Leibniz's Metaphysics

Gottfried Leibniz had a vision of a universal ambiguity-free language based on a new symbol set, a

*characterica universalis*, and a machine-like

*calculus ratiocinator* that would automatically prove all necessary truths, true in "all possible worlds."

Gottlob Frege called the idea "a system of notation directly appropriate to objects." In the three hundred years since Leibniz had this vision, logical philosophers and linguistic analysts have sought those truths in the form of "truth-functional" propositions and statements formulated in words, but they have failed to find a necessarily "true" connection between words and objects.

Information philosophy uses such system of notation, not in words, but in bits of digital information. And the interconnected computers of the Internet are not only Leibniz's* calculus ratiocinator*, but humanity's storehouse of shared experiences and accumulated knowledge. Like the individual Experience Recorder and Reproducer (ERR) in each human mind, the World Wide Web is our shared Knowledge Recorder and Reproducer. Computer simulations of physical and biological processes are the best representations of human knowledge about the external world of objects.

Leibniz's *Principle of Sufficient Reason* says that every event has a reason or cause in the prior state of the world. This appears to commit him to a *necessary* determinism, but like the ancient compatibilist Chrysippus, Leibniz argues that some empirical things are contingent.

Leibniz formulated many logical principles that play a major role in current metaphysical debates.

One is his *Principle of Contradiction* (Aristotle's *Principle of Non-Contradiction*), a proposition cannot be true and false at the same time, and that therefore A is A and cannot be not A.

That A is A follows from what Leibniz called the Indiscernibility of Identicals, the idea that no differences are perceivable between identical things. This came to be known as Leibniz's Law.

The Metaphysics of Identity

Leibniz calls identity of any object with itself as a primary truth.

Primary truths are those which either state a term of itself or
deny an opposite of its opposite. For example, 'A is A', or
'A is not not-A'; If it is true that A is B, it is false that A is
not B, or that A is not-B'; again, 'Each thing is what it is',
'Each thing is like itself, or is equal to itself, 'Nothing is
greater or less than itself—and others of this sort which,
though they may have their own grades of priority, can all be
included under the one name of 'identities'.
All other truths are reduced to primary truths by the aid of
definitions—i.e. by the analysis of notions; and this constitutes
a priori proof, independent of experience. I will give
an example. A proposition accepted as an axiom by mathematicians
and all others alike is 'The whole is greater than
its part', or 'A part is less than the whole'. But this is very
easily demonstrated from the definition of'less' or 'greater',
together with the primitive axiom, that of identity. The ' less'
is that which is equal to a part of another ('greater') thing.
(This definition is very easily understood, and agrees with the
practice of the human race when men compare things with
one another, and find the excess by taking away something
equal to the smaller from the larger.) So we get the following
reasoning: a part is equal to a part of the whole (namely to
itself: for everything, by the axiom of identity, is equal to
itself). But that which is equal to a part of the whole is less
than the whole (by the definition of 'less'); therefore a part
is less than the whole

("Primary Truths," in *Leibniz: Philosophical Writings*, ed. G. H. R. Parkinson, p.87)

The Identity of Indiscernibles

4. There are no two individuals indiscernible from one
another... Two drops of water or milk
looked at under the microscope will be found to be discernible.
This is an argument against atoms, which, like the void, are
opposed to the principles of a true metaphysic.

The Identity of Indiscernibles is the converse of Leibniz'z Law

5. These great principles of a Sufficient Reason and of the
Identity of Indiscernibles change the state of metaphysics,
which by their means becomes real and demonstrative;
whereas formerly it practically consisted of nothing but empty
terms.
6. To suppose two things indiscernible is to suppose the
same thing under two names.

("Correspondence with Clarke," in *Leibniz: Philosophical Writings*, ed. G. H. R. Parkinson, p.216)

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