Leibniz’ Cosmological Argument

For Leibniz’ cosmological argument to function we first need to establish the principle of sufficient reason. The principle of sufficient reason states that, “For every fact F, there must be a sufficient reason why F is the case.”¹ Or, in other words, everything that exists must have an explanation for its existence. Leibniz orders these explanations into analytic propositions and synthetic propositions (to use Kantian terms).

Analytic propositions are where we find the predicate iterating something found already in the subject. For instance, “all bachelors are unmarried men” is an analytic statement, for the predicate is expressing something already contained in the subject. Leibniz also argues math is analytic, for, 7+5 must always equal 12… However, Kant later goes on to argue math is synthetic (as I will explain later).

Synthetic propositions are where we find the predicate iterating something not found already in the subject. For instance, “the bachelors are blond” is a synthetic statement, for the predicate is expressing something not already contained in the subject — it’s communicating something new, not found self-contained in the subject. Kant would say math belongs in this group of things because,

“It might at first be thought that the proposition 7+5=12 is a mere analytic judgement, following from the concept of the sum of seven and five, according to the principle of contradiction. But on closer examination it appears that the concept of the sum of 7+5 contains merely their union in a single number, without its being at all thought what the particular number is that unites them. The concept of twelve is by no means thought by merely thinking of the combination of seven and five; and, analyze this possible sum as we may, we shall not discover twelve in the concept.”²

Now that we have that established, let’s look at the beginning of all that exists: the beginning of all that exists is only possible in virtue of a first cause. If there wasn’t a first cause, and I were to assert that the universe beginning to exist is true in virtue of B, and B is true in virtue of C, ad infinitum, it would suffer from constantly asserting synthetic claims. Leibniz solves this through asserting a first cause, this first cause of which necessitates being analytic (lest he fall into the trap earlier explained), and this first cause of which is God.

Leibniz’ argument can essentially be laid out as such:
1) For every X, there is a Y such that Y is the sufficient reason for X rather than not X (If is X is analytic it contains its own explanation, if it’s synthetic it necessitates another explanation).
2) The universe exists.
3) Therefore, the universe needs a sufficient reason outside of itself (in virtue of being synthetic).
4) There cannot be an infinite series of synthetic statements.
5) Nothing can only create nothing, something can only create something.
6) Therefore, the universe requires a cause that is transcendent/analytic.
7) God is transcendent/analytic.
8) Therefore, the universe’s cause is God.
Q.E.D.

Notes

1. Melamed, Yitzhak Y., and Martin Lin. “Principle of Sufficient Reason.” Stanford Encyclopedia of Philosophy, Stanford University, 7 Sept. 2016, https://plato.stanford.edu/entries/sufficient-reason/.
2. Kant, Immanuel. Prolegomena to Any Future Metaphysics That Will Be Able to Come Forward as Science. Translated by James Ellington, Hackett, 2001, p. 11.