Friday, August 30, 2013

The Argument from Mathematics

John Lennox and William Lane Craig have begun to defend this argument.  I suspect one reason is because nominalists, realists, and conceptualists can all agree with it.  Here's how I would summarize the argument:

1. The universe exhibits mathematical structure. (Premise)

2. Either the universe was designed by a deity who used the concepts of mathematics and imposed them upon the universe, or else the mathematical structure of the universe is a happy coincidence. (Premise)

3. It is not a happy coincidence. (Premise)

4. Therefore, a deity exists. (From 1 - 3)

Premises (1) and (3), I should hope, are uncontroversial.  To deny either of these premises is well beyond fringe philosophy.  It's premise (2) that's most important.  Even if one states that the mathematical structure of the universe is due to necessity, it's still just a happy coincidence.  Moreover, it is conceivable that the universe could operate under different and contradictory mathematical models.  Does the universe operate under a Euclidean or under a non-Euclidean geometry?  Both are consistent, so that would additionally undermine the notion that the universe's mathematical structure is due to necessity.

What about the nominalists with respect to premise (2)?  Well, according to them, abstract objects, including mathematical objects and systems, are just useful fictions.  This would mean the designer chose to use a specific system of mathematics by which the universe would behave.  A realist would say that the designer recognized which mathematical system was correct and then designed the universe accordingly.  Finally, the conceptualist's views already lead to a designer.  Similar to the realist, the deity on conceptualism already knew which mathematical system was correct, since the deity's mind is what grounds these mathematical truths.

In order to avoid this argument, one will have to deny (3).  To those who attempt such a strategy, good luck! 


  1. Fascinating argument. However, a question.

    Doesn't this get one into the realm of what Edward Feser would regard as 'naturalistic' gods? A personal, quite possibly limited being or beings, who themselves may be created?

    Not that I think it's a bad argument even then - I think the naturalist/atheist has to contend with far more Gods/gods than the God of classical theism and all.

  2. I'm not sure about Feser's objection/reservation. I haven't come across it yet. I think there are ways of reconciling the argument with classical theism even if Feser's reservation turns out to be correct. The God of classical theism creates the universe as well as angels. The angels are drawn to God's Logos - the locus of all rationality and goodness - and as a result, cause within the physical universe a mathematical structure in order to emulate God's rationality.

    Now, I don't think that's what really happened. However, in the above scenario, God alone is the creator, and he is ultimately responsible for the design, given that he created the angels in such a way that they would design the universe with a mathematical structure.

    Nevertheless, I don't see why God himself could not be directly responsible for both the creation and the design. As far as you know, does Feser think this conflicts with divine simplicity? Or, is it something else?

    1. Sorry, it wasn't until just now that I saw your reply.

      Feser typically has a problem with arguments that regard God as a designer/creator imposing His will directly on matter, as if according to a blueprint or the like. I -think- it may be related to Divine Simplicity, but all I know is it's at the heart of his issues with Intelligent Design.

      This link probably encapsulates his thoughts on it the best.

    2. Thanks for the link, Crude. If I understand Feser correctly, he's critical of the notion that God created a mechanistic universe which is capable of running on its own. The argument from mathematics doesn't do that, as far as I can tell. After all, God, as the first cause in the order of sustaining causes, must continue to sustain the laws of nature in order for them to have any mathematical correlation. Final causality, and efficient causality, as a result, aren't damaged by the argument from mathematics, even though Feser suggests that Paley's argument and the contemporary Intelligent Design arguments do.

  3. I've only seen William Lane Craig defend this argument, is there a place where I can read/watch John Lennox's formulation of the argument?

    1. Hi Jonathan,

      You can find one of Lennox's treatments of the argument here: