Numbers Need Worldviews

1+1=2. What has this got to do with worldview? Surely math has no need of a worldview, 1+1=2 in any worldview. Roy Clouser argues that 1+1=2 might be true in any worldview, but why it is true varies tremendously. Clouser considers the options and spots a mischievous assumption - all mathematical theories depend on a religious assumption.

To see this, Clouser asks us to consider what a number is. There are two main approaches to this question (Clouser has a few more, but I will focus on a couple for the purposes of brevity). The first option is to say that numbers are real things in another dimension of reality. This theory usually come in the form of positing that mathematical truths are eternal, unchanging and self-existent. Leibniz thought that the truths of mathematics would never change even if the whole material universe passed away. A variant version of this theory states that the laws of logic are eternal and unchanging and that math is merely a short-cut way to do logic and is dependant upon logic for its existence.

The second option is to say that numbers are only ways in which we engage with sensory experience. Math is not eternal or unchanging, but merely how our experience of this world turns out. This means, in principle, the truths of math could have been otherwise and are dependent upon the workings of the material world for their existence. Dewey thought that math was not a matter of truth, but of what turned out to work. Math is merely an instrument, useful, but not immutable, productive, but non-referential.

Roy Clouser argues that each of these theories are religious theories, they depend, in some way, on attributing divine status to something. Consider, the first option. Clouser notes that the status given to math is of necessary and independent existence and of supreme governance. Mathematical truths exist eternally and govern every aspect of the world. They are to be accorded with in life and in thought. This, to Clouser, sounds like divinity.

Consider Dewey's theory. Here, according to Clouser, we see the universe as independent. Clouser admits that Dewey denied that anything has independent existence, but argues that Dewey is inconsistent on this point. Dewey arrives at the implied conclusion that the universe has independent existence. To have independent existence, Clouser argues, is to have divine status.

For Clouser, the created universe cannot contain an independent aspect without attributing to it divine status. Christians, on the other hand, should not attribute divine status to aspects of created reality. Rather they should see God as independent, self-existent and eternal. If math is a dependent truth and the universe is a dependent reality then math does not need to be reduced to either status, divine in itself or dependent on divine universe. Rather, in Christianity, Clouser argues, math makes sense of created reality and is dependable, because God is dependable.

Taken from Roy Clouser, The Myth of Religious Neutrality (Notre Dame: University of Notre Dame Press, 2005). 


Veritasdomain said...

I really like this post. Goes to show how the Christian worldview is foundational for things most take for granted including accounting for the nature of numbers.

Ben Holloway said...

Thank you for your encouragement as ever Veritasdomain. I really appreciate you and your ministry.