# Lambert, Johann Heinrich (1728–1777)

# LAMBERT, JOHANN HEINRICH

*(1728–1777)*

Johann Heinrich Lambert, the German mathematician, physicist, astronomer, and philosopher, was born in Mulhouse, Alsace. He taught himself mathematics, philosophy, and Asian languages; after 1748 he served as tutor in a Swiss family, traveling about Europe with his pupils for several years. He became a member of the Munich Academy in 1759 and of the Berlin Academy in 1764. In 1765 he was appointed by Frederick II as Prussian surveyor of public works. He did research in heat, light, and color and was the founder of the science of photometry. In mathematics Lambert demonstrated that *π* is an irrational number, and he introduced the conception of hyperbolic functions into trigonometry. In his *Kosmologische Briefe über die Einrichtung des Weltbaues* (Cosmological letters on the structure of the universe; Augsburg, 1761), Lambert proposed a cosmogonic hypothesis based on Isaac Newton's theory of gravitation; it was similar to the nebular hypothesis proposed earlier by Immanuel Kant in his *Allgemeine Naturgeschichte und Theorie des Himmels* (Königsberg and Leipzig, 1755) but unknown to Lambert.

Lambert's *Neues Organon, oder Gedanken über die Erforschung und Bezeichnung des Wahren und dessen Unterscheidung von Irrtum und Schein* (New organon, or thoughts on the investigation and indication of truth and of the distinction between error and appearance; 2 vols., Leipzig, 1764) was an attempt to reform Wolffian logic. It was strongly influenced by the logical treatises of the Pietist philosophers A. F. Hoffmann and C. F. Crusius, and like their work it widened the field of logic to cover psychological and methodological questions. Although Lambert believed that metaphysics should follow a mathematical method, he assumed, like the Pietists and John Locke, a multiplicity of elementary notions. The a priori sciences (pure theoretical and practical philosophy) should be constructed by combining these elementary notions mathematically. The final section of the *Neues Organon* discusses appearance and gives a theory of experimental and probable knowledge. It contains rules for distinguishing false (or subjective) appearance from true (or objective) appearance, the latter arising from true perception of the phenomenal world. As a blend of Leibnizian, Wolffian, Lockean, and Pietist elements the *Neues Organon* was neither more original nor more influential in its time than several Pietist treatises on logic or J. B. Basedow's *Philalethie.*

The lesser-known *Anlage zur Architektonik, oder Theorie des Einfachen und Ersten in der philosophischen und mathematischen Erkentniss* (Foundation of architectonic, or theory of the simple and primary elements in philosophical and mathematical knowledge; 2 vols., Riga, 1771) was a much more important work. In this work Lambert, dissatisfied with classical German and particularly Wolffian metaphysics, proposed a far-reaching reform through an analysis of the sources, genesis, and development of the basic concepts and axioms of metaphysics and their interrelations. Reacting also against sensationalism, skepticism, and the new schools of commonsense and popular philosophy, Lambert wished to save metaphysics by presenting it in a phenomenalistic manner (as J. N. Tetens and Kant were to do later).

Following Locke, Lambert assumed a certain set of concepts as given and then examined them. Once the analysis was completed, Lambert held, it would be possible to change from an empirical to a rationalistic procedure—the a priori deductive construction, modeled on the procedures of mathematics, of a body of general sciences that are true both logically and metaphysically. The deduced propositions of these sciences would then be applied to experience in the manner of applied mathematics. The joining of such propositions with rules abstracted from observation and experiments would give a foundation for truth in each of the particular sciences.

There were thus two main aspects to Lambert's philosophy, the analytic and the constructive. The former was the predominating interest in the *Anlage zur Architektonik.* This work consists largely of detailed discussions of, and subtle distinctions between, many of the most common simple notions and axioms and elementary interrelations discussed in traditional metaphysics. This refined analysis, too detailed even to be sampled here, exerted a great influence on Teten's mature work and on the making of Kant's *Kritik der reinen Vernunft.* Kant had earlier been much impressed by the *Neues Organon*, and acknowledged to Lambert in correspondence his interest in Lambert's analyses.

The second, constructive, aspect of Lambert's philosophy was an attempt to develop a mathematical logic (or "intensional calculus") for deducing propositions by an easy and exact method from the simple notions and axioms, once they have been established analytically.

** See also ** Crusius, Christian August; Kant, Immanuel; Locke, John; Logic, History of; Metaphysics; Newton, Isaac; Tetens, Johann Nicolaus.

## Bibliography

### additional works by lambert

*Deutscher gelehrter Briefwechsel.* 5 vols. Edited by Johann Bernoulli. Berlin, 1781–1787. Correspondence.

*Logische und philosophische Abhandlungen.* 2 vols. Edited by Johann Bernoulli. Berlin and Dessau, 1782.

*Abhandlungen vom Criterium Veritatis.* Edited by K. Bopp. Berlin: Reuther and Reichard, 1915.

*Über die Methode, die Metaphysik, Theologie und Moral richtiger zu beweisen.* Edited by K. Bopp. Berlin: Reuther and Reichard, 1918.

### works on lambert

Arndt, H. W. *Der Moglichkeitsbegriff bei Chr. Wolff und J. H. Lambert.* Göttingen, 1959. A mimeographed thesis.

Baensch, O. *J. H. Lambert und seine Stellung zu Kant.* Tübingen, 1902.

Eisenring, M. E. *Johann Heinrich Lambert und die wissenschaftliche Philosophie der Gegenwart.* Zürich, 1942.

Huber, D. *J. H. Lambert nach seinem Leben und Wirken.* Basel, 1829.

Krienelke, K. *J. H. Lamberts Philosophie der Mathematik.* Berlin, 1909.

Lepsius, Johann. *J. H. Lambert.* Munich, 1881.

Zimmermann, R. *Lambert der Vorgänger Kants.* Vienna, 1879.

*Giorgio Tonelli (1967)*

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