Gottfried Wilhelm Leibniz

Only geometry can hand us the thread [which will lead us through] the labyrinth of the continuum’s composition, the maximum and the minimum, the and the infinite; and no one will arrive at a truly solid metaphysic except he who has passed through this [labyrinth].

''Dissertatio Exoterica De Statu Praesenti et Incrementis Novissimis Deque Usu Geometriae Leibniz, Leibnizens Mathematische Schriften, Herausgegeben Von C.I. Gerhardt. Bd. 1-7. 1850-1863. Halle. The quotation is found in vol. 7. on page 326 in ”Dissertatio Exoterica De Statu Praesenti et Incrementis Novissimis Deque Usu Geometriae”. Link (Spring 1676) Geometry and Monadology: Leibniz's Analysis Situs and Philosophy of Space, 1850

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, 1716

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)., 1714

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)., 1714

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)., 1714

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)., 1714

It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it.

Opening paragraph of Historia et Origo Calculi Differentialis (1714) Commercium epistolicum D. Joannis Collins et aliorum de analysi promota, see also Mathematische Schriften, Ed. C. I. Gerhardt, Georg Olms Verlag (1971) vol. 5, pp. 392–410; Tr. J. M. Child, "Newton and the art of discovery" Isaac Newton 1642–1727: A Memorial Volume (1927) Ed. W. J. Greenstreet, G. Bell, pp. 117–129., 1714

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)., 1714

Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.

Letter to Christian Goldbach, April 17, 1712., 1712

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.

Théodicée (1710)ː Préface, 1710

I am convinced that the unwritten knowledge scattered among men of different callings surpasses in quantity and in importance anything we find in books, and that the greater part of our wealth has yet to be recorded.

Discours touchant la méthode de la certitude et de l'art d'inventer pour finir les disputes et pour faire en peu de temps de grands progrès (1688–1690), 1688

Even in the games of children there are things to interest the greatest mathematician.

Discours touchant la méthode de la certitude et de l'art d'inventer pour finir les disputes et pour faire en peu de temps de grands progrès (1688–1690), 1688

Everything that is possible demands to exist.

De veritatibus primis (1686), 1686

Every substance is as a world apart, independent of everything else except God.

Discours de métaphysique (1686), 1686

The love of God consists in an ardent desire to procure the general welfare, and reason teaches me that there is nothing which contributes more to the general welfare of mankind than the perfection of reason.

Closing sentence of the Preface to the general science (1677) (in P. Wiener (ed.), Leibniz Selections, Macmilland Press Ltd, 1951)., 1677