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Book by Wiener, Philip P.
- GenresPhilosophy
Hardcover
First published January 1, 1951
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About the author
Gottfried Wilhelm Leibniz
1,382 books554 followersGerman philosopher and mathematician Baron Gottfried Wilhelm von Leibniz or Leibnitz invented differential and integral calculus independently of Isaac Newton and proposed an optimist metaphysical theory that included the notion that we live in "the best of all possible worlds."
Gottfried Wilhelm von Leibniz, a polymath, occupies a prominent place in the history. Most scholars think that Leibniz developed and published ever widely used notation. Only in the 20th century, his law of continuity and transcendental homogeneity found implementation in means of nonstandard analysis. He of the most prolific in the field of mechanical calculators. He worked on adding automatic multiplication and division to calculator of Blaise Pascal, meanwhile first described a pinwheel in 1685, and used it in the first mass-produced mechanical arithmometer. He also refined the binary number system, the foundation of virtually all digital computers.
Leibniz most concluded that God ably created our universe in a restricted sense, Voltaire often lampooned the idea. Leibniz alongside the great René Descartes and Baruch Spinoza advocated 17th-century rationalism. Applying reason of first principles or prior definitions, rather than empirical evidence, produced conclusions in the scholastic tradition, and the work of Leibniz anticipated modern analytic logic.
Leibniz made major contributions to technology, and anticipated that which surfaced much later in probability, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on politics, law, ethics, theology, history, and philology. Various learned journals, tens of thousands of letters, and unpublished manuscripts scattered contributions of Leibniz to this vast array of subjects. He wrote in several languages but primarily Latin and French. No one completely gathered the writings of Leibniz.
Gottfried Wilhelm von Leibniz, a polymath, occupies a prominent place in the history. Most scholars think that Leibniz developed and published ever widely used notation. Only in the 20th century, his law of continuity and transcendental homogeneity found implementation in means of nonstandard analysis. He of the most prolific in the field of mechanical calculators. He worked on adding automatic multiplication and division to calculator of Blaise Pascal, meanwhile first described a pinwheel in 1685, and used it in the first mass-produced mechanical arithmometer. He also refined the binary number system, the foundation of virtually all digital computers.
Leibniz most concluded that God ably created our universe in a restricted sense, Voltaire often lampooned the idea. Leibniz alongside the great René Descartes and Baruch Spinoza advocated 17th-century rationalism. Applying reason of first principles or prior definitions, rather than empirical evidence, produced conclusions in the scholastic tradition, and the work of Leibniz anticipated modern analytic logic.
Leibniz made major contributions to technology, and anticipated that which surfaced much later in probability, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on politics, law, ethics, theology, history, and philology. Various learned journals, tens of thousands of letters, and unpublished manuscripts scattered contributions of Leibniz to this vast array of subjects. He wrote in several languages but primarily Latin and French. No one completely gathered the writings of Leibniz.
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October 7, 2024
AN EXCELLENT COLLECTION EXCERPTS FROM MANY WRITINGS BY ONE OF THE GREAT 17TH CENTURY “RATIONALISTS”
Gottfried Wilhelm von Leibniz (1646-1716) was a German mathematician and philosopher; He developed calculus independently of Isaac Newton. Other works of his are 'Discourse on Metaphysics' and 'The Monadology.'
A statement in his “Dialogue on the Connection Between Things and Words” (1677) was very influential on the future discipline of Symbolic Logic: “Whence it is manifest that if we could find characters or signs appropriate for expressing al our thoughts as definitely and as exactly as arithmetic expresses numbers or geometric analysis expresses lines, we could in all subjects in so far as they are amenable to reasoning accomplish what is done in Arithmetic and Geometry. For all inquiries which depend on reasoning would be performed by the transportation of characters and by a kind of calculus, which would immediately facilitate the discovery of beautiful results.
"For we should not have to break out heads as much as is necessary today, and yet we should be sure of accomplishing everything the given facts allow. Moreover, we should be able to convince the world what we should have found or concluded, since it would be easy to verify the calculation either by going it over or by trying tests similar to that of casting out nines in arithmetic. And if someone would doubt my results, I should say to him, ‘Let us calculate, Sir,’ and thus by taking to pen and ink, we should soon settle the question.” (Pg. 15)
He says in his essay, The Art of Discovery (1685), “The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, in order to see who is right.” (Pg. 51)
In a letter to Bayle, he says, “Concerning free will I am of the sentiment of the Thomists and other philosophers who believe that everything is predetermined, and I see no ground for doubting it. However, that does not prevent us from having a freedom not only exempt from constraint but even from necessity, and in that we are like God himself who is always determined in his actions for he cannot fail to choose the best.” (Pg. 181-182)
He calls Spinoza “a subtle but profane author” (pg. 145), but also notes that “I do not hesitate to quote [Spinoza] when he says something good” (pg. 479). He states that “Sir Isaac Newton, and his followers, have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty needs to WIND UP his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God’s making is so imperfect, according to these gentlemen, that he is obliged to CLEAN it now and then by an extraordinary concourse, and even to mend it, as a clockmaker mends his work; who must consequently be so much the more unskillful a workman, as he is oftener obliged to mend his work and set it right.” (Pg. 216-217)
He asserts, “If the space… is not altogether empty; what is it then full of? Is it full of extended spirits perhaps, or immaterial substances, capable of extending and contracting themselves[?]… Nay, some have fancied, that MAN in the state of innocence, had also the gift of penetration; and that he became solid, opaque, and impenetrable by his fall. Is it not overthrowing our notions of things, to make God have parts, to make spirits have extension? The principle of the need of a sufficient reason does alone drive away all these spectres of imagination. Men easily run into fictions, for want of making a right use of that great principle.” (Pg. 255)
He contends, “This ‘tabula rasa,’ of which so much is said, is , in my opinion, only a fiction, which nature does not admit of, and which has its foundation in the incomplete notions of philosophers, like the vacuum, atoms, and rest, absolute or relative, of two parts of a whole, or like the primary matter … which is conceived as without form.” (Pg. 408) He suggests, “For not only do we receive images or traces in the brain but we also form them anew when we consider COMPLEX IDEAS. Thus the cloth, which represents our brain, must be active and elastic. This comparison would explain tolerably well what takes place in the brain; but as to the soul, which is a simple substance or MONAD, it represents without extension these same varieties of extended masses and has perception of them.” (Pg. 420)
In his famous Theodicy, he says, “it must be confessed that there is evil in this world which God has made, and that it was possible to make a world without evil, or even not to create a world at all, for its creation has depended on the free will of God… [But] the best plan is not always that which seeks to avoid evil, since it may happen that the evil is accompanied by a greater good… In this I have followed the opinion of St. Augustine, who has said … that God permitted evil in order to bring about good, that is, a greater good… To overcome this objection… it is sufficient to show that a world with evil might be better than a world without evil; but I… have even proved that this universe must be in reality better than every other possible universe.” (Pg. 509-510)
He argues, “the first question which should rightly be asked, will be, ‘Why is there something rather than nothing? For nothing is simpler and easier than something. Further, suppose that things must exist, we must be able to give a reason why they must exist so and not otherwise… Now this sufficient reason for the existence of the universe cannot be found in the series of contingent things; that is, of bodies and their representations in souls; for matter being indifferent in itself to motion and to rest, and to this or another motion, we cannot find the reason of motion in it, and still less of a certain motion.
"And although the present motion which is in matter, comes from the preceding motion… in this way we make no progress… for the same question always remains. Thus it must be that the sufficient reason, which has no need of another reason, be outside this series of contingent things and be found in a substance which is its cause, or which is a necessary being, carrying the reason of its existence within itself; otherwise we would still not have a sufficient reason in which we could rest. And this final reason of things is called God.” (Pg. 527-528)
Leibniz’s philosophy (which, perhaps surprisingly, was treated very respectfully by the arch-rationalist Bertrand Russell) is less popular these days than his fellow rationalists Descartes and Spinoza; but some of this ideas (e.g., the Principle of Sufficient Reason) have had lasting influence; this is an excellent collection of his writings, and makes a useful introduction to his thought.
Gottfried Wilhelm von Leibniz (1646-1716) was a German mathematician and philosopher; He developed calculus independently of Isaac Newton. Other works of his are 'Discourse on Metaphysics' and 'The Monadology.'
A statement in his “Dialogue on the Connection Between Things and Words” (1677) was very influential on the future discipline of Symbolic Logic: “Whence it is manifest that if we could find characters or signs appropriate for expressing al our thoughts as definitely and as exactly as arithmetic expresses numbers or geometric analysis expresses lines, we could in all subjects in so far as they are amenable to reasoning accomplish what is done in Arithmetic and Geometry. For all inquiries which depend on reasoning would be performed by the transportation of characters and by a kind of calculus, which would immediately facilitate the discovery of beautiful results.
"For we should not have to break out heads as much as is necessary today, and yet we should be sure of accomplishing everything the given facts allow. Moreover, we should be able to convince the world what we should have found or concluded, since it would be easy to verify the calculation either by going it over or by trying tests similar to that of casting out nines in arithmetic. And if someone would doubt my results, I should say to him, ‘Let us calculate, Sir,’ and thus by taking to pen and ink, we should soon settle the question.” (Pg. 15)
He says in his essay, The Art of Discovery (1685), “The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, in order to see who is right.” (Pg. 51)
In a letter to Bayle, he says, “Concerning free will I am of the sentiment of the Thomists and other philosophers who believe that everything is predetermined, and I see no ground for doubting it. However, that does not prevent us from having a freedom not only exempt from constraint but even from necessity, and in that we are like God himself who is always determined in his actions for he cannot fail to choose the best.” (Pg. 181-182)
He calls Spinoza “a subtle but profane author” (pg. 145), but also notes that “I do not hesitate to quote [Spinoza] when he says something good” (pg. 479). He states that “Sir Isaac Newton, and his followers, have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty needs to WIND UP his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God’s making is so imperfect, according to these gentlemen, that he is obliged to CLEAN it now and then by an extraordinary concourse, and even to mend it, as a clockmaker mends his work; who must consequently be so much the more unskillful a workman, as he is oftener obliged to mend his work and set it right.” (Pg. 216-217)
He asserts, “If the space… is not altogether empty; what is it then full of? Is it full of extended spirits perhaps, or immaterial substances, capable of extending and contracting themselves[?]… Nay, some have fancied, that MAN in the state of innocence, had also the gift of penetration; and that he became solid, opaque, and impenetrable by his fall. Is it not overthrowing our notions of things, to make God have parts, to make spirits have extension? The principle of the need of a sufficient reason does alone drive away all these spectres of imagination. Men easily run into fictions, for want of making a right use of that great principle.” (Pg. 255)
He contends, “This ‘tabula rasa,’ of which so much is said, is , in my opinion, only a fiction, which nature does not admit of, and which has its foundation in the incomplete notions of philosophers, like the vacuum, atoms, and rest, absolute or relative, of two parts of a whole, or like the primary matter … which is conceived as without form.” (Pg. 408) He suggests, “For not only do we receive images or traces in the brain but we also form them anew when we consider COMPLEX IDEAS. Thus the cloth, which represents our brain, must be active and elastic. This comparison would explain tolerably well what takes place in the brain; but as to the soul, which is a simple substance or MONAD, it represents without extension these same varieties of extended masses and has perception of them.” (Pg. 420)
In his famous Theodicy, he says, “it must be confessed that there is evil in this world which God has made, and that it was possible to make a world without evil, or even not to create a world at all, for its creation has depended on the free will of God… [But] the best plan is not always that which seeks to avoid evil, since it may happen that the evil is accompanied by a greater good… In this I have followed the opinion of St. Augustine, who has said … that God permitted evil in order to bring about good, that is, a greater good… To overcome this objection… it is sufficient to show that a world with evil might be better than a world without evil; but I… have even proved that this universe must be in reality better than every other possible universe.” (Pg. 509-510)
He argues, “the first question which should rightly be asked, will be, ‘Why is there something rather than nothing? For nothing is simpler and easier than something. Further, suppose that things must exist, we must be able to give a reason why they must exist so and not otherwise… Now this sufficient reason for the existence of the universe cannot be found in the series of contingent things; that is, of bodies and their representations in souls; for matter being indifferent in itself to motion and to rest, and to this or another motion, we cannot find the reason of motion in it, and still less of a certain motion.
"And although the present motion which is in matter, comes from the preceding motion… in this way we make no progress… for the same question always remains. Thus it must be that the sufficient reason, which has no need of another reason, be outside this series of contingent things and be found in a substance which is its cause, or which is a necessary being, carrying the reason of its existence within itself; otherwise we would still not have a sufficient reason in which we could rest. And this final reason of things is called God.” (Pg. 527-528)
Leibniz’s philosophy (which, perhaps surprisingly, was treated very respectfully by the arch-rationalist Bertrand Russell) is less popular these days than his fellow rationalists Descartes and Spinoza; but some of this ideas (e.g., the Principle of Sufficient Reason) have had lasting influence; this is an excellent collection of his writings, and makes a useful introduction to his thought.
July 25, 2025
A great collection of Leibniz's philosophical works. Although one of the world's foremost mathematicians (Leibniz is known for inventing calculus at the same time as Isaac Newton, despite doing far more with integrals than Newton did), in his spare time, Leibniz was Germany's greatest living philosopher. He can be classified as part of the Rationalist movement which was popular on the European continent.
There are dozens of short selections in this volume but the most important, in my opinion, are the works on the Principle of Sufficient Reason, Theodicy, and Monadology which are the hallmarks of Leibniz's philosophy. He presented the principle of sufficient reason where everything that exists must have an explanatory cause for it's existence, that is, if something does not exist sufficiently of itself (i.e. it is causal and not immutable) then there must be a causal explanation for it. Only God as the ground of all being is exempt from this. But why is the world rife with evil and suffering when God makes it? Leibniz's answer is that this must be the best of all possible worlds. Now, there is a lot that can be said against this idea but Leibniz at least presented an idea for the world to discuss. Lastly, his Monadology put forward the concept that all things reduce to irreducible monads (even ideas) where these form the building blocks of reality. Again, an interesting (albeit flawed, as Kant would discuss in his "Critique of Pure Reason") idea for discussion.
There are dozens of short selections in this volume but the most important, in my opinion, are the works on the Principle of Sufficient Reason, Theodicy, and Monadology which are the hallmarks of Leibniz's philosophy. He presented the principle of sufficient reason where everything that exists must have an explanatory cause for it's existence, that is, if something does not exist sufficiently of itself (i.e. it is causal and not immutable) then there must be a causal explanation for it. Only God as the ground of all being is exempt from this. But why is the world rife with evil and suffering when God makes it? Leibniz's answer is that this must be the best of all possible worlds. Now, there is a lot that can be said against this idea but Leibniz at least presented an idea for the world to discuss. Lastly, his Monadology put forward the concept that all things reduce to irreducible monads (even ideas) where these form the building blocks of reality. Again, an interesting (albeit flawed, as Kant would discuss in his "Critique of Pure Reason") idea for discussion.
November 4, 2013
I read this in addition to the required readings for The History of Classical Modern Philosophy during the first semester of 1980/81 at Loyola University Chicago.
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