Philosophy (general) In sections 37 thru 45 of the Monadology Leibniz offers three different proofs of the existence of God. Explore the way in which each of these proofs is derived from the 'two great principles' introduced immediately before.

The 'two great principles' expounded in paragraphs 31-2 of the Monadology are the principle of contradiction and the principle of sufficient reason. The principle of contradiction states that any statement containing a contradiction is false, and its opposite is true (para. 31); the principle of sufficient reason states that no state of affairs can exist, and no statement can be true, unless there is a sufficient reason why it is so and not otherwise, and that these reasons cannot usually be humanly known (para. 32). If these principles are accepted then it follows that there are two kinds of truths, each being based upon one of the two principles. Truths of reasoning are based upon the principle of contradiction; they are necessary truths, and their opposite is impossible. Truths of fact are based upon the principle of sufficient reason; they are contingent and their opposite is possible. These principles are of fundamental importance in understanding Leibniz's philosophy and underpin his approach to the question of the existence of God, which he believed to have been unsatisfactorily answered by other philosophers such as Rene Descartes.

In paragraphs 37-45 of the Monadology Leibniz proposes three proofs of the existence of God. They are: (1) an 'a priori' proof, that is, one not dependent upon experience for its authority but reflecting necessary truths that exist independent of reason but can be understood through reason; (2) an 'a posteriori' proof, that is, one that is dependent upon experience for its authority and reflects contingent truths that are dependent upon observable facts; and (3) a cosmological proof, derived from the supposed nature of the universe. This final proof could justifiably be seen as a subcategory of the second proof rather than as a distinct proof in its own right, relying as it does upon human experience of the existing universe for its basis, but given the importance of the cosmological proof for Leibniz's entire philosophical system it is helpful to treat it separately.

The first proof, which is the 'a priori' proof, is Leibniz's development of what is normally known as the ontological argument for the existence of God. Fundamentally, this argument states that God is the greatest and thus most perfect being that could be conceived. Human reason can conceive the notion that God does not exist; such a conception is of a God that would possess all the perfections except that of existence, because He would be a fiction, existing only in human imaginations. But an imperfect God would not be God, because God is of necessity perfect; therefore to conceive of God at all is to conceive of a being that possesses all perfections, including that of existence, so it is not possible to conceive of God not existing. In asserting that 'God is absolutely perfect' Leibniz went beyond the ontological argument as presented by Descartes and others, for they had failed, in his view, to prove that a perfect being is impossible. Leibniz believed that he had provided this proof:

For perfection is nothing but amount of positive reality, in the strict sense, leaving out of account the limits or bounds in things which are limited. And where there are no bounds, that is to say in God, perfection is absolutely infinite. Thus God alone (or the necessary Being) has this prerogative: that He must necessarily exist, if He is possible. And as nothing can interfere with the possibility of that which involves no limits, no negation and consequently no contradiction, this is sufficient of itself to make known the existence of God a priori. (paras. 44-45)

This argument reflects directly Leibniz's first great principle, that...

31): the concept of God cannot contain a contradiction, and so cannot be false. This conclusion is also in accord with the second principle, that of sufficient reason, 'by virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise' (para. 32), which can be summarized as the claim that nothing is without a reason for its being, and for being as it is. That there is sufficient reason for God's existence can be argued from external truths, that is from the evidence that actual things do have an existence:
It is farther true that in God there is not only the source of existences but also that of essences, in so far as they are real, that is to say, the source of what is real in the possible. For the understanding of God is the region of eternal truths or of the ideas on which they depend, and without Him there would be nothing real in the possibilities of things, and not only would there be nothing in existence, but nothing would even be possible. (para. 43)

If existing things can only derive their existence from God, then God contains 'the final reason of things' (para. 38) and necessarily therefore encompasses all that is possible; so, God must be perfect, because without that quality of perfection He would not be God. Leibniz asserts therefore that there is sufficient reason for God's being, and for God being as God is.

The second, a posteriori, proof derives similarly from the principle of sufficient reason. Existing beings have their source of existence in the perfection of God, but are themselves necessarily imperfect - they do not contain their own sufficient reason for existence: 'created beings derive their perfections from the influence of God, but... their imperfections come from their own nature, which is incapable of being without limits' (para. 42). Yet there must be a sufficient reason traceable somewhere, or else such beings would not exist at all. This point also connects with the first principle of contradiction, for a being that existed without their being sufficient reason for it to exist would involve a contradiction and would be impossible. Given that only the 'substance we call God' (para. 38) is without limits and contains its own sufficient reason, the reason for all other created beings must also be found in God:

For if here is a reality in essences or possibilities, or rather in eternal truths, this reality must needs be founded in something existing and actual, and consequently in the existence of the necessary Being, in whom essence involves existence, or in whom to be possible is to be actual. (para. 44)

The third proof rests fundamentally on the same approach as the second, the experience of the nature of the universe available to human reason. The universe, argues Leibniz, confronts human beings with a system of vast complexity in which the reason for any given thing depends on other things which also have their reasons dependent on further things, and so on, defying the explanatory or even the conceptualizing powers of the human mind: 'as all this detail again involves other prior or more detailed contingent things, each of which still needs a similar analysis to yield its reason, we are no further forward' (para. 37). Yet, given the principle of sufficient reason, there must be final sufficient reason why everything in the universe is the way it is, and that must be located outside the created entities that comprise the universe:

the sufficient or final reason must be outside of the sequence or series of particular contingent things, however infinite this series may be. Thus the final reason of things must be in a necessary substance, in which the variety of particular changes exists only eminently, as in its source;…