Born in 1646 in Leipzig, at the end of the Thirty Year old war, when Germany undergoes a strong political crisis and nun, Leibniz is formed as an autodidact, using the library of his/her father, professor of philosophy and right.

Before the fifteen years age, it is initiated with the Greek and with Latin, get excited the humanities, logic, theology scholastic and, later, it reads old philosophers, discovers Luther and the Jansenists.  

Entered at the university of Leipzig in 1661, one authorizes it to study the modern thinkers - Bacon, Campanella, Gassendi, Hobbes and, indirectly, Descartes and Galileo -, which enables him to discover the mechanism and the atomism. In 1663, it writes its thesis on the principle of individuation then, in Iéna, looks further into its knowledge in mathematics, before continuing studies of right to the university of Altdorf, close to Nuremberg, where it obtains, in 1666, its doctorate. The same year appears its combinative Art, which confirms its taste for logic and calculation mathematics.

In fact the applied sciences and the alchemy impassion it at the twenty years age, when it enters the company of the Rosicrucian brotherhood. Become to advise of the Electorate of Mainz, in 1667, it prepares a project of unification of the German right and works with the reunification of the Churches catholic and Protestant. From 1672 to 1676, it remains in Paris, where it returns visit in Malebranche, the Cartesian philosopher, and studies questions of philosophy and theology at the sides of Arnauld, as well as mathematical problems accompanied by Huygens. Its discoveries concerning differential and integral calculus, its calculating machine, more sophisticated than that of Pascal, reveal his full dimension of European scientist. Also it meets Spinoza, in $the Hague, and the naturalist Antonie Van Leeuwenhoek, in Amsterdam.  

A multidisciplinary research activity
During thirty-nine years, Leibniz will reside at Hanover, where it fills, as of its return of Paris, dual employment of librarian and advising justice at the court. Whereas he is consulted on the economic affairs, the mines, manufactures, the taxation, the meeting of the Churches, he applies his new calculation to the geometry, mechanics and physics. These multiple activities do not prevent it carrying out face of work of right and religious philosophy, creating a “universal characteristic”, from working out a new logic and of matured the philosophical ideas started for the Parisian period. Even if it does not publish anything, years 1677-1680 are among most fertile of its life, because to its preceding activities searchs for geology are added, and it is named historiographer of the house of Brunswick. Its work of historian and archivist leads it to the court of Vienna, where it meets prince Eugene from Savoy, to which it dedicates Monadologie. Also it maintains the relations with Charles VI, the emperor of Austria, like with the Pierre tsar the Large one and Charles XII of Sweden. In 1700, it founds the Company of sciences of Berlin, which it will chair during ten years.  

Leibniz is more often in Vienna than in Hanover, where it feels to come his disgrace. Indeed, in August 1714, the Voter of Hanover reaches the throne of Great Britain under the name of George I er, but the philosopher is not invited to follow it. Death, in 1705, of Sophie-Charlotte, Electrice de Brandebourg, which took it under its protection, and the death of his/her mother, in 1714, accentuate its loneliness. Its health has left him little respite for its fifty years. It is however in the last part of its life that he writes the New Tests on the human understanding - a work written in French, as most his works -, but which he does not publish because of the death of his John Locke adversary; the Tests of théodicée, plea in favor of God, as well as Monadologie and the Principles of nature and the grace, are its most controlled texts.  

After an exceptional notoriety during the major part of his existence, Leibniz knew a tragic loneliness. He dies in November 1716; only its secretary attends his burial. But in Paris, the Academy of Science pays homage to him.  
 

One of the central theses of the doctrines is that nothing is founded without reason, order, absolute necessity (subjected to the only principle of non-contradiction, which orders with the gasolines), or without hypothetical need (depend on the prerequisites, which orders with the existences). All is in conformity, in addition, with the rule of best. God, choosing to make occur with the existence this world rather than another, wanted to carry out the richest harmony and, for the creatures, greatest excellence. The double principle of best contains in fact the principle of continuity, according to which “nature never makes jumps”, and the principle of the indistinguishable ones, according to which there are never two identical beings in nature because they are always marked of a difference, was it infinitesimal.  

In the Leibnizian vision, very thus organizes itself in order to emphasize the infinite variety to be it and of knowing, all contributes to give a reason and a direction to this diversity. The effort to release the unit and to determine true reality - named substance then monad - crosses all the areas of the knowledge which the imposing doctrines of Leibniz embrace.

Geometry and metaphysics
It is in the wake of Ars got a move on (1275) of Raymond Lulle that Leibniz plans, since 1666, to constitute an alphabet of the human thoughts, signs or elementary characters invariable, likely to give place to all the possible combinations (i.e. noncontradictory). This general science has to provide a universal symbolic system: “characteristic” - alphabetical or numerical - which should be at the same time independent of the languages particular and richer, more precise and simpler than them, but also easy to handle and applicable to any discipline, in particular with the geometry.  

 Leibniz will develop a computational tool and a marking system in a field which did not appear to lend itself to the arithmetic apprehension: infinite sizes. He works out a method of addition or of integration of the infinitely small quantities, tests several notations, and, independently of the calculation of the fluxions established by Newton, arrives, in 1675, with the algorithm which then makes possible the calculation of the infinitely smalls in all the orders of magnitude.  

The analysis of the infinitely smalls leads Leibniz to conceive space and time like reports of coexistence or successiveness and to be opposed to the Cartesian design of the extent: divisible ad infinitum, the extent cannot be the gasoline of the matter. The atomism is him also to fly in glares, because it is not the ultimate ones and indivisible material particles which resist the analysis. The movement is not considered by Leibniz like a visible local displacement, but like an expressive process of an invisible force. Whereas the Cartesian axiom indicates it like “or the product momentum of the masses by the speed which is preserved” (translated by mv), Leibnizian dynamics defines it as “the quantity of lifeblood or product of the masses by the squares their speeds” (translated by mv 2). It is the concept of conatus - the infinitely small of the movement, internal principle, almost spiritual element - which prepared, since 1670, the doctrines of the force activates (screw activ a).  

 Convinced that “same mechanical principles, i.e. the general laws of nature, are born from higher principles and could not be explained by the quantity alone and geometrical considerations”, Leibniz rejects the pure geometrism: he challenges the Cartesian design of the substance (in particular extent-substance, which does not express the change, essential quality of the concept) and refuses to design like substance the matter, space and time. For him, they are only “phenomena” related to our perception. Behind the phenomenon, it is necessary to reveal the substance, only real entity. Thus, at Leibniz, physics joined metaphysics.  

The monad, only substantial unit
Determined outside, the substance is force; determined inside, it is form, heart, spirit. The substantial unit is simple, without extent, figure and divisibility: the monad does not start nor does not finish naturally, it cannot be modified in its interior by some other creature. Struck seal of the intrinsic difference, it cannot be defined by itself but only by his relationship with the others.  

 “Without doors nor windows”, but equipped with perception (representation of the multiple in the unit) and with appétition (tendency to pass to more distinct perceptions), the monads do not have the same degree of perfection. Thus, at the living beings, they go from the simple substance (entéléchie), which is without memory, with the heart equipped with memory and feeling, then with the spirit (heart) reasonable specific to the man. Two great principles govern the life of the spirits: the principle of non-contradiction and that of sufficient reason. And “the last reason of the things must be in a substance necessary and perfect”, i.e. God.  

 Beginning first and term of the series, only God has the concept supplements of all that was, is and will be. He only is necessary and “has this privilege which it is necessary that there exists if it is possible”. Its gasoline implies the existence. The metaphysical need founds and orders the physical and hypothetical need, i.e. the world of the contingent existences. Monad of the monads, “God alone is the primitive unit, or the originating simple substance of which all the monads are productions”.  

Each monad is alive mirror of the universe. Superior with the other substances, the spirit is the image of the divinity: he “imitates in his department and his small world where it is allowed to him to exert, which God makes in the large one”. Thus, all the spirits are members of the City of God, as in Augustin saint.  

 The preestablished harmony
Leibniz initially seeks to show the harmony of the two natural reigns, that of the body (controlled by efficient causes) and that of the heart (controlled by final causes). Thereafter, he affirms that the “harmony preestablished from time immemorial” characterizes as much the report of the various monads as that which exists between the physical reign of nature and the moral reign of the grace. Because, right from the start, God regulated the agreement between all the substances by imperceptibly bringing nature to the grace which improves it. There still, the philosopher applies the principle of continuity.  

The beauty and kindness harmonics of the world, which “exempts the most happiness or of possible joy”, are contradictory seemingly with the evil which makes suffer here or there and involves irrational decisions. Shades good, dissonance which makes taste still the consonance more, the evil does not blame the principle of harmony: it is source of afflictions which are, in fact, from the ways shortened towards the greatest perfection.  

Just as the problem of the evil in failure the principle of harmony puts by no means, in the same way the need does not destroy freedom. The free choice, which “inclines without requiring”, belongs to the spirits, which, with the image of God, are determined by reasonable reasons and the will. Thus, the freedom of indifference is, for Leibniz, a pure extravagance or a fiction.

To reconcile rationalism and empiricism

The Leibnizian doctrines of insensitive perceptions order the showpieces of the system: the preestablished harmony of the heart and the body, but also of the monads; the theory of freedom and the choice; the thesis on the intrinsic differences with the hearts and the things; design of death and the life on an infinitesimal scale; the definition of the movement infinitely small; the theory of knowledge. This last tent to reconcile the two traditionally opposite approaches: rationalism and empiricism.  

Leibniz refutes, indeed, the thesis of the “clean slate” according to which all knowledge is provided by the directions; he is opposed to this vision which compares the heart to a material entity. While admitting that “it is nothing in the heart which does not come from the directions”, it however considers which those give us only of the individual examples: the directions cannot found sciences where reign the truths necessary. For him, it is the heart which “contains the being, the substance, one, the same one, the cause, perception, the reasoning and quantity of other concepts that the directions could not give”. However, the spirit contains, before even any experiment, of “small insensitive perceptions”, too small to be apprehended by us.  

Leibniz thought of having found the axioms of a “also distant philosophy of the formalism and materialism which will reconcile and preserve what there is of Juste in one and the other”. Channeling the extremes, its system tends towards the ideal of Aristote: it aims at the medium, the mathematical point of excellence.