Leibniz Part 1

Short Biography Leibniz ( ) was the son of a professor of philosophy who had earned his doctorate in law by 21. He invented both the integral and differential calculus (at the same time as Newton); and the binary language that makes computer software possible. He was also a diplomat and a royal courtier who traveled widely and contributed to the jurisprudence and international policies of the time.

Short Biography Unfortunately, due to Leibniz’s peripatetic life his philosophical views are scattered among hundreds of letters, personal manuscripts, and publications. There is no one text that gives us a stereoscopic view of his thought. Rather, Leibniz’s broad philosophical outlook has been pieced together by scholars.

Outline of Leibniz’s Thought Leibniz’s metaphysics is based on two principles: 1.Nothing exists except substances and attributes (for Leibniz, pace Newton, this implies that space and time are illusions). 2.Substances are composed of unextended points of force/consciousness called monads.

Subject-Predicate Logic Let’s begin by noting Leibniz’s commitment to a subject-predicate logic. This logic holds that every proposition is of the subject-predicate form (e.g., ‘Socrates is wise’). For Leibniz, the truth of such statements is ultimately analytic.

Analysis In other words, if we could list all of the predicates associated with a particular subject, that list would exhaust the meaning of the subject term. So, whenever we have a true subject- predicate sentence, the predicate is contained in the concept of the subject.

Analysis This ‘concept containment’ has metaphysical implications. For Leibniz, a substance is individuated (distinguished from other things) by its complete list of properties. So, to say that the concept of a subject contains the concept of a predicate applicable to it is to say that the substance referred to by that subject term contains the property referred to by the predicate term.

3 Fundamental Principles This subject-predicate logic and notion of analysis are the foundation of three fundamental principles that run through Leibniz’s work: 1.The Principle of Sufficient Reason. 2.The Principle of Identity. 3.The Principle of Perfection.

Sufficient Reason According to his ‘analysis’ of propositions, a proposition is true if and only if the predicate is contained within the subject. This leads Leibniz to claim that every true proposition is analytic (or, true by definition). Of course, since some ‘definitions’ are infinite, and many finite definitions are too large for human comprehension, real analysis can only be conducted by God.

Principle of Identity (or Contradiction) If every proposition is analytic because the predicate is contained in the concept of the subject, then we can substitute the defined term (the subject) with its definition (the complete list of predicates). This process turns every true proposition into an overt logical identity.

Principle of Identity For instance, suppose we have a proposition of the form: The F is G If Leibniz is right, then the definition of ‘The F’ is given by a list of predicates, and ‘G’ is on that list. So, by (partial) substitution we arrive at: G = G

Principle of Identity Given a complete list of properties: The F is P 1 & P 2 & P 3 &... & P n A complete substitution could be made: P 1 & P 2 &... & P n = P 1 & P 2 &... & P n But, of course, only God could make a complete substitution because only God can comprehend the complete list of properties of any substance.

Principle of Identity But this means that all true propositions are necessarily true (since by Sufficient Reason all true propositions are analytic - compare to Spinoza). Leibniz was the first to specify what it means for a proposition to be necessarily true. For him, it means that the proposition is true in all circumstances – or as we now say, in all possible worlds.

Principle of Identity (or Contradiction) When a proposition is necessarily true, its denial would be a contradiction. That’s because to claim that a true proposition is false amounts to the claim that the predicate is not contained in the subject. But that’s like saying A ≠ A, which is not true in any possible world.

Principle of Perfection Consider a possible substance, The F. For The F to be possible, it must exist in some possible world – under some set of circumstances (whether or not those circumstances actually obtained). The F is defined by its properties, but those properties change over time. Whatever properties The F has now is a function of the circumstances in which it exists.

Principle of Perfection The circumstances that make The F possible include every other substance that exists in that possible world (and their relations to one another). And since those circumstances determine the properties The F has at any time, those properties are a reflection of the complete set of circumstances that make The F possible.

Principle of Perfection Thus, within a possible world, every substance ‘reflects’ every other substance in that world. But the accuracy of this ‘reflection’ or ‘representation’ varies by degree. Leibniz calls the degree to which the properties of a substance (and so the substance itself) accurately reflect its possible world the degree of perfection of that substance.

Principle of Perfection Again, only God could comprehend the degree of perfection of any substance at any state in its development. But notice that since every substance within a possible world has a degree of perfection, so does the possible world itself (for Leibniz). The degree of perfection of a possible world is the sum of the degrees of perfection of all of its substances.

Principle of Perfection Now, God selected one of these possible worlds to bring into existence. Consistent with his nature, he chooses the possible world with the maximum amount of total perfection to bring into existence. Of course, that world is the world we live in, since our world actually exists.

Contingency The Principle of Perfection allows Leibniz to explain what it means for a proposition to be contingently true (true in the actual world but not in all possible worlds). A proposition is contingently true if its analysis reflects the best possible state of affairs.

Contingency Why? Because every substance in the actual world ‘reflects’ every other substance in that world through its properties This means that its complete definition is a description of the entire world. And since God chose this world to exist, this description is the description of the best possible state of affairs.