Friday, January 2, 2015

My Favorite Theistic Arguments - Part IV - The Argument from Regularity, Intelligibility, and Mathematics

In the previous note we examined how physics is shot through with physical constants which govern its effects in reality.  So, for instance, we look at the equation for gravitational attraction.

Today we’re going to come at this from a slightly different angle.  The fourth argument I’d want to take a look at has various forms, but I think they all point to the same thing.



Aquinas’ Fifth Way:

One formulation of this argument is given by Saint Thomas Aquinas.  It goes like this:
The fifth way is taken from the governance of the world. We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. 
 Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God.



This argument can sound odd to modern ears.  Perhaps some people will mistake it for an argument from the complexity of the cosmos.  That is to say, a person may exclaim:
“Look at the great complexity we find in biology and astronomy!  Natural processes are insufficient to create such things.”
But that isn’t what the Angelic Doctor is saying.  No, his argument has nothing to do with complexity, but with regularity and intelligibility.  He looks at the regularity found in nature and asks:
“Why should such intelligible regularity exist in non-intelligent things?  Why does a struck match always produce fire… and not music?”  
To reply, “Because of physics”, doesn’t get at the question at hand.  Because the thing which we’re looking for an explanation of…. is physics itself.


Pope Benedict XVI’s Argument from Intelligibility:

In his book "Introduction to Christianity", Joseph Ratzinger (who later became Pope Benedict XVI), made the following observation and argument.
The universal intelligibility of nature, which is the presupposition of all science, can only be explained through recourse to an infinite and creative mind which has thought the world into being. No scientist could even begin to work unless and until he assumed that the aspect of nature he was investigating was knowable, intelligible, marked by form. But this fundamentally mystical assumption rests upon the conviction that whatever he comes to know through his scientific work is simply an act of re-thinking or re-cognizing what a far greater mind has already conceived.


So what Professor Ratzinger pointed to was largely the same thing as Aquinas.  Before one can even do the fine work of natural science, the scientist must first assume that nature is ordered to processes which can be predicted and understood through the intellect.

Why, asked the future Pope, should such an inductive observation be possible?  Why expect intelligibility in a nature?  And doesn’t that point us to an intelligence which built and ordered nature according to reason?  According to the logos?


Argument From the Unreasonable Applicability of Math:

I usually like to begin explaining this argument by asking a person:
 “What is math?” 
“What do you mean?” asks the hearer.
“Well… do you suppose it is just humanity’s after-the-fact description of the world?  That it is a fictitious model which we attribute to nature after observing it?  That it is, in the final accounting, not a truly real thing.  Or do you suppose that mathematics is something real, something woven into the fabric of reality… almost like a source code for a program.  That nature actually follows physical laws which can be truly expressed using mathematics?”
The more science-minded people, those with an appreciation for mathematics, physics, and programming, will almost invariably choose the latter option.
“How is it possible…”, I ask, “… that there would be a source code without a programmer?  Why should we expect to find nature adhering to what is – in reality – a primitive form of philosophy, namely, mathematics, if there is not also a philosopher behind it?”
It is fun to pose that question to a person and watch the light suddenly flicker on.



In 1960, Hungarian physicist Eugene Wigner published a paper called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences".  In it he said:
“This property of the regularity is a recognized invariance property and, as I had occasion to point out some time ago, without invariance principles similar to those implied in the preceding generalization of Galileo's observation, physics would not be possible.”
And he concluded:
“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”
A couple of examples to think about:

Albert Einstein developed his Theory of General Relativity on a blackboard.  He published his paper on it in 1916.  In 1919, it was confirmed by measurement during a solar eclipse.

Likewise, the standard model of particle physics predicted the existence of 17 different types of fundamental particles (which break down into different “flavors”).  One by one, these particles were discovered experimentally.  Most recently and famously was the Higgs Boson.



If Mathematics was merely the pattern we ascribe to nature… why should it have this sort of predictive power?  Why is theoretical physics even possible?

And more broadly, why should any scientist look out into nature and expect to find results which can be understood through mathematics and thereby predicted in the future?

Again, the presence of a source code implies a programmer.  The presence of philosophy demands a philosopher.


Wrapping Up:

Whereas the Fine Tuning Argument focused on the elements within the equations of nature, their strengths and quantities, this species of argument focuses on the equations themselves.  Why should there be any ordering principle in nature if there is no one to order it?

That concludes the various cosmological and teleological arguments.  Next time we'll start getting into the intangible.


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