This site is dedicated to the memory of Dr. Alan William Smolowe who gave birth to the creation of this database.
German Mathematician, Philosopher, Political Advisor and Logician, Developed Infinitesimal Calculus independently of Isaac Newton
"Now, as in the Ideas of God there is an infinite number of possible universes, and as only one of them can be actual, there must be a sufficient reason for the choice of God, which leads Him to decide upon one rather than another."
"Now, as there is an infinity of possible universes in the Ideas of God, and as only one of them can exist, there must be a sufficient reason for God's choice, which determines him toward one rather than another. And this reason can be found only in the fitness, or the degrees of perfection, that these worlds contain, since each possible thing has the right to claim existence in proportion to the perfection it involves."
"Now where there are no parts, there can be neither extension nor form [figure] nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things."
"Observable perceptions come by degrees from those which are too small to be observed."
"Of all beings those which are the most perfect and occupy the least possible space, that is to say those which interfere with one another the least, are the spirits whose perfections are the virtues."
"On the same principle it has an insipid effect if we always eat sweet things; sharp, acid, and even bitter things should be mixed in to stimulate the taste. He who has not tasted what is bitter has not earned what is sweet, not will he appreciate it. This is the very law of enjoyment that positive pleasure does not come from an even course; such things produce weariness, and make men dull not joyful."
"Often beautiful truths are arrived at by Synthesis, by passing from the simple to the compound."
"Of all the questions that bewilder the human race, none is pursued with more passion, more often repeated, more dangerously and cruelly pressed than this point of contention: “how the free will of man, punishment, and reward can exist, given the omnipotence and omniscience of an all-ruling God.”"
"Our reasonings are based on two great principles: the principle of contradiction, by virtue of which we judge to be false that which involves a contradiction, and true that which is opposed or contradictory to the false."
"One cannot explain words without making incursions into the sciences themselves, as is evident from dictionaries; and, conversely, one cannot present a science without at the same time defining its terms."
"Punishment belongs to the evil will—no matter whence it comes. Otherwise, no misdeed would be punished. There is always a cause of the will outside of the willing subject, and yet it is the will that makes us human beings and persons—sinners, blessed, damned."
"Since each mind is as it were a world apart, sufficient unto itself, independent of all other created things, including the infinite, expressing the universe, it is as lasting, as subsistent, and as absolute as the very universe of created things itself. We must therefore conclude that it must always play its part in the way most suited to contribute to the perfection of that society of all minds which constitutes their moral union in the City of God. Here, too, is a new and wonderfully clear proof of all the existence of God. For this perfect agreement of all these substances, which have no point of communication with one another, could only come from the one common cause."
"Reality cannot be found except in One single source, because of the interconnection of all things with one another... I do not conceive of any reality at all as without genuine unity... I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general."
"So long as we do not distinguish what is genuinely a complete entity, or substance, we shall never have any fixed point at which we can stop; and such fixed point is the one and only means of establishing solid and real principles."
"Something quite other than mere presence is needed for one thing to represent what takes place in another. For this some explicable communication is necessary, some kind of influence either of the things upon one another or of a common cause."
"Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half."
"That each single substance expresses the whole universe in its own way, and that in its notion are included all the events which will happen to it with all their circumstances, and the whole series of things outside it."
"The Aristotelians and the Cartesians, who do not admit the existence of a true void, replied to this experiment of M. Guericke's as well as to the experiment made by M. Torricelli of Florence (who emptied the air out of a glass tube by means of mercury), by saying that there is no vacuum at all in the tube or in the container since the glass has subtle pores, through which rays of light, magnetic rays, and other very fine things can pass. And I am of their opinion."
"The combination of all the tendencies to the good has produced the best; but as there are goods that are incompatible together, this combination and this result can introduce the destruction of some good, and as a result some evil."
"The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering in which an ingenious conjecture greatly shortens the road."
"The conception of God which is the most common and the most full of meaning is expressed well enough in the words: God is an absolutely perfect being."
"The connection of phenomena, which guarantees truths of fact with regard to sensible things outside us, is verified by means of truths of reason."
"The consequences of beliefs that go against the providence of a perfectly good, wise, and just God, or against that immortality of souls which lays them open to the operations of justice... I even find that somewhat similar opinions, by stealing gradually into the minds of men of high station who rule the rest and on whom affairs depend, and by slithering into fashionable books, are inclining everything toward the universal revolution with which Europe is threatened, and are completing the destruction of what still remains in the world of the generous Greeks and Romans who placed love of country and of the public good, and the welfare of future generations before fortune and even before life."
"The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity."
"The fact is, I think, that my objection is so simple that its very simplicity operated to deceive him, since he could not believe that a comment which was so easy could have escaped the notice of so many able people."
"The death of the illustrious M. Huygens is an inestimable loss. Few know this as well as I do. He equaled, in my opinion, the reputation of Galileo and Descartes, and, with the help of what they had done, he surpassed their discoveries. In a word, he was one of the chief ornaments of our time."
"The general knowledge of this great truth that God acts always in the most perfect and most desirable manner possible is in my opinion the basis of the love which we owe to God in all things; for he who loves seeks his satisfaction in the felicity or perfection of the object loved and in the perfection of his actions."
"The German language, which has an abundance of meaningful terms for useful things belonging to common life, for things visible or intelligible, is the most convenient for that purpose; when applied to supposed philosophical chimeras, it can only seem false—it is violated. In contrast, the Latin language was robbed a long time ago of her virginity, and her daughters, the Italian and French languages, were all too inclined to take on the vice of the mother."
"The human race, considered in relation to the sciences which minister to our happiness, appears to me like a disorderly rabble marching in the darkness, having neither leader nor order, without password or other signals to regulate their march, or by which to know themselves. Instead of holding one another by the hand so as to guide one another and make sure of our way, we run about at random and to and fro, and even hurl ourselves one against another, far from helping and supporting each other. This means that we advance but little, or else that we know not where we are. We even plunge into morasses and shifting sands of doubt without end, wherein is nothing solid nor firm, or else we drag ourselves into the principles of very dangerous errors. Talibus in tenebris vitae tantisque periclis, it is given to no mortal to light a torch capable of dispersing this obscurity. Sects and leaders of sects serve merely to seduce us like the false lights of marsh fires; and it is left to the sun of our souls to enlighten us utterly, but in another life. Nevertheless, what we can do here is march together and in order, to share our journeyings, to make known the roads and to repair them: and finally to travel slowly, but with a firm unwavering tread, by the side of that pure and living stream of clear and simple knowledge, which has its source among us, which can serve as a comfort on our painful march, and as a thread which grows gradually larger and increases our knowledge, until at last it leads us, albeit by a roundabout way, to a delightful plain- I mean the most important practical truths which serve to content the mind and to preserve the health of the body, as far as this can be done by reason."
"The imaginary number is a fine and wonderful resource of the human spirit, almost an amphibian between being and not being."
"The immediate cause of sin is the man as he is then constituted with respect to intellect and will based on the external things that are posited. But the preceding or mediate cause of sin is the state of the man and of objects preceding the present. And the chain of these mediate causes is the series of things."
"The monad, of which we shall speak here, is nothing but a simple substance which enters into compounds; simple, that is to say, without parts. And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples. Now where there are no parts, there neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things… There is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of compounding… Indeed every monad must be different from every other. For there are never in nature two beings, which are precisely alike, and in which it is not possible to find some difference which is internal, or based on some intrinsic quality. I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one. It follows from what we have just said, that the natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being… And as every state of a simple substance is a natural consequence of its preceding state, so that the present state of it is big with the future."
"The natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being."
"The notion of the world’s being a great machine going on without the interposition of God… is the notion of material and fate… to exclude providence and God’s government in reality out of the world."
"The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic."
"The original proof of necessary truths comes from the understanding alone, and all other truths come from experiences or from observations of the senses. Our mind is capable of knowing both the one sort and the other, but it is the source of the first; whatever number of particular experiences we may have of a universal truth, we cannot assure ourselves of it for always by induction, without apprehending its necessity by reason."
"The present is big with the future."
"The senses, although they are necessary for all our actual knowledge, are not sufficient to give us the whole of it, since the senses never give anything but instances, that is to say particular or individual truths. Now all the instances which confirm a general truth, however numerous they may be, are not sufficient to establish the universal necessity of this same truth, for it does not follow what happened before will happen the same way again."
"The question he is discussing with the celebrated prelate, who has attacked him, is whether matter can think, and as this is an important point, even for the present work, I cannot avoid going into the subject a little and taking some account of their dispute."
"The success of experiments serves also as a confirmation of reason, more or less as verifications serve in arithmetic to help us avoid erroneous calculation when the reasoning is long. It is in this also that the knowledge of men differs from that of the brutes: the latter are purely empirical, and guide themselves solely by particular instances; for, as far as we can judge, they never go so far as to form necessary propositions; whereas men are capable of the demonstrative sciences. This also is why the faculty the brutes have of making sequences of ideas is something inferior to the reason which is in man. The sequences of the brutes are just like those of the simple empiricists who claim that what has happened sometimes will happen again in a case where what strikes them is similar, without being capable of determining whether the same reasons hold good. It is because of this that it is so easy for men to catch animals, and so easy for pure empiricists to make mistakes."
"The things that are, the things that have been, and those that are presently to come."
"The supernatural surpasses all the powers of created things. We must take an example. Here is one which I have often made use of with success. If God wished to cause a free body to circle in the ether round about a given fixed center, without any other created thing acting on it, this, I say, could only occur by miracle, not being explicable by the nature of bodies. For a free body naturally departs from a curve along the tangent. It is in this sense that I maintain that the attraction of bodies, properly so called, is a miraculous thing, since it cannot be explained by their nature."
"The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God... God alone is the primary Unity, or original simple substance, from which all monads, created and derived, are produced… I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general."
"THEOLOGIAN: But what is to love? PHILOSOPHER: To be delighted by the happiness of another."
"The whole future is doubtless determined; but since we know not what it is, nor what is foreseen or resolved, we must do our duty, according to the reason that God has given us and according to the rules that he has prescribed for us; and thereafter we must have a quiet mind, and leave to God himself the care for the outcome. For he will never fail to do that which shall be the best, not only in general but also in particular, for those who have true confidence in him, that is, a confidence composed of true piety, a lively faith and fervent charity, by virtue of which we will, as far as in us lies, neglect nothing appertaining to our duty and his service."
"There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible. When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached."
"There is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of compounding."
"There are two famous labyrinths where our reason very often goes astray. One concerns the great question of the free and the necessary, above all in the production and the origin of Evil. The other consists in the discussion of continuity, and of the indivisibles which appear to be the elements thereof, and where the consideration of the infinite must enter in."
"There is a connection between the perceptions of animals, which bears some resemblance to reason: but it is based only on the memory of facts or effects, and not at all on the knowledge of causes. Thus a dog runs away from the stick with which he has been beaten, because memory represents to him the pain that was caused by that stick. And men, in so far as they are empiricists, that is to say in three-fourths of their actions, only act like brutes. For example, we expect that the day will dawn tomorrow, because we have always experienced it to be so; it is only the astronomer who foresees it by reason, and even this prediction will ultimately fail when the cause of daylight, which is not eternal, ceases. But true reasoning depends on necessary or eternal truths (like the truths of logic, numbers and geometry) which make the connection of ideas indubitable, and the sequences inevitable. Animals in which such sequences cannot be observed are called brutes; but those which know these necessary truths are called rational animals, and their souls are called minds. These souls are capable of performing acts of reflection, and of considering what is called self, substance, soul, mind- those things and truths, in short, which are immaterial. It is this which makes us capable of understanding science or demonstrative knowledge."
"There is nothing without a reason."