Gottfried Leibniz

Gottfreid Wilhelm Leibniz was a philosopher, mathematician, and polymath born in Leipzig in 1646.

Historical Context

Gottfried Leibniz was educated in the classical and Scholastic tradition, but later claimed to have rejected the conclusions of the Scholastics by the age of 15 in favour of those of Descartes and the Mechanists. His philosophical influences thus included both old and new ideas, a blend that was later reflected in his many writings. Leibniz wrote extensively on many topics including metaphysics, epistemology, logic, and mathematics.

Main Contributions to the Philosophy of Scientific Change

Leibniz on the Rationality of Scientific Knowledge

Leibniz can be broadly categorized as an a priori rationalist about science and knowledge in general. He believed that all truths, necessary or contingent, could be derived logically (at least in theory) from a set of interconnected principles he took to be axiomatically true. The precise justificatory relationship between the principles themselves is subject to change between Leibniz’ writings. However, since most of the principles taken together imply the others, this subtlety can be overlooked. The formulations given here reflect those given in the Monadology, Leibniz’s great work of metaphysics.

• The Principle of Contradiction: That which involves a contradiction is false, and that which is opposite to a contradiction is true. This is one of the principles Leibniz uses to establish his a priori necessary truths.
• The Principle of Sufficient Reason: Nothing is true unless there is a sufficient reason why it should not be otherwise. Often this principle is abbreviated to ‘nothing happens without a reason’ or ‘no effect is without a cause’.
• The Principle of the Identity of Indiscernables: If two objects share all of their properties or, conversely, if two objects have only identical properties, they are identical. The Principle of the Identity of Indiscernables can be derived from the Principle of Sufficient Reason – for, if two objects truly shared all their properties, then we could conceive of a possible world in which those two objects were ‘switched’. In this case, God would have no sufficient reason to choose one over the other, and would be forced to act irrationally. Since this is impossible according to the Principle of Sufficient Reason, the antecedent can never occur. Leibniz uses this principle, and this style of argument, extensively in his science and metaphysics, most notably in his defense.
• Predicate-In-Notion Principle: Leibniz’s notion of truth. It can be stated as ‘In every true statement, the predicate of the statement is in some way contained within the subject’. Leibniz believed this premise to be necessary for his claim that all truths are provable a priori, at least in principle. |-
• The Principle of Continuity: The principle is formulated most simply as ‘nature does not make leaps’. This principle takes its impetus from Leibniz’s mathematics (where a notion of the continuum is necessary for, amongst other things, the fundamental theorem of calculus) but finds wide use in Leibniz’s metaphysics and theory of perception. The basic principle is that all changes must occur continuously, and that all objects subject to change must progress through all intermediate stages when subjected to that change. This principle draws its justification from the Principle of Sufficient Reason, Principle of the Identity of Indiscernables, and the Predicate in Notion Principle.
• The Principle of the Best: The principle of the Best states that, of all the theoretically possible worlds, the actual world must be the best. This principle is drawn from the Principle of Sufficient Reason and the existence of God, which Leibniz thinks is a necessary truth derivable a priori (Monadology 38).

Leibniz made great use of his principles (in particular the Principle of Sufficient Reason and the Principle of the Identity of Indiscernables) in his scientific and metaphysical work. For Leibniz, the principles are true A Priori synthetic propositions that are present inherently in the human mind. In the preface to Leibniz’s New Essay on Human Understanding (unsurprisingly, a response to John Locke’s Essay on Human Understanding), Leibniz explicitly presents himself as the Plato to Locke’s Aristotle. Locke denied that any principles are inherent in the human mind, since the mind is a tabula rasa, but for Leibniz, a mind free of all content at birth would violate the principle of the Identity of Indiscernables (since different minds would, initially at least, have all the same properties). With the concept of inherent ideas in hand, Leibniz is able to assert that the Principles are necessary, eternal, and present inherently in the minds of all people. They are the source of all general propositions, and hence, all knowledge. Leibniz goes so far as to say that reason based on only empirical observations is no better than that of animals.

Leibniz explicitly denies that any general propositions can be learned by experience alone. At times he even seems to suggest the opposite – that all truths are in theory discoverable without any input from the senses whatsoever. Leibniz does not deny the utility of experiment and observation to knowledge, but he does deny its necessity. In the preface to the New Essay Concerning Human Understanding, Leibniz likens experiments in the natural sciences to the use of empirical tests when doing mathematics – that is, occasionally helpful, but certainly never necessary. In this way Leibniz is truly committed to the strongest form of rationalism, belief in the power of a mind to gain knowledge of factual matters without any sense data whatsoever.

Of course, Leibniz did not think that humans could reason entirely a priori about the world as it is. The progression from his a priori principles to contingent truths of fact is an infinite series, and Leibniz believes that the whole of an infinite series can only be understood by God. In the Preface to the New Essays Concerning Human Understanding, Leibniz claims that, “Although the senses are necessary for all our actual knowledge, they are not sufficient to give us all of it”. This statement epitomizes Leibniz’s beliefs on knowledge, and sets up the major problem his philosophy will face: how to connect the a priori knowledge provided by the Principles to the a posteriori knowledge given by the senses.

Leibniz's Epistemology and the Principle of Sufficient Reason

The Principle of Sufficient Reason is the key principle of Leibniz’s epistemology. Whether or not the principle requires other principles to ground it, it is the key to the justification of knowledge of general synthetic propositions (or truths of fact) on Leibniz’s schema.

Leibniz delineates two kinds of truth – truths of reason and truths of fact. These categories correspond to Kant’s classifications of analytic and synthetic propositions, respectively. The difference between the two kinds of fact are that truths of reason can be reached by a finite sequence of a priori reasoning, whereas truths of fact require an infinite series – the kind only available in principle to God. So, while all knowledge is inherently reachable a priori, finite beings are forced to rely on a posteriori arguments to demonstrate most facts about the world. Therefore, despite the fact that all truths are reachable a priori, Leibniz’s epistemology is still subject to challenges posed by the Problem of Induction and Pyrrho’s Problem.

Leibniz on the Problem of Induction

The Problem of Induction as formulated by Hume states that there is no inherent justification for the move between many instances of a particular proposition (“this swan is white”) to predictive general propositions (“all swans are white”). To make that inductive jump, Leibniz’s program needed some sort of general principle to justify why nature does not lie to us or change her course on a whim. Leibniz addresses this worry in the Preface to the New Essays Concerning Human Understanding. It is not necessarily true that the future will resemble the past, since the converse is certainly conceivable. However, from the Principle of Sufficient Reason, Leibniz argued that under sufficiently similar conditions, the world must behave in a sufficiently similar way. Thus, the Principle of Sufficient Reason is the general a priori principle that grounds Leibniz’s epistemological program. The Principle of Sufficient Reason, like all of Leibniz’s principles, is an a priori synthetic proposition. It need not obtain in all possible worlds. However, as Leibniz notes in On Contingency, it is evident that God made humans with the faculty of reason, and surely if human reason did not correspond with the world He made, this would not be the best possible world, thus contradicting the Principle of the Best. Thus, the Principle of Sufficient Reason must hold in this possible world, and it may be used to justify inductive generalizations.

Leibniz on Pyrrho's Problem

Pyrrho’s Problem is the skeptical hypothesis originating from Pyrrho of Elis. The problem can be formulated as a challenge to the reliability of human senses. It is impossible, in general, to know that human perceptions are trustworthy, since any test of them must rely on the same perceptions being tested. Leibniz’s philosophy of the mind relies on far more perceptions than most philosophers consider, (since he believes that all substances perceive all other substances in the universe all the time, though subtly) so this problem is prima facie a serious one for Leibniz. However, the Principle of Sufficient Reason is enough to establish that sense data must correspond with the external world. If the opposite were true, there would have to be a sufficient reason for the fact that human perceptions do appear to be reliable. By the Principle of the Best, that reason just is that the world does correspond to human senses.

Criticisms & New Directions

Though Leibniz’s writings remained obscure and largely unpublished during his lifetime, they have had a powerful and lasting influence after his death. In particular, Leibniz’s influence on Immanuel Kant is difficult to overstate. Much of Kant’s Critique of Pure Reason is dedicated to a refutation of Leibniz’s rationalist claim to have knowledge of things in themselves through the Principle of Sufficient Reason. For more, see Immanuel Kant.

Authors

Jennifer Whyte, 2015