Gottfried Wilhelm von Leibniz

Biography

Orphan of mother at 6 years, it is raised by his father, professor of moral Philosophie to the Université of Leipzig. This one learns how to him to read, but Leibniz, early child, affirmed to have learned by itself the Latin . In 1663, it obtains its baccalaureat in old philosophy, then between at the university of right of Leipzig. In 1666, he becomes doctor in right to Nuremberg and refuses shortly after a post of professor. It is affiliated at a company of the Rose Croix, of which he will be secretary during two years.

In 1669, he becomes adviser with the Chancellery of Mainz, near the baron Johann Christian von Boineburg. He works then on several works on political topics ( Modèle of political demonstrations for the election of the king de Pologne ) or scientists ( Nouvelles Assumption physics , 1671).

He is sent in 1672 to Paris, on mission diplomatic says one, to convince Louis XIV to rather carry his conquests towards the Egypt than the Germany. He remains there until 1676 and meets the large scientists of the time there: Huygens and Malebranche, inter alia. It is devoted to mathematics and laisse in Paris its manuscript on the arithmetic squaring of the circle. He also works on what will be the Infinitesimal calculus. He conceives in 1673 a calculating machine the following the example of Blaise Pascal. Before joining Hanover, it goes to London to study certain writings of Isaac Newton, throwing, both, the bases of the Integral calculus and differential. It also passes by $the Hague where it meets Baruch Spinoza.

In 1676, with died of its guard, the baron von Boyneburg, the duke of Brunswick appoints it librarian of the Hanover. It remains at this station with the service of the dukes of Hanover during nearly 40 years. It also deals of mathematics, physics, Religion and Diplomatie. In 1684, it publishes in the Acta Eruditorum its article on the Différentielle S and in 1686 that on the integral . In 1686, it publishes in French his Discours of metaphysics . In 1687, it launches out in a Histoire of the house of Brunswick , for which it traverses Italy in search of documentations. In 1691, it publishes in Paris, in the Journal of the scientists , a Essai of dynamics which defines the energy and the action. In 1700, it creates a Académie with Berlin which will be inaugurated only in 1711. In 1710, it publishes its Essais of Théodicée , results of discussions with the philosopher Pierre Bayle.

Recognized like more large intellectual of Europe, and pensioned by several large course (Pierre Large the in Russia, Charles VI in Austria which does it Baron), he dies the November 14th 1716.

Like philosopher, it was interested extremely early in the Scolastique and the syllogistic . He conceived the project of a Encyclopédie or “universal library”:

“It imports with the happiness of mankind that an Encyclopedia is founded, i.e. an ordered collection of truths sufficient, as far as possible, with the deduction of all useful things. ” Initiated and specimina scientiae generalis , 1679 - 1680.

As mathematician, it inserted sciences in the new era of the analyzes integro-differential.

April 9th 1673 -->

Philosophy

The Monadologie

Written in 1714 and not published the alive one of the author, the Monadologie represents one of the last stages of the thought of Leibniz. In spite of apparent resemblances to former texts, the Monadologie is strongly distinguished from works like the Discours of metaphysics or the new Système of the nature and the communication of the substances . The concept of individual substance present in the Discours of metaphysics should not be confused with that of monade.

The force

For Leibniz, the Physique has its Raison in the Métaphysique. If physics studies the movements of the Nature, which reality is this movement, which Cause does have he? The movement is relative, C. - with-D. a thing is driven according to the prospect from where look at we it. The movement is thus not reality itself; reality is the force which remains apart from any movement and which is the cause: the force remains, the rest and movement being relative phenomenal differences.

Leibniz defines the force as “what there is in the state present, which carries with oneself a change for the future. ” This Théorie is a rejection of the atomism; indeed, if the Atome is an absolutely rigid reality, it cannot lose of force in the shocks. It is necessary thus that what one names atom is actually composed and elastic. The idea of absolute atom is contradictory:

“the atoms are only the effect of the weakness of our imagination, which likes to rest and to hasten to come under divisions or analyzes. ”

Thus the force is reality: the force is Substance, any substance is force. The force is in a state, and changes according to laws of the change. This succession of changing states has a regular order, C. - with-D. each state has a reason (cf principle of sufficient reason): each state is explained by that which precedes, it finds its reason there. To this concept of Loi is also attached the idea of individuality: individuality is for Leibniz a series of changes, series which is presented in the form of a formula:

“the law of the change makes the individuality of each particular substance. ”

The monade

Any substance develops thus according to interior laws, according to its own tendency: each one has its own law. Thus, if we know the nature of the Individu, let us can us derive all the changing states from them. This law of individuality implies passages in states not only new, but more perfect.

What exists is thus for Leibniz the individual one; there exist only units. Neither the movements, nor even the bodies have this substantiality: the Cartesian wide substance supposes something of wide indeed, it is a compound, an aggregate which does not have by itself reality. Thus, without absolutely simple and indivisible substance, there would be no reality. Leibniz names monade this reality. The monade is conceived according to the model of our heart:

“unit substantial asks being achieved, indivisible and naturally indestructible, since its concept wraps all that must arrive to him, which one could find neither in the figure nor in the movement… But well in a heart or substantial form, with the example of what one calls me. ”

We make the observation of our internal states, and these states (Sensation S, Pensée S, Sentiment S) are in a perpetual change: our heart is a monade, and it is according to it that we can conceive the reality of the things, because there is undoubtedly in the nature of others monades which is similar for us. By law of analogy (law which is formulated “this just like”), we conceive all Existence like being only one difference in degree relative to us. Thus, for example, there are lower degrees of Conscience, obscure forms of the psychic Vie: there are monades with all the degrees of clearness and darkness. There is a continuity of all the existences, continuity which finds its base in the principle of reason.

Consequently, since there exists only being gifted of more or less clear representations, whose gasoline is in this representative activity, the matter is reduced with the state of Phénomène. The Birth and the Mort are also phenomena in which the monades are darkened or clear up themselves. These phenomena have reality insofar as they are connected by laws, but the world, generally, exists only as a Représentation.

These monades, while developing according to an internal law, does not receive any influence of outside:

“7. II does not have there average also to explain how Monade can be faded or changed in its interior by some other creature, since one could there nothing transpose, nor to conceive in it any internal movement which can be excited, directed, increased or decreased in it, as that may be in the compounds or there is change between the parts. Monades do not have windows by which something there can enter or leave. ” (Monadologie)

The preestablished harmony

Consequently, how to explain that all occurs in the world as if the monades were influenced really mutually? Leibniz explains this agreement by a universal Harmonie between all the beings, and by a common creator of this harmony:

“Also God alone makes the connection and the communication of the substances, and it is by him that the phenomena of the ones meet and agree with those of the others, and consequently that there is reality in our perceptions. ” (Speech of metaphysics)

If the monades seem to hold account from/to each other, it is because God created them so that it is thus. It is of God that the monades are created of a blow by fulguration , to the state of individuality which does them like small gods. Each one has a point of view of on the world, a sight of the Univers in miniature, and all its prospects have an internal coherence together, while God has the infinity from the points of view which it creates in the form of these individual substances. The force and the thought close friends of the monades are thus a divine force and a thought. And it harmony is right from the start in the spirit of God, C. - with-D. it is preestablished.

It finally comes out from this idea of the monade that the universe does not exist apart from the monade, but that it is the whole of all the prospects. These prospects are born from God. All the problems of the Philosophie are thus moved in the Théologie.

This transposition poses problems which are not really solved by Leibniz:

how an absolute substance can be born?
how God can it have an infinity of prospects and make substances within a preestablished harmony of them?

Malebranche will summarize all that in a formula: God does not create gods . What also means that Spinoza was more consequent when he admitted the existence only of only one substance.

Union of the heart and the body

Its Theory of the union of the heart and the body follows its idea of the monade naturally. The body is an aggregate of monades, whose relationship with the heart is regulated from the beginning as two clocks that one would have synchronized. Leibniz describes thus the representation of the body (C. - with-D. multiple) by the heart:

“the hearts are units and the bodies are multitudes. But the units, though they are indivisible, and without part, do not leave represent multitudes, about as all the lines of the circumference meet in the center. ”

Théodicée

The term of “ théodicée means” étymologiquement “; justification of Dieu ” (of the Greek théos, God, and dikè, justification), it is in other words a speech proposing to take the defense of God, face in particular to the question of its responsibility relating to the existence for the evil in this world. It is essential to underline the main issue of théodicée the leibnizienne. The question is initially: how to grant the existence of the evil with the idea of the general perfection of the universe? But, across the internal difficulties with metaphysics leibnizienne, one finds the problem following: how to grant the idea of the responsibility or the culpability of the man in the evil with the feeling which this man acts in the only way of which it was possible that it acted. The response of Leibniz to the conflict between need and freedom is original.

The example of Judas the traitor, such as it is analyzed in section 30 of the Speech of Metaphysics is lighting: admittedly, it was foreseeable of any eternity that this Judas-là from which God let the gasoline come to the existence, would sin as it sinned, but nevertheless it is well him which sins. The fact that this limited being, imperfect (like any creature) enters the general plan of creation, and thus car in a direction its existence of God, does not wash it in itself of its imperfection. It is well him which is imperfect, just as the toothed wheel, in a watch, is anything else only one toothed wheel: the fact that the clock and watch maker uses it to manufacture a watch makes this clock and watch maker responsible owing to the fact that this toothed wheel is not anything else, nothing for better than a toothed wheel.

The sufficient , sometimes named reason “determining reason” or the “great principle of why”, is the principle which guided Leibniz in its research: nothing is without a reason which explains why it is rather than it is not, and why it is thus rather than differently. Leibniz does not deny that the evil exists. He affirms however that all the evils cannot be less: they find their explanation and their justification as a whole, in the harmony of the table of the universe. “The apparent defects of the whole world, these spots of a sun of which ours is only one ray, raise well its beauty far from decreasing it”. ( Théodicée , 1710 - publication in 1747).

Answering Bayle, it establishes the following demonstration: if God exists, it is perfect and single. However, if God is perfect, he is “necessarily” the Almighty, any kindness and any justice, any wisdom. Thus, if God exists, he, by need, been able, wanted and knew to create the least imperfect of all the imperfect worlds; the world best adapted for supreme purposes.

In 1759, in the philosophical Tale Ingenuous, Voltaire makes of his Pangloss character the spokesperson of the providentialism of Leibniz. It voluntarily deforms its doctrines there by reducing it to the formula: “all is as well as possible in Brave New World possible”.

It should be noted that this formula is not in work leibnizienne. Jean-Jacques Rousseau will recall to Voltaire the aspect forcing of the demonstration of Leibniz: “These questions refer all to the existence of God. (…) If the first proposal is granted to me, never the following ones will not be shaken; if it is denied, one should not discuss on its consequences. ” (Letter of the August 18th 1756)

Criticism voltairienne of Leibniz rests on a misinterpretation, confusing the concepts of perfection and optimum. According to Leibniz, all does not go to wonder and all is not perfect in this world. This philosopher knows well that the universe is not Eldorado nor one of the “Utopias” of “novel”, but the real universe, with his procession of evils and imperfections. The error of Voltaire, refuted in advance by Leibniz, is to distribute the perfection of the whole of the universe to each one of its elements. If the greatest unit is that which comprises the greatest number of elements, the most beautiful unit is not always that whose each element, considered separately, is most beautiful. To take again its words, “the part of best all is not necessarily the best than one could make this part, since the part of a beautiful thing is not always beautiful”; often, indeed, “they are some disorders in the parts which marvelously raise the beauty of the whole”. To emphasize a diamond in an ornament, it is necessary precisely that the bottom is not itself out of diamond. Which merit would be there to be virtuous in a world where it would be impossible to make the evil? The virtue does not have a value that as it must resist the moral evil. No matter what Voltaire said some, Brave New World is not the perfect world, since it is because same of its harmonious imperfections that it is optimal.

New tests on the human understanding

It is the response of Leibniz to the Essai on the human understanding of John Locke. The English philosopher defends a position empirist, according to which all our ideas come us from the experiment. Leibniz, in the form of an imaginary dialog between Philalèthe, which quote the passages of the book of Locke, and Theophilus, which opposes the arguments leibniziens to him, defends a position inneist: certain ideas are in our Esprit as of the birth. In fact the Idée S are constitutive of our Entendement even, like that of Causalité. However one can admit that all that is in our understanding comes from the Expérience, except the understanding itself. As for the innate ideas like that of causality, it is the experiment which makes it possible certainly to activate them, but it was necessary for that they exist initially potentially in our understanding.

The Nouveaux tests are finished in 1705. But the death of Locke convinces Leibniz to defer to later their publication. They will appear finally only in 1765.

Mathematics

Mathematical work of Leibniz is in the Journal of the scientists of Paris, the Acta Eruditorum of Leipzig (which it contributed to found) like in its abundant correspondence with Huygens, the brothers Bernoulli, the Hospital, Varignon, etc

The “ new calcul ”

The algorithm différentio - integral completes a research begun with coding from the algebra by Viète and the algebrisation from the geometry by Descartes. All the 17th century studies the indivisible one and the infinitely small. Like Newton, Leibniz early dominates the indeterminations in the calculation of the derivatives. Moreover it develops an algorithm which is the major tool for the analysis of a whole and its parts, founded on the idea that any thing integrates small elements whose variations contribute to the unit. Its work on what it called the “ specious supérieure ” will be continued by the brothers Bernoulli, the marquis of Hospital, Euler and Lagrange.

Notation of Leibniz

Infinitesimal calculus: Newton or Leibniz?

In the History of the infinitesimal calculus, the lawsuit of Newton against Leibniz remained famous. Newton and Leibniz had found art to raise the indeterminations in the calculation of the tangents or derived. But Newton published (its lawsuit late intervenes in 1713, almost 30 years after the publications of Leibniz: 1684 and 1686) and, especially, Newton neither the différentio-integral algorithm based on the idea has that the things are made up small elements, nor arithmetic approach necessary to differentials conceived like “ small differences finies ”.

Other work

Leibniz is interested in the systems of equations and has a presentiment of the use of the determinant S. In its treaty on combinative art, general science of the form and of the formulas , it develops techniques of substitution for the solution of equation. He works on the convergence of the series S, the development in whole Série of the functions like the Exponentielle, the Logarithme, the goniometrical functions (1673). He discovers the Courbe brachistochrone and is interested in the Rectification curves (calculation their length). He studied the treated conical of Pascal and written on the subject. He is the first to create the function

x \ mapsto a^x

( conspectus calculi ). He studies the envelopes of curves and the search for extremum for a function ( Nova methodus pro maximis and minimis 1684). He designs an arithmetic machine inspired of the Pascaline. He tries also an incursion into the Graph theory and the Topologie ( analysis situs ).

For the anecdote, one finds in the Report of the Academy of Science (Paris, 1703, pp. 85-89 of the Memories) an article of Leibniz entitled Explication of arithmetic binary, which makes use of only characters 0 & 1, (…) . Recognizing this manner of representing the numbers as being a very remote heritage of the founder of the Chinese Empire “ Fohy ”, Leibiz wonders lengthily about the utility of the concepts which it has just presented, in particular with regard to the arithmetic rules which it develops. Finally it seems to conclude that the only utility which it sees in all this is a kind of essential beauty, which reveals the intrinsic nature of the numbers and their mutual bonds. It is a quarter of millenium before the appearance of the Informatique…

Physics

Leibniz was also physicist like all the mathematicians of his time. Its contributions in physics are considerable.

Logic

The Logical which developed Leibniz was undoubtedly one of most important since the invention of the syllogistic aristotelician.

The two great characteristics of the logic of Leibniz consist on the one hand in the fact that he wanted to constitute a universal language (the lingua caracteristica universalis ) fascinating of account not only knowledge Mathématiques, but as the Jurisprudence, the ontology (Leibniz criticized the definition as Rene Descartes gave Substance) even music.

Concurrently to this universal language, Leibniz dreamed of a logic which would be algorithmic Calcul and thus mechanically décidable ( calculus ratiocinator ). Leibniz announces the artificial and purely formal Langue thus developed by Frege.

See too

In Metaphysical philosophy

Descartes
Characteristic of Leibniz
Compossibilité
Monadologie
Spinoza

In mathematics

Formulas of Leibniz: for the Derived nth from a product, for the calculation of $\ pi$ , for the calculation of the determinant
vector Function and scalar function of Leibniz in the Barycentre S as well as the Theorem of Leibniz in this same field
Criterion of Leibniz for the convergence of a alternate series
Mathematical in Europe at the XVIIe century

In cookie factory

the famous German cookies “Choco Leibniz” and the Small butter German Leibniz Keks , manufactured since 1891, were named in the honor of the philosopher of Hanover by the cookie factory Bahlsen, founded in this same city.

Works

The work of Leibniz was written for half in Latin and a third in French.

Of arte combinatoria (1666)
New method for the study of the right (1668)
Theory of the concrete movement and the abstract movement (1670)
arithmetic Squaring of the circle, the ellipse and the hyperbole ( C . 1674)
differential Calculus: New method for maximum and minimum one, as well as the tangents, which butts neither against the fractions nor against the irrational ones, with an original mode of calculation (in Latin, Acta Eruditorum, 1684)
Intégrales: Higher geometry and analyzes the indivisible ones like infinite (in Latin, Acta Eruditorum, 1686)
Discours of metaphysics , (1686)
Dissertation on combinative art (1690)
Essai of dynamics (Newspaper of the Scientists, 1691)
new Système of the nature and the communication of the substances (1695)
Nouveaux Tests on the human understanding , (1705)
Essais of théodicée (1710)
Monadologie (1714)
Discours concerning the method of certainty and art to invent to finish the arguments and to make in little time of great progress

Translations in mathematical French of works:

arithmetic Squaring of the circle, the ellipse and the hyperbole and trigonometry without trigonometrical tables which is the corollary ; introd., transl. and notes of Marc Parmentier; Latin text published by Eberhard Knobloch. Paris: J. Vrin, 2004. (Mathesis). ISBN 2-7116-1635-5.
regard of appearances. 21 manuscripts of Leibniz on the probabilities, the game theory, the life expectancy ; established text, transl., introd. and annotated by Marc Parmentier. Paris: J. Vrin, 1995. (Mathesis). ISBN 2-7116-1229-5.
the geometrical characteristic ; text established and annotated by Javier Echeverría; translated, annotated by Marc Parmentier. Paris: J. Vrin, 1995. (Mathesis). ISBN 2-7116-1228-7.
Birth of differential calculus. 26 articles of the Acta Eruditorum ; introd., transl. and notes by Marc Parmentier. Preface of Michel Serres. Paris: J. Vrin, 1989. (Mathesis). ISBN 2-7116-0997-9.

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