Bruno believed that the universe was infinite, containing every possible world. While Leibniz, too, believed in an infinite universe, one in which no definite coordinates could be made, only relational statements, the two had a very important distinction in their beliefs. Leibniz famously claimed that we lived in “the best of all possible worlds,” a singular infinite universe made by God for us. Bruno, in contrast, believed that the universe contained infinitely many life forms and that every possible world was contained as a subset of this infinite universe. In essence, while Leibniz saw the universe as one infinite world, Bruno saw the universe as an infinite number of worlds.
The example of how each would see an “inverted” or “upside-down” world sheds more light on this granular distinction. If you were to propose an idea of an upside-down world to Leibniz, he would say it is the same as our current one. Leibniz would claim that, since space is relative and there is no absolute container on the universe, an “upside-down” world would contain the same spatial relations between all objects and would therefore be the same as our current world. Bruno, on the other hand would claim that an “upside-down” world is somewhat nonsensical. Since the universe is infinite and contains every possible permutation of itself, an “upside-down” version would simply be a subset of the universe. One could argue that what they really meant was taking the entire universe and upturning it, including the upside-down subset. This, however, would create a literal copy of the original universe even in absolute coordinates and doesn’t speak to the relativity of the universe. So, Bruno’s view of the universe would likely say that the “upside-down” universe is just a subset of the infinite universe, although the exact answer would depend upon how one defines turning the universe upside-down.
Fig. 1. Giordano Bruno, Cause, Principle, and Unity, 1584
Leibniz and Bruno could probably exchange many words on how the universe is constructed, but it really comes down to one simple thing: was the universe made just for us or not? The arguments these two would have for their views gets a bit into their different conceptions of God, the arguments for which I will deconstruct separately. We can at least touch on the extensive argument that could be had on this topic. Bruno may open this argument by invoking the Principle of Sufficient Reason. Both of them being rationalists, they both try to follow this principle fairly closely. While both of their boundless universes are based on the aforementioned principle, Bruno takes it much further, arguing that there isn’t a reason that our solar system should be the only one or that Earth should be the only habitable planet or that humans should be the only intelligent life. This is where Bruno’s infinite universe with infinite worlds comes from: that there is no sufficient reason for any possible world to not exist. Leibniz would say that we were made in God’s image. If the universe was made for us, then there is no need for any other worlds or intelligent life forms. Being that God is omniscient, He wouldn’t create unnecessary worlds as He must have an intelligent reason behind His actions. This is where the different conceptions of God come into play. Bruno fundamentally disagrees with Leibniz and they would argue (possibly more than they would argue about the construction of the universe) extensively on what God’s form and function is as well as what perfections He contains.
Let’s first define what Bruno’s God looks like, as it is very different from nearly every other philosopher we’ve read. Bruno was a pantheist, similar to Spinoza. His God is different from Spinoza in how it is manifested in things. Rather than an infinitely attributed being, Bruno’s God is the “soul of the universe,” as J. Lewis McIntyre put it in his book on Bruno. This God is described less as an inhabiter of matter, the container of all possible attributes, and more as an animating force. This God is likened to the power of life itself. The idea of God animating and giving life to all matter in the universe, and specifically the self-motion that results from this, is reminiscent of Cavendish’s account of matter. Notably, Bruno does specifically connect this conception of self-moving, perceptive matter to a form of God as opposed to Cavendish’s natural philosophy.
Moving back to the main point of Bruno’s differences with Leibniz, we see that these two views of God’s form are very distinct. Leibniz saw God as an infinitely intelligent being that created the best possible world in the best possible way and need not interfere in the world because it started out as perfect as possible. Where Leibniz values God’s omniscience here, Bruno seems to value God’s omnipresence. Bruno would push back against Leibniz by saying that stopping God from meddling in the physical world reduces His omnipresence. Leibniz may argue that God’s omnipresence is realized through this world that was created perfectly from the start. While Bruno might debate this idea of how the world is constructed, he could also pose a more Newtonian argument that Leibniz’s God has reduced omnipotence (although he would use similar arguments against the Newtonians). The fact that Leibniz’s God does not involve Himself in the physical world (and even the Newtonian God only does so periodically) suggests a limited omnipresence and omnipotence. Bruno’s God is within all matter and gives said matter its motion. Bruno’s God has taken omnipotence and omnipresence to their extremes, making God the lowest-level building block of all physical matter in an infinite universe.
It seems the next natural argument for Leibniz would be to suggest that this God lacks some omniscience, being that He could not create a universe in which He did not have to take the active role as the building block of matter. Bruno, on the other hand, conceptualizes God’s omniscience differently. He believes that God must have omniscience because God contains within Himself all concepts (as this is required to form all constructions of matter) and created an infinite universe with every conceivable world within it. While Bruno’s God certainly shows less active intelligence than Leibniz’s, Bruno’s undeniably has an infinite mind.
We have now reached a point at which the two philosophers disagree on the construction of the world and the form of the universe, the definitions of omniscience, omnipotence, and omnipresence, and the very nature of God. While on a surface level it seems Leibniz and Bruno’s mutual embrace of relative coordinates within an infinite universe made them more similar to each other than to Newton, it now appears that Leibniz and Bruno have two world views that are different in just about every aspect (although I’m not sure Newton’s view would have many more similarities to Bruno’s). This just goes to show how truly radical Giordano Bruno’s conceptions of nearly everything in the universe truly were.