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LEIBNIZ, GOTTFRIED WILHELM (b. Leipzig,
Germany, 1 July 1646; d. Hannover, Germany,
14 November 1716), mathematics, philosophy, metaphysics.
LEIBNIZ: Physics, Logic, Metaphysics
proposition.24 Viewed methodologically, this means
that, in the principle of sufficient reason, there is a
teleological as well as a causal principle; the particular
import of the proposition is that both principles may
be used in the same way for physical processes and
human actions.
Defending the utility of final causes in physics
(in opposition to the view of Descartes), Leibniz
explained that these often provided an easier path
than the more direct method of mechanical explanation
in terms of efficient causes.25 Leibniz had himself
in 1682 used a variation of Fermat's principle in an
application of his method of maxima and minima to
the derivation of the law of refraction. Closely
associated with the principle of sufficient reason is the
principle of perfection (principium perfectionis or
melioris). In physics, this principle determines the
actual motion from among the possible motions, and
in metaphysics leads Leibniz to the idea of “the best
of all possible worlds.” The clearest expression of
Leibniz' view is to be found in his Tentamen anagogicum,26
written in about 1694, where he remarks that
the least parts of the universe are ruled by the most
perfect order. In this context, the idea of perfection
consists in a maximum or minimum quantity, the
choice between the two being determined by another
architectonic principle, such as the principle of
simplicity. Since the laws of nature themselves are
held by Leibniz to depend on these principles, he
supposed the existence of a perfect correlation between
physical explanations in terms of final and efficient
causes.
In relation to Leibniz' analytical theory of judgment
and his distinction between necessary and contingent
propositions, the principle of sufficient reason entails
that, in the case of a well-founded connection between,
for example, physical cause and physical effect, the
proposition that formulates the effect may be described
as a logical implication of the proposition that
formulates the cause. Generalized in the sense of the
analytical theory of truth and falsehood that Leibniz
upholds, this means: “nothing is without a reason;
that is, there is no proposition in which there is not
some connection between the concept of the predicate
and the concept of the subject, or which cannot be
proved a priori.”27 This
logical sense of the principle
of sufficient reason contains also (in its formulation
as a principium reddendae rationis) a methodological
postulate; propositions are not only capable of
being grounded in reasons (in the given analytical
manner) but they must be so grounded (insofar as they
are formulated with scientific intent).28
In addition to the principle of sufficient reason, the
principle of contradiction (principium contradictionis)
and the principle of the identity of indiscernibles
(principium identitatis indiscernibilium) are especially
in evidence in Leibniz' logic. In its Leibnizian formulation,
the principle of contradiction, ?(A ? ?),
includes the principle of the excluded middle, A ? ?A
(tertium non datur): “nothing can be and not be at
the same time; everything is or is not.”29 Since
Leibniz' formulation rests on a theory according to
which predicates, in principle, can be traced back
to identical propositions, he also classes the principle
of contradiction as a principle of identity. The
principle of the identity of indiscernibles again defines
the identity of two subjects, whether concrete or
abstract, in terms of the property that the mutual
replacement of their complete concepts in any
arbitrary statement does not in the least change the
truth value of that statement (salva veritate). Two
subjects s1 and s2 are different when
there is a predicate
P that is included in the complete concept S1 of
s1
but not in the complete concept S2 of
s2, or vice versa.
If there is no such predicate, then because of the
mutual replaceability of both complete concepts
S1 and S2, there is no sense in talking
of different
subjects. This means, however, that the principle of the
identity of indiscernibles, together with its traditional
meaning (“there are no two indistinguishable
subjects”30), is synonymous with the definition of
logical equality (“whatever can be put in place of
anything else, salva veritate, is identical to
it”31).
Metaphysics (Logical Atomism).
Since the investigations
of Russell and Couturat, it has become clear
that Leibniz' theory of monads is characterized by an
attempt to discuss metaphysical questions within a
framework of logical distinctions. On several occasions,
however, Leibniz himself remarks that dynamics was
to a great extent the foundation of his system. For
example, in his De primae philosophiae emendatione
et de notione substantiae, Leibniz comments that the
notion of force, for the exposition of which he had
designed a special science of dynamics, added much to
the clear understanding of the concept of substance.32
This suggests that it was the notion of mechanical
energy that led to the concept of substance as activity.
Again, it is in dynamics, Leibniz remarks, that we
learn the difference between necessary truths and
those which have their source in final causes, that is to
say, contingent truths,33 while optical theory, in the
form of Fermat's principle, pointed to the location of
the final causes in the principle of perfection.34
Even the subject-predicate logic itself, which forms
the rational foundation of Leibniz' metaphysics,
seems to take on a biological image, such as the
growth of a plant from a seed, when Leibniz writes
to De Volder that the present state of a substance must