William M. Briggs

Statistician to the Stars!

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More Reasons Not To Use The Precautionary Principle: Update

A member of Congress in repose?

A member of Congress in repose?

All probability is conditional and we are always interested in some proposition, call it X. We want to know “the probability of X”. Well, there is none: not ever. There is no unconditional “probability” of anything.

There is, however, Pr(X | E), where E is some evidence (data, observations, premises, surmises, whatever). Change the evidence, change the probability.

In the precautionary principle, X is some disaster or undesirable event. Now it is easy to supply some E to deduce a probability of X. If there was widespread agreement on this E, then there would be agreement on the probability of X. The opposite case is also true. In global warming, there is great disagreement about evidence, usually because lovers of models chose to forget their creations’ flaws. Love is blind.

But the precautionary principle doesn’t quite work that way in practice. Usually the X is dire and the E is missing except to say E_c = “X is possible”, which is another way of saying X is contingent. All contingent things are logically possible; i.e. they are not impossible. With E_c, officially 0 < Pr(X | E_c) < 1, which tells us almost nothing except that X is not logically impossible and that X is not logically necessary. Weak evidence indeed.

Notice very carefully that Pr(X | E_c) is not 0.5, nor any other single number. You can’t use this interval to argue the probability “may be likely”. This is a false reading. The probability is the interval.

Another point of stress: if we knew or agreed upon decent E such that Pr(X|E) is greater than some decision threshold, then we do not need to use the precautionary principle. We’d have Pr(X|E) and we can use the some regular form of decision making. The precautionary principle is only invoked when such evidence is missing. Indeed, it is used to supply the missing evidence. The argument is that we don’t know E so we don’t know the probability but we do know E_c, thus X could happen, therefore X is sufficiently likely, thus we ought to do something. This is obviously a fallacy.

Or the precautionary principle is used when evidence exists which shows the chance of X is very low indeed. Say E_r (for realized evidence) then Pr(X|E_R) = ε > 0, but only just. It’s then said that because this probability is greater than 0, this is sufficient if the doom in X is disastrous enough. That’s why yesterday at The Stream I illustrated the precautionary principle with a hostile alien invasion.

An invasion is a contingent event, so it’s logically possible. There exists lots of (non-quantitative) evidence that this chance is near-zero low, such as the vast distances of space and so forth. But it could happen! And, like I said, if it did, nothing short of the Apocalypse would be as bad. Thus, according to the precautionary principle, we should—even must!—act to stop it.

Yet alien invasions are only the start of contingent doomsday events that might destroy us all. Rocks from space, viral mutations, planetary plagues, black holes plunging into the ocean, serial volcanic eruptions, the core of the Earth spinning out of control, Hillary presidency, rapacious nanobots, rogue humanoid robots, and on and on. Because each is possible and each would destroy mankind, no amount of protection is too little.

And then there are the troubles I mentioned yesterday, the precautionary principle applied to itself. If we can’t agree on the evidence such that we can say something about the probability of X, then the effects of protecting against X by manipulating the causes or possible causes of X are also likely unknown, and just as likely as hazardous, or perhaps even more hazardous, than X itself.

The solution is boring. Return to the hard work of amassing evidence such that we can agree on the evidence and compute reasonable probabilities. Tough, grueling, time-consuming labor.

Or you can run around like an addled fool and call your detractors “Deniers!” or “Troglodytes!”


Update Another Twitter interaction.

I hope readers can see that.

If a “black swan” is defined as X = “an event which we know nothing about”, then we cannot find evidence E probative of it. There is no probability. Notice that that “nothing” is a very strong word. Make sure you get this.

What I have seen is that some define “black swans” as events which we can characterize at least partly. For instance, X = “Destruction of the human race” (or, in vulgar terms, X = “Loss of all capital”) . No idea in X how the event comes about, thus finding evidence probative of it is a problem. Like I said above, we can go on endlessly positing different ways the world can end. All these can form E, which, taken together, make X all but certain. Ponder this.

But because we packed everything into E, and formed a frightening probability of X, we have learned nothing. Which of the elements of E should we protect against—if it’s even possible? We can’t say “all of them”, because this is silly.

Stream: Attack Of The Black Swans From Outer Space!


Today’s post is at The Stream: “Attack Of The Black Swans From Outer Space: Nassim Nicholas Taleb and his co-authors fail to show their precautionary principle provides any guidance in climate policy.

Aliens from outer space utterly hostile to humanity might attack! They’ll know we’re here because of our electronic emissions, which continuously bathe the earth in a soft glow. If these aliens discover us and manage to get here, it’s obvious that mankind is kaput. As in wiped out. À la mort.

Solution? Hide! Cease immediately all use of anything and everything powered by electricity. Sure, this necessary action will cause some inconveniences such as the ruination of the world’s economy and maybe the odd mass starvation since food will become scarce. But, hey, we’re talking about the survival of the human race. Don’t you care what happens to people? You brute.

What’s the likelihood of an alien attack? It’s complicated, but all the best scientists say it’s not impossible. Anyway, what’s the difference? As long as the chance is non-zero and the costs of failing to act are near infinite, shutting down the world is the only sane move.

What’s that you say? The burden of proof is on me? There’s no evidence of a forthcoming invasion?

What are you, some kind of denier? …

Go there to read the rest.

I was asked on Twitter about the “falsification” of climate models. Models are falsified when they say, conditional on their innards, “The probability of X is 0” and X happens. Since the output of the global average temperature from any given model is a point, or anyway that’s what we see, then unless the actual temperature matches that point, the model is formally falsified.

The way around this is either to add some uncertainty to the point or to use an ensemble of models and interpret them probabilistically. The latter approach is more usual. But it isn’t done well. If the “envelope” of the ensemble doesn’t contain the reality, again the models are falsified. Unless a statistical model is fit to the ensemble, as is done sometimes in weather forecasting, it’s very easy to falsify the models.

Mental “fuzz” is usually added to deterministic models so that, in the minds of their creators, the models aren’t falsifed. And this isn’t crazy because it’s rare in physics experiments to expect the reality to perfectly match the predictions. But unless this is done formally, there can be disagreements.

This is why skill is often used to verify. Skill is a measured improvement over some simplified model, like persistence. Persistence says next year will be just like this year. Climate models can’t beat persistence, thus they don’t have predictive skill. I speak loosely here, and even more loosely in the Stream piece, but it’s obvious that the models are busted.

Whether they have hindcasting skill is irrelevant. Hindcast skill is the ability to fit past data, which is no great feat.

There’s More Than Physics: A Review Of Nagel’s Mind and Cosmos. Guest Post by Bob Kurland


Kurland provides us with a succinct review of Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False. This will ease us into the week with a discussion why our intellects cannot be explained by science. But can be otherwise. For a more comprehensive view, Ed Feser’s in-depth series on the book—almost book length itself!—is not to be missed.

The aim of this book is to argue that the mind-body problem is not just a local problem…but that it invades our understanding of the entire cosmos…I believe a true appreciation of the difficulty of the problem must eventually change our conception of the place of the physical sciences in describing the natural order.

What? An eminent philosopher of the mind, Thomas Nagel, a professed atheist, taking up the theistic argument that “the materialist, neo-darwinian conception of nature is almost certainly false”—who wood-a thunk it?

In a nutshell, Nagel argues that current belief that there is a physical theory of everything—a theory that includes human mentality and values—is unbelievable:

I find this view [reductive materialism and neo-Darwinism] antecedently unbelievable–a heroic triumph of ideological theory over common sense. [p 136]

This disbelief is founded on the following propositions:

  • physical science cannot account for the incredibly unlikely beginning of life;
  • physical science and the neo-Darwinian model cannot account for the development of consciousness;
  • physical science and the neo-Darwinian model cannot account for the development of cognition from consciousness;
  • physical science and the neo-Darwinian model cannot account for the role of value in human activity.

The fundamental difficulty with the currently accepted physical picture, according to Nagel, is that the ways in which materialism and neo-Darwinism try to account for mentality are inadequate.

The first way is to deny that the mental is an irreducible aspect of reality, either (a) by holding that the mental can be identified with some aspect of the physical, such as patterns of behavior or patterns of neural activity, or (b) by denying that the mental is part of reality at all, being some kind of illusion (but then, illusion to whom?). The second way is to deny that the mental requires a scientific explanation through some new conception of the natural order, because either (c) we can regard it as a mere fluke or accident, an unexplained extra property of certain physical organisms — or else (d) we can believe that it has an explanation, but one that belongs not to science but to theology, in other words that mind has been added to the physical world in the course of evolution by divine intervention. [emphasis added] The Core of Mind and Cosmos

Nagel rejects divine intervention, both for the presence of mind and for the beginning of life. Instead he proposes a teleological principle that operates to achieve values (undefined) that include consciousness and cognition; mutations that work to such an end are preferred, that is have a higher probability. Nagel terms the failure of materialism and neo-Darwinism to account for the above “a materialism of the gaps”. The arguments Nagel gives to support the above propositions are involved. Were I not already convinced of his propositions, I would find his arguments unconvincing.

Since a detailed examination of these arguments would require an article almost as long as the book, I’ll not do that. Instead, I invite the reader to go to the book, or if you don’t want to spend the bucks, look at Chapter 4 of the book, on Cognition (it’s available online for free–use the link).

Finally, I wonder why the addition of a “teleological principle” is not more ad hoc than that of a creating God. It does seem to be the case that for many atheists, their faith (or non-faith?) cannot be shaken.

Summary Against Modern Thought: Can God Know Things That Aren’t?

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

Some simple arguments showing God knows both singulars and things that are not. I don’t think there will any dispute about the contentions, so in the Notes we do a little wandering. Next week is more controversial material.

Chapter 65 That God Knows Singulars (alternate translation)

[2] …For it has been shown[1] that God knows other things in as much as He is their cause. Now God’s effects are singular things: because God causes things in the same way as He makes them to be actual; and universals are not subsistent, but have their being only in singulars, as is proved in 7 Metaph.[2] Therefore God knows things other than Himself not only in the universal but also in the singular.

Notes In re “universals are not subsistent”. St Thomas means universals don’t exist actually as some ideal to which singulars are compared. Plato’s forms are not real. We are Aristotelians here.

[4] …Moreover. The nature of a genus cannot be known perfectly unless its first differences and proper passions be known: thus the nature of number would not be perfectly known if odd and even were unknown. Now universal and singular are differences or proper passions of being. Therefore if God, in knowing His essence, knows perfectly the common nature of being, it follows that He knows perfectly the universal and the singular. But, just as He would not know the universal perfectly, if He knew the intention of universality without knowing the thing in the universal, such as man or animal, so too He would not know the singular perfectly if He knew the nature of singularity without knowing this or that singular thing. Therefore God must needs know singulars.

Notes Like we said last week, there is little—really, no—dispute that God knows singulars, and these proofs are therefore adequate. The tidbit to note here is about numbers. Two points. The first is what we might call the commoner’s fallacy, which might also be called the we-now-know fallacy, and which is the practice whereby anything that is known by one of us (human beings) it is therefore knowledge for or of all of us, knowledge any of us might claim to know. As Wilhelmsen says in his delightful Man’s Knowledge of Reality: An Introduction to Thomistic Epistemology, “What is the difference between a master sergeant reading the Articles of War to a company of recruits and a lawyer citing the same in a court-martial?”

So just because there may be some person out there who knows all about the nature of number—and this is the second point—that knowledge does not belong to you or me, too by default. Plus, as much knowledge about numbers that exists among us, it’s unlikely anybody knows all about the nature of number. Readers who are mathematicians will probably agree with this.

[1] Ch. xlix.
[2] D. 6. xiii., xiv.

Chapter 66 That God Knows Things That Are Not (alternate translation)

[1] In the next place we must show that God lacks not the knowledge of things that are not.

[3] …Again. The knowledge of God’s intellect stands in the same relation to other things as the knowledge of a craftsman to the works of his craft: since He is cause of things by His knowledge.[3] Now the craftsman by the knowledge of his art knows even those things which are not yet produced by his art: since the forms of his art pass from his knowledge into external matter so as to produce the works of his art: and consequently nothing prevents forms which have not yet materialized outwardly from being in the craftsman’s knowledge. Therefore nothing prevents God from having knowledge of things that are not.

[5] …Moreover. Our intellect, in respect of the operation by which it knows what a thing is, can have knowledge of those things also that are not actually: since it is able to comprehend the essence of a lion or horse, even if all such animals were slain. Now the divine intellect knows, as one who knows what a thing is, not only definitions but also enunciations, as shown above.[7] Therefore it can have knowledge of those things also that are not.

Notes The difficulty here is that we had to have some experience of actual lions or horses before we can know what they were like would they were all gone. Think dinosaurs.

[6] Again. An effect can be foreknown in its cause even before it exist: even so an astronomer foreknows a future eclipse by observing the order of the heavenly movements. Now God’s knowledge is of all things through their cause: for by knowing Himself, Who is the cause of all, He knows other things as His effects, as we proved above.[8] Nothing, therefore, prevents Him from knowing those things also that are not yet.

Notes Predictions, like all probability and all statements of logic, are conditional. As long as we grasp the conditions, the deductions follow, and we can know them. But some predicitons (as regular readers know) are probabilitistic. Given the normal conditions, the probability of a head in a coin flip is 1/2. We know this 1/2 and not the outcome; but this is still knowledge (in the strong sense of that word).

And now another tidbit for our mathematical friends (only the first part of the argument is given).

[7] Moreover. There is no succession in God’s act of understanding, any more than there is in His existence.[9] Hence it is all at once everlasting, which belongs to the essence of eternity,[10] whereas the duration of time is drawn out by the succession of before and after. Wherefore the proportion of eternity to the whole duration of time is as the proportion of the indivisible to the continuous, not indeed of the indivisible that is the term of the continuous, and is not present to each part of the continuous—for such is likened to an instant of time—but of the indivisible that is outside the continuous, and yet synchronizes with each part of the continuous, or with each point of a signate continuous: because, since time does not exceed movement, eternity, being utterly outside movement, is altogether outside time…

Notes Math can be done without symbols! Although symbols are eminently useful, they do tend to tempt one into the Deadly Sin of Reification.

[8] By these arguments it is made clear that God has knowledge of not-beings. Nevertheless not-beings have not all the same relation to His knowledge. For those things which neither are, nor shall be, nor have been, are known by God as possible to His power. Wherefore He knows them, not as existing in themselves in any way, but as merely existing in the divine power. Such things are said by some to be known to God according to His knowledge of simple intelligence.

Notes Even God can imagine. That’s enough for us. I don’t think there is any dispute, used as we are to mathematical-like proofs, that God knows singulars or things that are not. Next week we ask whether God knows future contingents, which is a juicier question.

[1] Ch. lxi.
[2] Categ. v. 18.
[3] Bk. II., xxiv. See above, ch. lxv.: Moreover. God’s intellect . . . p. 137.
[4] Chs. xlix., liv.
[5] Ch. xliii.
[6] Ch. xlvii.
[7] Chs. lviii., lix.
[8] Ch. xlix.
[9] Ch. xlv.
[10] Ch. xv.

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