In existographies, Gottfried Leibniz (309-239 BE) (1646-1716 ACM) (IQ:190|#24) (Cattell 1000:34) (RGM:25|1,350+) (PR:146|65AE / mathematician:4) (Murray 4000:14|CS / 6|M / 11|WP) (Gottlieb 1000:88) (Becker 160:79|3L) (Becker 139:18|13L) (Stokes 100:37) (Listal 100:17) (Norlinger 22:3) (GME:8) (LUG:#) (LPKE:#) (CR:280) (LH:10) (TL:299|#26) was a German mathematician, physicist, and philosopher, aka “German Plato” (Erman, 1828), noted for 
In 1686, Leibniz, in his “Brief Demonstration of the Notable Error of Descartes and Others Concerning the Law of Nature: According to Which God Always Preserves One and the Same Momentum and Which Is, By the Way, Wrongly Applied to the Practice of Mechanics”, expand on Christiaan Huygens’ model of the vector nature of momentum.
- “Even if some of these seem reconcilable with that hypothesis which estimates power by the product of mass by velocity, this is only accidentally, since the two hypotheses coincide in the case of ‘dead forces’ [potentia mortuus] in which only the beginning or end of ‘conatuses’ is actualized. But in ‘living forces’, or those acting with an actually completed impetus, there arises a difference, just as the example shows which I have given above in the published paper. For ‘living power’ is to ‘dead power’, or impetus (actual velocity) is to conatus, as a line is to a point or as a plane is to a line. Just as two circles are not proportional to their diameters, so the living forces of equal bodies are not proportional to their velocities but to the squares of their velocities. But since we cannot stop with an appeal to authority in this matter, and the mind which seeks to know will not be satisfied with mere inductions and hypotheses, we will now give a demonstration of our proposition, so that it can be placed for the future among the immutable foundations of the science of mechanics.”
- — Gottfried Leibniz (1686), “Brief Demonstration of the Notable Error of Descartes and Others” (pg. 299)
In 1692, Leibniz introduced the term “animate forces”, supposedly (Alekseev, 1978), and theorized about the conservation of animate forces, and extended this principle to a universal law of nature.
In 1697, Leibniz introduced his monad theory.
On Human Understanding
In 1704, Leibniz, in his On Human Understanding, presented a rebuttal of John Locke's An Essay Concerning Human Understanding, wherein he argues that "man is not at liberty to will to will or not". This turned up via key word search for Schopenhauer's "man can do what he will, but not will what he wills" quote.
In 1714, Leibniz penned Monadology, his presumed magnum opus, a 90 numbered paragraph, 6,000-word treatise, which attempted to derive the laws of motion from mathematics, based on the hypothesis of the 'monad', aka "simple substances", as the fundamental particles of the universe, a step above that of the "substantial forms" model of Plato and Aristotle. The following is gives an historical account of the theory:
- “I have tried to uncover and unite the truth buried and scattered in the opinions of different philosophical sects, and I believe I have added something of my own to take a few steps forward. The circumstances of my studies, from my earliest youth, have given me some facility in this. I learned Aristotle as a lad, and even the Scholastics did not put me off; I am not at all regretful of this even now. But at that time Plato too, and Plotinus, gave me some satisfaction, not to mention other ancient thinkers whom I consulted later. After leaving the trivial schools, I fell upon the moderns, and I remember at the age of fifteen taking a walk by myself in a grove on the outskirts of Leipzig, called the Rosental, in order to deliberate about whether I should retain ‘substantial forms’? Mechanism, however, finally prevailed and led me to apply myself to mathematics. It is true that I did not enter into its depths until after I had conversed with Huygens in Paris. But when I looked for the ultimate reasons for mechanism, and for the ‘laws of motion’ themselves, I was very surprised to see that it was impossible to find them in mathematics, and that I should have to return to metaphysics. This is what led me back to entelechies, and from the "material" to the "formal", and ultimately brought me to understand, after a number of corrections and improvements to my notions, that monads, or "simple substances", are the only true substances, and that material things are only phenomena, albeit well-founded and well-connected.”
- — Gottfried Leibniz (1714), Publication (pg. #)
Quotes | By
The following are quotes by Leibniz:
- “As for bodily substances, I maintain that mass, when one considers only what in it is divisible, as a pure phenomenon, that every substance has a genuine unity, in metaphysical rigor, and that it cannot be divided, engendered or corrupted, and that the whole of matter must be full of substances animate or at least living, that procreations and corruptions are only transformations from the smaller to the greater or vice versa, and that there is no particle of matter in which does not exist a world of infinite number of creatures, both organic and agglomerated.”
- “It is wrong to reduce all the multiformity of nature to pure mechanics. I see a corroboration of this in the principle law of nature which implies not the conservation of one and the same momentum but requires the conservation of one and the same amount of ‘active force’ [and] one and the same quantity of ‘motive activity’ which is far from the Cartesian idea of momentum. ”
- — Gottfried Leibniz (c.1690), Publication (pg. #)
- “Having made progress in my thinking, I have found that the void and the atoms cannot exist. In the Memoires de Trevoux, some letters which I had exchanged with Mr Hartsoeker have been published, where I have formulated some overall reasons - drawn from higher principles - which subvert the atoms, but I can produce many others, for my whole system is opposed to them.”
- “I believe that all creatures in the world are made up solely of simple substances or monads and of combinations of them. All of them have perception (which is nothing but the representation of multitude in unity) and appetite (which is nothing but the inclination of one perception to another) - which is called passion in animals and will in humans where the perception is cognitive.”
- (a) Erman, Paul. (1828). “Speech to the Academy of Berlin”, Celebration of Leibniz’s Birthday. Publisher.
(b) Klemme, Heiner; Kuehn, Manfred. (2016). The Bloomsbury Dictionary of Eighteenth-Century German Philosophers (pg. 453). Bloomsbury.
- (a) Leibniz, Gottfried. (1686). "A Brief Demonstration of the Notable Error of Descartes and Others Concerning the Law of Nature According to Which God Always Preserves One and the Same Momentum and Which Is, By the Way, Wrongly Applied to the Practice of Mechanics". Publisher.
(b) Leibniz, Gottfried. (1716). Philosophical Papers and Letters: a Selection (editor: Leroy Loemker) (§36: A brief Demonstration of a Notable Error of Descartes and Others Concerning a Natural Law, pgs. 296-302). Kluwer, 1989.
(c) Alekseev, Georgij. (1978). Energy and Entropy (pg. 87). Mir.
- Alekseev, Georgij. (1978). Energy and Entropy (pg. 87). Mir.
- New Essays on Human Understanding – Wikipedia.
- Leibniz, Gottfried. (1704). On Human Understanding (pg. 187). Publisher.
- Strickland, Lloyd. (2014). Leibniz’s Monadology: a New Translation and Guide (intro) (pg. #). Edinburgh.
- Substantial form – Wikipedia.
- Rosental (Leibzig) (German → English) – Wikipedia.
- Leibniz, Gottfried; Arnauld, Antoine. (1967). The Leibniz-Arnauld Correspondence (editor and translator: Haydn Mason; Introduction: G.H.R. Parkinson) (pg. 161). Manchester.
- Leibniz, Gottfried. (1814). “Letter to Nicolas Remond” (txt) in: Die philophischen schriften von Gottfried Wilheim Leibniz, Volume Three (editor: C.I. Gerhardt) (pgs. 618-24). Publisher.
- Hartz, Glenn A. (2006). Leibniz’s Final System: Monads, Matter, Animals. Routledge.
- Alonzi, Adam. (2015). “The Life of Gottfried Wilhelm Leibniz” (YT), Adam Alonzi, Feb 12.