monadology 8 and 49). Here is the argument:
If atoms (indivisible material things) exist then they would be completely inert: they would have no ability to actively resist and push back and thus they would be completely passive.
But according to the Principle of Agency (to be is to act) nothing can be completely passive.
Therefore, atoms cannot exist.
A third argument is based on Leibniz’s Principle of Individuality or Identity of Indiscernibles: Substances are identified through their unique properties. Thus there cannot be two beings in nature perfectly alike: if there were, we would not have two things but one (Monadology 9). Daniel Garber summarizes his argument against atoms based on this principle: “In some places he [Leibniz] argues against the existence of atoms from his principle that no two things in the world can be perfectly similar. While the argument is not altogether clear, his idea seems to be that if there were only one kind of matter, and it was always perfectly hard, then there would be no physical features to distinguish pieces of it from the same volume” (see his article “Leibniz: physics and philosophy” in the Cambridge Companion to Leibniz, pp. 321-233). If we ask why two things cannot have exactly the same properties, Leibniz would respond with reference to aforementioned Principle of Sufficient Reason: if there are no differences between x and y, then there can be no reason for x having the properties it has and y having the properties it has. And this, again, would commit us to the existence of something absurd without sufficient reason.
At least three interesting implications follow from the above arguments: (1) If nothing is inert then everything is active and thus alive: “Thus there is nothing fallow, sterile, or dead in the universe, no chaos and no confusion except in appearance, almost like it looks in a pond at a distance, where we might see the confused and, so to speak, teeming motion of the fish in the pond, without discerning the fish themselves” (Monadology 69; see 67 and 68 as well). Therefore we see that the Principle of Agency entails the Principle of Organicism as well: Everything that exists has life (Monadology 66-73); (2) if there are no absurd leaps in nature then all matter is continuous with all other matter and thus we see that the Principle of Community applies as well, namely, that every agent is affected by everything that happens in the universe: “All things conspire” (sympnoia panta) as the ancient Greek Hippocrates asserted (Monadology section 61); and (3) if there are no atoms or indivisible material particles then matter is infinitely divisible and we can never “get to the bottom of it” so to speak.
 Nicholas Rescher, G. W. Leibniz’s Monadology: An Edition for Students (Pittsburgh: University of Pittsburgh Press, 1991). See pp. 43-44. Rescher’s book is an indispensible resource for studying Leibniz. A very helpful collection of essays on Leibniz is The Cambridge Companion to Leibniz, ed. Jolley (New York: Cambridge University Press, 1995).
 This paraphrase draws upon Daniel Garber’s excellent analysis in his essay Leibniz: physics and philosophy, in The Cambridge Companion to Leibniz, ed. Jolley (New York: Cambridge University Press, 1995), p. 323.