Leibniz's MetaphysicsGottfried 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 IdentityLeibniz 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
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.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. Normal | Teacher | Scholar