Thursday, August 20, 2015

The Leibnizian Cosmological Argument (LCA)

I haven't spent much time defending the LCA, but it's not because I think it's a weak argument.  As my readers know, the vast amount of time defending theism proper I spend vigorously defending St. Thomas Aquinas' Five Ways.  With that said, I consider the LCA, the conceptualist argument, and the argument from desire to be the next strongest.  Let's take a look at the LCA:

1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise)

2. The universe exists. (Premise)

3. Hence, the universe has an explanation of its existence. (From 1 and 2)

4. If the universe has an explanation of its existence, that explanation is a timeless, changeless, immaterial, powerful cause. (Premise)

5. Therefore, a timeless, changeless, immaterial, powerful cause exists. (From 3 and 4)

Premise (2) is hardly controversial.  Premise (1) is known through experience.  If there were an elephant standing in the middle of the street, and someone claimed that the elephant has no explanation whatsoever, then surely people would think he is either crazy or merely jesting!  Nobody would take such a claim seriously.

Since the remaining premises, except (4), are equally uncontroversial, let's focus on premise (4).  Would it really be reasonable to think the universe exists necessarily?  Does every quark exist necessarily?  Moreover, to exist necessarily is to have its existence and essence identical.  Yet, the universe has diverse essences, which makes a necessary universe impossible.


  1. Would it really be reasonable to think the universe exists necessarily?

    I don't think so, for reasons that are kind of hard to spell out non-technically [1]. But I'll give it a go.

    Suppose we have a set of N causally-interrelated contingent entities. We can represent each of these entities as a vertex on a graph - like one of the vertices of a triangle, say. We can further represent the causal [2] relations between these entities as arrows running from vertex to vertex. If we have two entities, the cause would be at the tail of the arrow, and the caused would be at the tip.

    If you want this collection of contingent entities to be causally complete (no uncaused contingent entities, in other words), then you'll want each of the entities to lie at the end of one of these arrows. If you only have contingent entities, moreover, you can't have any repeated loops, where a single entity is both the origin and the terminus of some causal loop -- you can't, in other words, have a chain like this: E1-->E2-->....En-->E1. That would result in an entity being the cause of itself, and such an entity is by definition not contingent. So, in order to have a causally complete network of N vertices, you need at least N arrows.

    But we run into a problem, since you can have at most N-1 arrows without a repeated loop [3]. This implies that at least one of the N vertices will not lie at the end of the arrow, and therefore will not be causally explained by any member of your set of contingent entities.

    The upshot of all that up top is that you can't have a network of N events where all the events are contingent and where the network is causally complete simultaneously. From which follows that the universe, as a set of N contingent entities (for a very, very large but less than countably infinite value of N), can't be causally complete. So, if you want a causally complete universe (IOW, if you want some version of the PSR), there has to be an extra-universal entity which causes the whole show and is not contingent.

    And this all men call God.

    [1] To make this argument rigorously, I'd have to use some graph theory. I don't really think that's a commonly-known bit of mathematics, so I tried to do it in common, though slightly technical, English.

    [2] You can run the same argument with grounding relations instead of causal ones, which I think works better.

    [3] I could give a formal proof of this statement, but that would involve a good deal of upper-level undergrad/lower-level grad student math, so I'll simply leave it as stated. It's pretty intuitively plausible on its own, I think.

  2. The materialist could argue that all we have warrant to believe is
    P1' - everything that exists has a physical explanation

    **insert here anti-platonist arguments and arguments for eliminative materialism about minds***
    and so we don't have a reason to infer theism from the existence of the universe.

  3. Kolten, one could make that objection, but then he would be committed to saying that the universe's explanation is found in the necessity of its own nature. The universe is the sum total of all physical space, time, matter, and energy, so if the universe has an external cause, then that cause will be timeless, changeless, immaterial, as well as very powerful.

  4. Thanks, I hadn't thought of that