Tentamen Anagogicum: An Anagogical Essay in the Investigation of Causes

A light ray's path, used to argue that physics needs purposes and to doubt that Descartes found the law of refraction.

by Gottfried Wilhelm Leibniz20 passages held

French, the original language

Original title: Essai anagogique dans la recherche des causes
First published: 1890(published posthumously)
Original language: French

Overview

Anagogical, Leibniz explains at the start, is the philosophers' and theologians' word for whatever leads up to the supreme cause, and this French essay of about 1696 argues that physics leads there too. The mechanical philosophers of the century, Descartes among them, had banished final causes, explanation by purpose, from the study of nature. Leibniz answers that the laws of motion cannot be derived from geometry alone, and that looking for the simplest or most determined outcome is sometimes the way to find a law. His chief example comes from optics, where he had once proposed, as a general principle, that light travels from one point to another by the easiest path. Pierre de Fermat, the French mathematician, had explained refraction with a similar principle, the path of least time, and was criticised because the principle seemed to appeal to purpose; Leibniz found it all the finer for that. He also doubts that the law of refraction was Descartes' discovery at all. He credits Willebrord Snell, the Dutch mathematician, who died before publishing it but taught it to his students, and suggests that Descartes picked it up in Holland. A marginal note names William Molyneux as the author of a work on optics, published in England, that had acknowledged Leibniz's principle.

Key concepts

What does ‘anagogical’ mean in the title?

Leading upward to the supreme cause. Leibniz explains at the start that philosophers and theologians use the word for whatever leads up to the highest cause, and his essay argues that physics does this too: the study of how bodies and light behave points beyond geometry to a wisdom that chooses.

What are final causes, and why had physics banished them?

Explanations by purpose: saying what something happens for, rather than only what pushes it. The mechanical philosophers of the century, Descartes among them, had banished them from the study of nature. Leibniz answers that the laws of motion cannot be derived from geometry alone, and that looking for the simplest or most determined outcome is sometimes the way to find a law.

What is the principle that light takes the easiest path?

Leibniz’s general principle in optics: light travels from one point to another by the easiest path. Pierre de Fermat had explained refraction with a similar principle, the path of least time, and was criticised because it seemed to appeal to purpose. Leibniz found it all the finer for that: it showed a law found by asking which outcome is simplest or most determined.

Who discovered the law of refraction, according to Leibniz?

Willebrord Snell, the Dutch mathematician, who died before publishing it but taught it to his students. Leibniz doubts the law was Descartes’ discovery at all and suggests Descartes picked it up in Holland. A marginal note adds that William Molyneux’s work on optics, published in England, had acknowledged Leibniz’s own principle.

Themes of the book

What this book returns to, gathered into themes and ordered by how much of the text each one occupies.

The Easiest Path of Light

Does nature act for purposes, and may a physicist say so? The mechanical philosophers had banished final causes; Leibniz uses a ray of light to argue for them.

Anagogical, Leibniz explains, names whatever leads up to the supreme cause, and his claim is that physics leads there too. The laws of motion cannot be derived from geometry alone, and looking for the simplest or most determined outcome is sometimes how a law is found. Optics is his proof: light travels from one point to another by the easiest path. Fermat had explained refraction by the path of least time and was criticised for seeming to appeal to purpose; Leibniz found the principle all the finer for that. He also doubts the law of refraction was Descartes’ discovery, and credits Willebrord Snell.

final causes
teleology
mechanism
optics
refraction
least action
optimization
laws of nature
divine wisdom
perfection
simplicity
explanation
philosophy of physics

Enter a dialogue

Within this work

passages held: 20
distinct concepts: 44
by passages held, corpus-wide: #779

What this book thinks together

The wheel takes this book’s leading concepts and shows how often they come up together. The wider the band between two, the more of its passages speak of both. Among them, most often together: “optics” and “teleology”.

Concept co-occurrence, strongest first 2 concepts, joined by 1 pairing. 16 pairings reach beyond these concepts and are not drawn.
Concept	Paired concept	Shared passages
optics	teleology	2

Works held

The author's work in order, this book marked in place. Your-language title first, the original beneath it where the two differ; side chips show which full texts are held.

1684 Meditations on Knowledge, Truth, and Ideas (Meditationes de cognitione, veritate et ideis)
A journal article of 1684, written into the Arnauld–Malebranche quarrel over ideas; its grades of knowledge return in the Discourse on Metaphysics and the New Essays.
LA
1691 Whether the Essence of a Body Consists in Extension (Lettre sur la question si l'essence du corps consiste dans l'étendue)
Against the Cartesian view that body is nothing but extension: a letter to the Paris Journal des Sçavans in 1691, followed by a second in 1693.
FR
1695 New System of Nature (Système nouveau de la nature et de la communication des substances)
Leibniz's first public statement of his system, printed in Paris in 1695; his replies to Foucher and Bayle kept it in the journals until 1698.
FR
1698 On Nature Itself (De ipsa natura)
An answer to Johann Christoph Sturm in the Acta Eruditorum of 1698, defending forces inside created things and tying the dynamics to the metaphysics of substance.
LA
1710 Theodicy (Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal)
Published anonymously at Amsterdam in 1710, it was the book by which the eighteenth century knew Leibniz, and the one Voltaire answered with Candide.
FR
1717 The Leibniz-Clarke Correspondence (Recueil des lettres entre Leibniz et Clarke)
Ten papers exchanged through the Princess of Wales in 1715–16, cut off by Leibniz's death and published by Clarke in 1717.
FR
1718 Principles of Nature and Grace, Based on Reason (Principes de la nature et de la grâce fondés en raison)
A companion summary from the same Vienna months as the Monadology, long mistaken for it and printed before it, in 1718.
FR
1720 Monadology (Monadologie)
Written in French in 1714, it was known for over a century only in German and Latin translation.
FR
1765 New Essays on Human Understanding (Nouveaux Essais sur l'entendement humain)
The book-length reply to Locke, written as a dialogue in 1703–04, withheld after Locke's death and first printed in 1765.
FR
1840 Discourse Touching the Method of Certitude and the Art of Discovery (Discours touchant la méthode de la certitude et l'art d'inventer)
A plea for royal patronage of the sciences, addressed to an unnamed king, apparently Louis XIV, setting out the method of certainty and art of discovery Leibniz pursued for decades.
FR
1840 On the Ultimate Origination of Things (De rerum originatione radicali)
A short Latin essay of 1697 on why there is a world at all, left in manuscript until 1840.
LA
1840 Reflections on the Doctrine of a Single Universal Spirit (Considérations sur la doctrine d'un Esprit Universel Unique)
A French essay written in 1702 at the Prussian queen's palace outside Berlin, and left unprinted until 1840.
FR
1846 Discourse on Metaphysics (Discours de métaphysique)
The opening statement of Leibniz's mature metaphysics, written early in 1686 and left unprinted until 1846.
FR
1846 The Leibniz-Arnauld Correspondence (Correspondance de Leibniz et d'Arnauld)
The exchange of 1686 to 1690 between Leibniz and Arnauld over the Discourse on Metaphysics, every letter carried by the Landgrave of Hessen-Rheinfels.
FR
1854 Refutation of Spinoza (Animadversiones ad Joh. Georg. Wachteri librum de recondita Hebraeorum philosophia)
Private Latin notes on Wachter's book about Spinoza and the Kabbalah, given their title by the French scholar who published them in 1854.
FR
1890 Tentamen Anagogicum: An Anagogical Essay in the Investigation of Causes (Essai anagogique dans la recherche des causes) you are here FR
1903 New Openings (Nouvelles Ouvertures)
Written in French in 1686, by the Academy edition's dating, and left in manuscript until Couturat printed it in 1903.
FR
1903 Preface to the General Science (Préface de la Science générale)
Probably from 1677, an unfinished preface to the universal language of reasoning, unprinted until 1903.
FR
1915 Confessio Philosophi (Confessio philosophi)
Leibniz's first developed theodicy, a Latin dialogue from his Paris years; revised after Steno's objections, its account of sin returns much changed in the Theodicy of 1710.
LA

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