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Gottfried Leibniz

Gottfried Wilhelm von Leibniz (1 July 1646 {21 June O.S.} – 14 November 1716) was a German philosopher and mathematician.

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  • Theologus: Amare autem?
    Philosophus: Felicitate alterius delectari.
    • Theologian: But what is to love?
      Philosopher: To be delighted by the happiness of another.
    • Confessio philosophi (1673)

  • To love is to be delighted by the happiness of someone, or to experience pleasure upon the happiness of another. I define this as true love.

  • Omne possibile exigit existere.
    • Everything that is possible demands to exist.
    • De veritatibus primis (1686)

  • Chaque substance est comme un monde à part, indépendant de toute autre chose, hors de Dieu...

  • TO LOVE is to find pleasure in the happiness of others. Thus the habit of loving someone is nothing other than BENEVOLENCE by which we want the good of others, not for the profit that we gain from it, but because it is agreeable to us in itself.
    CHARITY     is a general benevolence. And JUSTICE is charity in accordance with wisdom. ... so that one does not do harm to someone without necessity, and that one does as much good as one can, but especially where it is best employed.

  • Pour ce qui est des connaissances non-écrites qui se trouvent dispersées parmi les hommes de différents professions, je suis persuadé qu’ils passent de beaucoup tant à l'égard de la multitude que de l'importance, tout ce qui se trouve marqué dans les livres, et que la meilleure partie de notre trésor n'est pas encore enregistrée.


  • La nature ne fait jamais des sauts.

  • [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.
    • Nouveaux essais sur l'entendement humain (1704)

  • Il y a deux labyrinthes fameux où notre raison s’égare bien souvent : l'un regarde la grande question du libre et du nécessaire, surtout dans la production et dans l'origine du mal ; l'autre consiste dans la discussion de la continuité et des indivisibles qui en paraissent les éléments, et où doit entrer la considération de l'infini.
    • 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.
    • Essais de Théodicée: Préface (1710)

  • Musica est exercitium arithmeticae occultum nescientis se numerare animi.
    • Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.
    • Letter to Christian Goldbach, April 17, 1712.
    • Arthur Schopenhauer paraphrased this quotation in the first book of Die Welt als Wille und Vorstellung: Musica est exercitium metaphysices occultum nescientis se philosophari animi. (Music is a hidden metaphysical exercise of the soul, which does not know that it is philosophizing.)

  • J'ay marqué plus d'une fois, que je tenois l'espace pour quelque chose de purement relatif, comme le temps; pour un ordre des coëxistences, comme le temps est un ordre des successions.
    • I have said more than once, that I hold space to be something purely relative, as time; an order of coexistences, as time is an order of successions.
    • Third letter to Samuel Clarke, February 25, 1716

  • Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it.
    • As quoted in The World of Mathematics (1956) by J. R. Newman, p. 1832

  • De quelque manière que Dieu aurait créé le monde, il aurait toujours été régulier et dans un certain ordre général. Mais Dieu a choisi celui qui est le plus parfait, c’est-à-dire celui qui est en même temps le plus simple en hypothèses et le plus riche en phénomènes...
    • In whatever manner God created the world, it would always have been regular and in a certain general order. God, however, has chosen the most perfect, that is to say, the one which is at the same time the simplest in hypothesis and the richest in phenomena.
      • Discours de métaphysique (1686); Leibniz famously tried to show that ours is the best of all possible worlds (see also Monadologie 53 & 54, below). These attempts were mercilessly parodied in Voltaire's Candide. Quotations from Voltaire's novel are often mistakenly attributed to Leibniz. Other statements by Leibniz upon the subject include these:
    • S'il n'y avait pas le meilleur (optimum) parmi tous les mondes possibles, Dieu n'en aurait produit aucun.
      • If there were no best among all possible worlds, God would not have created one.
        • Théodicée (1710)
    • I do not believe that a world without evil, preferable in order to ours, is possible; otherwise it would have been preferred. It is necessary to believe that the mixture of evil has produced the greatest possible good: otherwise the evil would not have been permitted.
      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.

  • Ce miracle de l'Analyse, prodige du monde des idées, objet presque amphibie entre l'Être et le Non-être, que nous appelons racine imaginaire.
    • This miracle of analysis, this marvel of the world of ideas, an almost amphibian object between Being and Non-being that we call the imaginary number.
    • Quoted in Singularités : individus et relations dans le système de Leibniz (2003) by Christiane Frémont

  • We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind.

The Monadology (1714)

  • On est obligé d’ailleurs de confesser que la Perception et ce qui en dépend, est inexplicable par des raisons mécaniques, c’est-à-dire par les figures et par les mouvements. Et feignant qu'il y ait une Machine, dont la structure fasse penser, sentir, avoir perception ; on pourra la concevoir agrandie en conservant les mêmes proportions, en sorte qu’on y puisse entrer, comme dans un moulin. Et cela posé, on ne trouvera en la visitant au dedans, que des pièces, qui poussent les unes les autres, et jamais de quoi expliquer une perception. Ainsi c'est dans la substance simple, et non dans le composé, ou dans la machine qu’il la faut chercher.
    • Moreover, it must be confessed that perception and that which depends upon it are inexplicable on mechanical grounds, that is to say, by means of figures and motions. And supposing there were a machine, so constructed as to think, feel, and have perception, it might be conceived as increased in size, while keeping the same proportions, so that one might go into it as into a mill. That being so, we should, on examining its interior, find only parts which work one upon another, and never anything by which to explain a perception. Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for.
    • La monadologie (17).

  • Et comme tout présent état d'une substance simple est naturellement une suite de son état précédent, tellement, que le présent y est gros de l'avenir.
    • And as every present state of a simple substance is naturally a consequence of its preceding state, so its present is pregnant with its future.
    • La monadologie (22).

  • Il y a aussi deux sortes de vérités, celles de Raisonnement et celle de Fait. Les vérités de Raisonnement sont nécessaires et leur opposé est impossible, et celles de Fait sont contingentes et leur opposé est possible.
    • There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible.
    • La monadologie (33).

  • Or, comme il y a une infinité d'univers possibles dans les idées de Dieu, et qu'il n'en peut exister qu'un seul, il faut qu'il y ait une raison suffisante du choix de Dieu qui le détermine à l'un plutôt qu'à l'autre. Et cette raison ne peut se trouver que dans la convenance, dans les degrés de perfection que ces mondes contiennent, chaque possible ayant droit de prétendre à l'existence à mesure de la perfection qu'il enveloppe.
    • 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.
    • La monadologie (53 & 54).

  • Ainsi on peut dire que non seulement l'âme, miroir d'un univers indestructible, est indestructible, mais encore l'animal même, quoique sa machine périsse souvent en partie, et quitte ou prenne des dépouilles organiques.
    • Thus it may be said that not only the soul, the mirror of an indestructible universe, is indestructible, but also the animal itself, though its mechanism may often perish in part and take off or put on an organic slough.
    • La monadologie (77).
    • Sometimes paraphrased as: The soul is the mirror of an indestructible universe.
 
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