The logic of Leibniz^{1}
is assuredly that part of his system that has been most neglected by historians
of philosophy and mathematics. Philosophers, understandably seduced by
his metaphysics, have accorded little attention to his purely logical doctrines
and have barely studied his project for a universal characteristic—no doubt
because of the mathematical form it assumed. Mathematicians, on the other
hand, have looked to Leibniz primarily as the inventor of the differential and
integral calculus and have been engaged neither by his general theories on the
value and importance of the mathematical method nor by his attempts at applying
algebra to logic, which they have contemptuously dismissed as
metaphysics. As a result, neither group has fully grasped the principles
of his system, nor have they been able to reach the source from which both the
infinitesimal calculus and the *Monadology* flow.

There is, of course, the excuse that Leibniz's logical
essays have been published only slowly and very incompletely. Even today
they are scattered piecemeal among various partial editions, most notably the
two in which Gerhardt has so unfortunately separated the mathematical and
philosophical writings,^{2} as if one could
dissect the work of an encyclopedic savant whose philosophy was nourished by
the study of all the sciences and in turn inspired all of his scientific
discoveries. If there is one thinker whose thought cannot be divided with
impunity in this way, it is certainly the one who said, "My metaphysics is
entirely mathematical,"^{3} or again,
"Mathematicians have as much need to be philosophers as philosophers have
to be mathematicians."^{4} This
artificial and arbitrary division between contemporaneous works that mutually
depend on and illuminate one another has had the result of concealing the unity
of the system and of hiding its true principles. Thus the absurd and deplorable
schism between letters and sciences not only compromises the future of
philosophy, but also falsifies its history and renders its past unintelligible
by isolating it from the scientific speculations where it has always taken
root. One sees readily that Leibniz's philosophy was bound to suffer more than
any other, and within this philosophy his logic, precisely because it is the
center of, and the link between, his metaphysical speculations and his
mathematical inventions.^{5}

Not only are the existing editions of Leibniz's
writings incomplete and one-sided, but the logical works have been particularly
neglected in them. Without a doubt, Raspe, then Erdmann, and finally Gerhardt
have each in turn bestowed upon us some fragments; but for every one they have
published, they have left twenty by the wayside that are just as important and
just as polished, if not more so. What is most unbelievable is that they have
passed over nearly all the *dated* fragments. One cannot account for such
negligence except to say that Leibniz's editors have understood nothing of
these fragments and have not been able to appreciate their value. In order to
complete our work, therefore, we have had to investigate the manuscripts
preserved in the library at Hanover and to extract from them the most
interesting fragments, which we shall soon publish.^{6}
We would have thought that after so many editors there would be nothing more to
glean, but we have brought back so rich a harvest of new documents that we have
been obliged to recast our book entirely and to rewrite certain chapters
completely.^{7}

Nevertheless, however important these documents may
be because of their number, scope, and interest, they have not in the least
required us to modify our plan or even to correct our chronological
conjectures; they have served merely to fill some gaps and to confirm our
interpretation. They have chiefly provided a supplementary proof of the
essential conclusion of our work: that Leibniz's metaphysics rests solely on
the principles of his logic and proceeds entirely from them.^{8}

This conclusion, sufficiently justified by works
already published, is corroborated by, among others, a wonderful unpublished
fragment in which Leibniz summarizes in four pages his entire metaphysics by
deducing it from the *principle of reason*. This he formulates rigorously
as follows: in every true proposition, universal or singular, necessary or
contingent, the predicate is contained in the subject; in other words, every
truth is reducible to an identical proposition and must be demonstrable *a
priori* by analysis of its terms.^{9}
From this, Leibniz first deduces the principle of symmetry and the principle of
indiscernibles, and then a series of metaphysical consequences: there are no
purely extrinsic denominations; the complete concept of an individual substance
includes all of its predicates—past, present, and future—and as a result the
entire universe with all of its successive states; all created substances are
only different expressions of a single universe; an individual substance exerts
a physical action on all others, but not a metaphysical action, from which
follows the hypothesis of preestablished harmony; there is no void, nor are
there any atoms; every particle of matter is actually divided infinitely;
bodies have no actual determinate shape; space, time, and motion are no more
than true phenomena; the substance of bodies is a "form" analogous to
the soul; and finally, no substance is able either to come into being or to
pass away naturally. As one sees, these are all the essential theses of the *Monadology*,
and they derive from this single principle of reason, the precise and exact
sense of which is *every truth is analytic*. As a consequence,
everything in the world must be intelligible and logically demonstrable by
means of pure concepts, and the only method of the sciences is deduction. This
can be called the postulate of universal intelligibility. The philosophy of
Leibniz thus appears as the most complete and systematic expression of
intellectualistic rationalism. There is a perfect accord between thought and
things, between nature and the mind; reality is completely penetrable by
reason, because it is penetrated with reason. To characterize this metaphysics
in a single word, it is a *panlogism.*^{10}

This word serves to indicate the fundamental place
that logic must occupy in Leibniz's system. We neither sought this conclusion
nor even foresaw it; we reached it unintentionally and almost in spite of
ourselves. We were proposing simply to study Leibniz as the precursor of modern
algorithmic logic, to analyze his logical and geometrical calculi, and to reconstruct
the basis for his universal characteristic. But when we wanted to return to the
philosophical principles of these theories, we saw on the one hand that they
proceeded from Leibniz's seminal conception of a universal mathematics and from
his youthful invention of the combinatory; on the other hand, that they were
tightly bound up with his attempts at a universal language, as well as with his
great project for a demonstrative encyclopedia, which occupied his entire life.
Finally, it was clear that he had deduced all of his philosophical theses from
the principles of his general science, i.e., from his methodology. In this way,
we were led to discover that his logic was not only the heart and soul of his
system but also the center of his intellectual activity and the source of all
his inventions. In it, we recognize the obscured, or at least concealed, source
from which so many luminous *fulgurations* burst forth.

1. We have adopted the spelling 'Leibniz' in accordance with the philosopher's customary signature (cf. Klopp, IX, 51).

2.
[Here cited as *Math*. and *Phil*., respectively.] In *Phil*.,
there are letters and even some essays with a mathematical content, such as the
letter to Malebranche of 4 August 1679 (*Phil*., I, 342) and *An
Anagogical Essay* (*Phil*., VII, 270; filed in the manuscripts as LH
XXXV 7 Bl. 5). On the other hand, in the mathematical writings there are
numerous letters and fragments of great philosophical interest, notably the
correspondence with Tschirnhaus, and several small works on the philosophy or
logic of mathematics (see Chap. 6, §7; Chap. 9, §4).

3.
Leibniz to L'Hospital, 27 December 1694 (*Math*., II, 258).

4.
Leibniz to Malebranche, 13/23 March 1699 (*Phil*., I, 356). Cf.
Leibniz to the Electress Sophie, 12 June 1700 (quoted p. 262, n. 1). Concerning
his correspondence with Arnauld, which he planned to publish, Leibniz himself
said: "There will be a curious mix of philosophical and mathematical thoughts
which will perhaps in places have the virtue of novelty." Letter to
Basnage de Beauval, 3/13 January 1696, P.S. (*Phil*., IV, 499).

5. The close connection between the infinitesimal calculus and Leibniz's metaphysics is expressly affirmed and clearly defined in a letter to Fardella of 3/13 September 1696: "Perhaps it would not be unprofitable if you were to mention in the preface of your work something about our infinitesimal analysis, which is derived from the deepest roots of philosophy and by means of which alone mathematics has so far carried itself beyond ordinary notions, i.e., beyond imaginable things, in which up till now geometry and analysis have been almost entirely immersed. On the one hand, these new mathematical discoveries will receive illumination from our philosophizing, and on the other they will give to it, in return, their authority" (Grotefend, 210). Is it not a crime to separate what was so intimately related in Leibniz's thought?

6. We do not wish to wait for that occasion to make known our full gratitude to Mr. Laird, director of higher education, who in entrusting us with a mission in Germany allowed us to bring to fruition a double labor; to Counselor Bodemann, chief librarian in Hanover, who freely opened to us the treasure that he guards; and to Mr. Vacca, assistant in mathematics at the University of Turin, who showed us the way to it.

7. Notably Chap. 3 (The Universal Language) and Chap. 8 (The Logical Calculus).

8.
This is the same conclusion that Mr. Russell has arrived at, albeit by a
completely different interpretation, in his *Critical Exposition of the
Philosophy of Leibniz* (Cambridge, 1900).

9. LH IV 8 Bl. 6-7. See the extracts quoted in Chap. 6, §17, especially p. 208, n. 1.

10.
This interpretation seems to us useful for clarifying the relationship between
Leibniz and Kant. The latter radically distinguishes himself from his
predecessor by maintaining the existence of *synthetic a priori*
judgments.

Donald Rutherford, University of California, San Diego / drutherford@ucsd.edu

Last update: March 19, 2002