Here is the next video from the Alternatives to Methodological Naturalism conference. In this video, Jonathan Bartlett describes how, at least in principle, one can model non-naturalistic causes mathematically.

Bartlett shows how modern mathematics yields functions which can be described but not predicted, and how they may relate to different modes of causation. He then uses randomness as a bridge case, and shows how randomness shows that such functions can be readily incorporated into models without harm to science in general.

## 12 Replies to “Describable but not Predictable: Modeling Non-Naturalistic Causation”

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And, yes, I am Jonathan Bartlett.

johnnyb,

Do you plan on posting to arXiv, or to submit for peer-review?

We are publishing the proceedings of the conference hopefully before the year is out. About a third of the papers are just starting review, a third have received reviews and are awaiting revisions, and a third have their revisions returned and are with the editors.

And, yes, I am Jonathan Bartlett.Are you sure?

People have griped a lot in the past if I have referred to my own work without explicitly saying it was mine. I find that silly (I actually write in the third person because it lets the work stand on its own so comments are about the work, not me) but other people think it is somehow dishonest like I’m trying to get away with something (though what, I’m really not sure).

I confess I have not yet viewed the video. But a question:

If I throw a pair of standard dice is the outcome predictable or merely describable?

If the outcome is truly random, then it would be describable.

johnnyb,

This is a very nice talk. When you were writing this, did you have any particular phenomena in mind that these describable but not predictable functions would model especially well?

daveS –

The one I have gone into in the most depth is using Turing Oracles to model human insight. Here is the video.

Paper is here.

With an engineering add-on here.

I don’t remember if I mentioned this one in the video, but I’ve always wondered if continuations would make a good model for causation in physics. In compsci, a continuation allows a program to backtrack to a previous point and start over with a new value if some assertion is not met. Thus, I have always wondered if the way that God avoided having things like divide-by-zeroes in nature was by providing nature a small range of possible values with a backtrack function. This would be interesting, because such a function would be de facto evidence of teleology in nature (since it backtracks until a “correct” value is found).

I also think that the interactionist problem in dualism might be solvable with the Cantor function or something like it. In such a mode, physics would provide past-to-present causation, and teleological principles (i.e., the soul) would provide future-to-present causation, with the in-between being filled in from the interactions of those two. The power of the teleological principle would be related to the distance in time across which it could interact. Thus, for instance, God can affect the present from His end-of-time goals, while human souls would have significantly shorter abilities (I’m guessing that would be on the order of sub-seconds).

Thus, naturalism describes the “push” of the past to the present, and teleology describes the “pull” of the future on the present. The present and in-between moments are made by a mutual negotiation of these principles, continually filling out the in-between space.

Thanks for the links to the papers and the additional examples, johnnyb. I’ll take a look at them once I get back to my regular computer. This is quite interesting. It would be remarkable if the Cantor function or something similar could be put to use in an applied setting.

I know this post has dropped out of sight, but I listened to it last week (and I seldom watch videos), because I’m interested in the topic. I’ve been on vacation, but have a bit of time now to offer a few comments.

First, right off the bat, defining the demarcation between naturalism and non-naturalism as one of computability is, in my opinion not a good criteria. Johnny offers some rationale for this: that computability is well established and unambiguous, and it matches current intuitive concepts. He goes on to say that methodological naturalism means that behavior happens in a calculable manner. I think these statements are wrong.

I recently read Chaos by James Gleick, a history of the development of the concepts and applications of chaos theory during the past 50 years, and I’ve also studied more mathematical books on chaos and fractals. Johnny sounds like he’s pretty mathematically well-versed, and he listed a number of odd functions, but he isn’t, perhaps, familiar with chaos theory.

Chaos theory was developed to model and describe some previously intractable natural phenomena, such as turbulence and weather. I can’t begin to offer even a basic summary here, but the basic idea is that a set of three non-linear differential equations, which can be a very simple model for phenomena like turbulence, is not calculable by ordinary analytic means. The system is extremely sensitive to initial conditions, and thus behaves chaotically as opposed to predictably. These are mathematical systems which model natural phenomena that are describable, but not predictable.

Therefore, chaos theory shows clearly that johnny’s use of computability as a demarcation line for naturalism is out-dated. It may fit older “intuitive” ideas that nature can be modeled with continuous predictable functions (trig functions, exponential functions, etc.), but the modeling of natural phenomena has moved beyond that.

Another reaction I had to johnny’s talk is that despite mentioning some odd functions that go beyond the traditional predictive functions, he never says anything about what might constitute a non-natural phenomena to which these odd functions might apply. (The one exception is his reference to his unfinished idea of an Insight function, but that doesn’t really relate to any of the rest of the talk.)

So my summary of that the talk is that it is out-of-date and inaccurate about the state of naturalistic mathematical models, and has no details to offer about any non-natural phenomena.

There are a few other remarks johnny made that I would like to comment on.

Around 8:57, johnny says we don’t have infinities of things under naturalism. We don’t have countable infinite numbers of discrete things in the natural world, but we do assume, by assuming continuity of functions and in our definitions of derivative, that we do have a continuum of a infinitely dense set of points in space and moments of time. It may be that in fact space and time are discrete, but the intervals would be/are so small that I seriously doubt we will ever replace mathematics based on continuity. So I don’t think the fact that we don’t have countable infinite numbers of discrete things in the natural world has any bearing on making a case for mathematics of non-natural phenomena (whatever they may be).

At 16:45, johnny says that strange functions allow us to make statements that don’t follow the presuppositions of naturalism. But, as I have said, chaos theory uses functions (and processes with functions) that are at least as strange as the ones offered by johnny to model purely natural phenomena: johnny is wrong about what he sees as the presuppositions of naturalism.

At 17:55, johnny says we should not assume that reality must conform to popular notions of causation. That is exactly right! Quantum physics showed us that, and so does chaos theory. However this point actually contradicts johhny’s demarcation criteria, which in the beginning declared that naturalism was limited to popular notions of causation. Chaos theory has taken us past those popular notions, but in doing so it has just expanded our understanding about how to describe and model the natural world: they haven’t passed over into saying anything about the existence, much less the behavior, of anything non-natural.

(P.S. – FWIW, I am the poster previously known as aleta, who retired from this site.)

Bump, cause I’m interested in at least a short reply from johhnyb.