Class 40: Welcome To Cause!

This is it. We have reached our one true purpose: understanding cause. Cause is much richer than ordinarily thought in science. But it is everything. Today we begin one of many discussions of how we can, and cannot, know cause.

Uncertainty & Probability Theory: The Logic of Science

Video

Links: YouTube * Twitter – X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty

HOMEWORK: Given below; see end of lecture.

Lecture

This is an excerpt from Chapter 7 of Uncertainty.

“Anybody who writes a book in order to generate doubt on causality refutes the message by the very means that carries it.”—Stanley Jaki.

“Felix, qui potuit rerum cognoscere causas“—Virgil.

Be-cause

A philosopher writes a book to convince his readers that causality is nonexistent. He hopes by his actions to cause his reader to adopt his view. How did the words get on the pages of the book demonstrating causality doesn’t exist? The contradiction is never noted, perhaps because many expositors of theories exempt themselves from the consequences of their creations. Many modern philosophers are deeply suspicious about causality, a doubt reaching even to philosophical skepticism. Much of the distrust and misunderstanding of causality is because of post-Decartesian philosophy, which laid aside Aristotelian views prematurely, especially about the nature of cause. And this is odd because to Aristotle, the goal of science, and not necessarily its practice, is a matter of rerum cognoscere causas, or knowledge of the cause of things. This goal has largely been replaced by predictive ability in many of the sciences, which has much going for it, and which is a goal I suggest is returned to in fields which must use probability. But the ultimate aim of science must be the knowledge of the cause of things. If that is science, the predictive goodness and useful is not science per se, but techne or engineering.

That causality is doubted by some philosophers probably accounts for why many physical scientists routinely ignore philosophers. Scientists make their livings pursuing and even sometimes discovering (secondary) causes and can’t countenance the idea that causes don’t exist. Except for those scientists who are earnest in their attempts to say their measurements happened by magic, i.e. just happened for “no reason.” On the other hand, some scientists enthusiastically believe all causal relationships can be discovered by applying the right computer algorithm or scientific “procedure”. In an influential book, Judea Pearl writes , “The possibility of learning causal relationships from raw data has been on philosophers’ dream lists since the time of Hume (1711-1776).” He, like Solomonoff in the last Chapter, believes he has found this Statistician’s Stone (this is my term). He hasn’t because it can’t exist. And at any rate, learning causal relationships has been on philosophers’ lists since the pre-Socratics: causality did not come into existence with Descartes, Hume, or Kant. And indeed, their view and the views of some other moderns is particularly stunted.

Cause is analogical. There is not one type or flavor or aspect of cause, but four: a formal, material, efficient, and final or teleological. Most causation concerns events which occur not separately, as in this before that, but simultaneously, where simultaneous events can be spread through time. Many causal data are embedded in time, and there two types of time series which are often confused: per se and accidental. These should not be mistaken for non-causal data series which are all accidental.

Causes, if they exist and are present, must always be operative, a proposition that has deep consequences for probability modeling. Falsifiability is rarely of interest, and almost never happens in practice. And under-determination, i.e. the possibility of causes other than those proposed, will always be with us.

Here is an example. Suppose scientists, via one of the NASA Rovers, found a device on Mars. It is roundish, the color of the Martian soil and occasionally displays, or is thought to display, what appear to be numbers. Scientists have decided the device has two “inputs”, which are thought to be two protuberances in the “back”. Through a series of inferences, it has been decided that the displayed numbers are correlated (I mean this word in its plain English sense) to the “inputs”, which have been discovered to be “activated” (they flash different colors) in the same base of numbers as the display.

Put plainly, and I’ll convert the numbers to base 10 for ease of understanding, the display is the sum of activations of input $A$ and of input $B$. Mathematically, $A + B = D(isplay)$. So far, since the Rovers have not had much chance of observing the object, dubbed The Calculator, the activations of $A$ and $B$ have never been greater than 56 individually. I mean $A,B < 57$, which necessarily implies $D < 113$.

Naturally, since it is plain this is a device, scientists want to know its purpose. Theories are flying around NASA thick and fast. Though there are more theories than there are scientists, three rough camps have coalesced. Camp 1 says its coincidental that so far $A,B < 57$, thus always $A + B = D$ no matter the number of activations of $A$ and $B$. Camp 2 theorizes that the activations are “obviously” caused by two types of cosmic rays, which if they were to exceed some tolerance, they would cause $D = 5$. This, they say, is a derivation of string theory. I mean, if either $A,B > 56$, then the function is no longer a straight plus, but is instead a “quus”; i.e.

$A + B = D \mbox{ if } A,B < 57,$

$A + B = 5 \mbox{ if } A,B > 56.$

Camp 3 says $A + B = D$ for any number of activations, but that after some period of time the device must start to degrade and that, because of various technical reasons,

$A + B = D \mbox{ before Date,}$

$A + B = C < D \mbox{ after Date.}$

and where the inequality is strict. We have plus and quus already, so call this (and this is my suggestion, not the scientists’) “cuus”.

The observations of the device are consistent with each of these three theories—and with many more theories, too. Recall I’ve only given you the three most popular. Obviously, none of the theories put forward by any of the scientists are inconsistent with the observations. We conclude from this that the physical observations are indeterminate; I mean, the state of the device, or the world plus the device, do not fully determine the device’s purpose.

Still, even though the facts are indeterminate, we’d still like to know which of the plus, quus, cuus theories is right. I have no idea. Later we’ll learn that no theory “has” a probability, so there is no joy to be found in searching which of theories is more “likely”. Of course, we could use each theory to make predictions and see which is better in some decisionable sense, which is very useful. But we’ll never know which of plus, quus, cuus, or even some other theory, is true until we understand the purpose of the device. And we’ve seen that the facts alone do not and can not determine what this purpose is.

To understand the purpose is to understand, in part, the cause of the device. Cause, as explained, is of four aspects: the formal or form, the material, the efficient, and the purpose, final, or end. In this case, the form is obvious enough: the device is “disguised” or made to look like a rock. The material is unknown at this point, but it’s thought to be at least a rocky covering, or something which simulates rock. The efficient cause is, all agree, some kind of intelligence and whatever comprises the internal workings. Whether the designer is Martian or some clever human is unknown.

But what about the purpose of the device? Well, that’s what the real unknown is. If it turns out that some Martian (or whomever) designed the device to count activations, however these are brought about, then plus is the right theory. If instead the final goal of the device was to count cosmic rays, then we’re on to quus. Now it could be that quus and cuus are right, on the guess that the harsh cosmic rays are causing the degradation. That means the quus-purpose is right, but the cosmic rays efficiently cause a degradation which leads to cuus. So we have to be careful to keep in mind what part of the cause we’re examining.

If somehow we discover the user’s manual or tech specs for the device (and could translate them), then we’d know the cause of $D$—we’d know all aspects of the cause, and then we’d know the theory. And, as should now be obvious, what holds for this Martian device holds for all devices, whether made by Martians or via natural processes. It is only after we have knowledge of cause that under-determination ceases to be a problem.

Knowledge of cause is above, or rather beyond or deeper than, knowing what happens. Even beasts can know what happens, but they don’t and can’t understand why. Knowledge of cause is the grasping of essence, of the natures and substantial forms of the objects under consideration. None of these things are material in themselves, but are universals above and beyond the material world. Thus to come to knowledge of cause is to understand universals, which we get through a form of induction. Induction is the immaterial “movement” from finite particularities to an infinite generality and is such that only rational creatures can accomplish it.

The “quus” example is from Saul Kripke, as many will recognize. Quus isn’t usually presented with respect to under-determination, but of language and thought and how the intellect must be immaterial. I have concentrated on the epistemology, because uncertainty is our main interest.

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