William M. Briggs

Statistician to the Stars!

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Reasoning To Belief: Feser’s The Last Superstition: A Refutation of the New Atheism — Part IV

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

It’s God All The Way Down

Talk about causality without foreshadowing a tie to God is coming and, if they can maintain an interest in the subject, people are receptive and willing to debate the argument on its merits. But hint that God is at the bottom of it all, as He will be here, and scholarly repose morphs into a sharp and anxious wariness. People tear into the argument with the zeal of Bill Clinton lecturing us about is. This is fine if the criticisms which arise from the increased scrutiny are valid, but usually they are not. In their suspicion that no good can come from tying causality to God, people are apt to convince themselves of objections which have long been refuted.

So I repeat the warning which I gave as we commenced this review: unless you are a specialist, it is unlikely the counter-arguments which occur to you are valid; further, it is highly probable that they are common and have well known rebuttals. This warning is not proof that the argument to come is valid, of course. It is instead a reminder that space is limited; I can only present a sketch while Feser offers chapters (in TLS and Aquinas). Dip into these volumes if you are convinced of a fallacy.

History, as it has been said, is one damn thing after another. Events which are one damn thing after another often form part of a causal series. Moe slaps Larry which causes him to slap Curly which induces him to slap Moe, etc. (start at 30 seconds). My great grandfather William produced a son William, my grandfather, who in turn produced my father William, who had a hand in me (William), and then I had a go with my number one son, William. This is where this time series stands at the moment.

Both of these are examples of causal series per accidens, first one thing, then another, etc. The object to notice is that my great grandfather, after he had done the work which resulted in my grandfather, no longer had to be present when my grandfather helped produce my father, and so on. And my grandfather need not have been alive when my father made me, etc. And this is so for all series per accidens: whatever set the chain in motion need not be present for the continuance of the chain.

This is not the only kind of causal series. There is another called per se, or essentially ordered causal series. This is the juicy kind, which when understood proves that God exists, and so forms Aquinas’s First Way.

Suppose you are incensed that the owners of Chick-fil-A have political opinions which dare to differ from your own. And so you buy up a bagful of chicken sandwiches and head over to the Family Research Council offices with gun in hand with the intent of teaching Chick-fil-A a lesson. You take out the gun and pull the trigger. Out flies the bullet, wending its way toward and eventually lodging itself into the arm of a security guard. So far we have a series ordered per accidens: you fire, the guard is eventually hit.

But consider the moment you squeeze the trigger. The movements of the hammer and of your finger happen simultaneously. The pressure of your finger is in turn simultaneous with the nerve impulses sending the squeeze signal to your muscles. The contraction of the muscles is simultaneous with the individual molecules in the muscles changing from one state to another, which in turn in simultaneous with the changing of the atoms in the molecules, which in turn is simultaneous with the changing of the forces operating to change the various sub-atomic particles, which in turn in simultaneous with whatever it is that operates on those forces which cause the change, and so on. But not “and so on” forever. This simultaneous, here-and-now series must come to an end: it cannot extend infinitely, otherwise nothing would ever get moving.

Now recall our earlier lesson: nothing that is a potential can be a cause, only something actual can be a cause. As Feser says in the article quoted below, “No mere potency can actualize a potency: only something actual can do so.” All those changes in the trigger-per se series are changes into potentials caused by something actual below them, and this series has to end in a first mover.

Now, a first mover in such a series must itself be unmoved or unchanging; for if it was moving or changing—that is, going from potential to actual—then there would have to be something outside it actualizing its potential, in which case it wouldn’t be the first mover. Not only must be be unmoved, though, it must be unmovable. For notice that, especially toward the “lower” levels of the series we were considering—the nervous system’s being actualized by its molecular structure, which is in turn actualized by its atomic structure, etc.—what we have is the potential existence of one level actualized by the existence of another, which is in turn actualized by another, and so forth…[T]he only way to stop this regress and arrive at a first member of the series is with a being whose existence does not need to be actualized by anything else. The series can only stop…with a being that is pure actuality. [Feser uses the example of a hand holding a stick moving a stone.]

And that being is, as Aquinas said, what we call God. Now I know that this example is too telegraphic to be convincing, or lastingly convincing. But let’s be clear what this argument is not saying. There isn’t one word here about the origins of the universe. For Aquinas, the universe could have begun at a single point in time, or existed forever, or even existed as a multiverse. Consequently, any physical discovery about branes or M-theory or cycles in big bangs, or whatever, have no bearing. This is not an argument about what caused things to be, or what set things moving as in a series per accidens, but about what causes any change whatsoever here and now.

To emphasize: the Unmoved Mover is an argument about what happens now, right now, this second, this very instant, about what is the first cause of every change. Anything that becomes actual is subject to a per se causal series, which must always terminate in a first cause, which is Pure Actuality. Feser continues:

[There cannot be] more than one being who is Pure Actuality [because] in order for there to be two (or more) purely actual beings, there would have to be some way of distinguishing them, some feature that one of them had that the other lacked…For to lack a feature is just to have an unrealized potentiality, and a purely actual being, by definition, as no unrealized potentialities…

A being of Pure Actuality, lacking any potentiality whatsoever, would also have to be immaterial, since to be a material thing entails being changeable…The Unmoved Mover is in any event that to which every motion or change in the material universe…traces back.

Besides monotheism, other traits of God can thusly also be deduced: like Omnipotence, Omniscience, Goodness, and so forth. Feser lays these out well, but in his discussion “privation,” which explains how God who has every perfection, relates to causing the absence of perfection, he stops short. It would surely be a privation to you if you were have your arm bitten off by a shark, but it would be a privation to the shark to miss his lunch. So there appears to be an order or hierarchy of privations (or perhaps this is only apparent due to my poor reading).

He also says little on the implications of the Unmoved Mover to us as rational creatures. Intrigued readers will be left with questions. Since God causes everything, at base, that seems to imply that God is with you as you err, even helping you pull the trigger, as it were. Is this God doing evil? Well, it was your will to do evil, not His. But since you’re dragging Him along in the per se trigger series, no wonder He’s not so happy about sin. Good grief! Can any of that be right?

True, Feser was not attempting to give us a complete theological treatise, but since his purpose was to show the errors of New Atheism, he might have expected to cause a few conversions, that some of his audience would want to know What’s Next?, where to go to resolve the tougher questions. Perhaps then in his second edition, he can provide a reading guide. It’s unlikely many will jump right to the Summa Theologica or Summa Contra Gentiles. A list of intermediate works would thus be of extreme utility.

Feser gives us two more of Aquinas’s Five Ways (in Aquinas, which he highly recommends, we get the whole package), each as compelling, but we’ll skip these and move on to his discussion of the soul.

Technical addendum

Here is a quotation from Feser’s article “Existential Inertia and the Five Ways” published in American Catholic Philosophical Quarterly. This version of the proof won’t be to everybody’s taste; but as somebody trained in mathematics and physics, I find its shape familiar and the chain of reasoning particularly compelling. Perhaps you will as well.

  1. That the actualization of potency is a real feature of the world follows from the occurrence of the events we know via sensory experience.
  2. The occurrence of any event E presupposes the operation of a substance.
  3. The existence of any natural substance S at any given moment presupposes the concurrent actualization of a potency.
  4. No mere potency can actualize a potency: only something actual can do so.
  5. So any actualizer A of S‘s current existence must itself be actual.
  6. A‘s own existence at the moment it actualizes S itself presupposes either (a) the concurrent acutalization of a further potency or (b) A‘s being purely actual.
  7. If A‘s existence at the moment it actualizes S presupposes the concurrent actualization of a further potency, then there exists a regress of concurrent actualizers that is either infinite or terminates in a purely actual actualizer.
  8. But such a regress of concurrent actualizers would constitute a causal series ordered per se, and such a series cannot regress infinitely.
  9. So either A itself is purely actual or there is a purely actual actualizer which terminates the regress of concurrent actualizers.
  10. So the occurrence of E and thus the existence of S at any given moment presupposes the existence of a purely actual actualizer.

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

The Tyranny of Artistic Modernism: Ugly Buildings, Ugly Paintings, Ugly Words, Ugly Life

Title before the colon taken from by Mark Anthony Signorelli and Nikos A. Salingaros’s piece at New English Review. No real post today, just quotes from an article which is mandatory reading.

We who live in the Western world at the present time continue to suffer under the reign of a great tyranny — the tyranny of artistic modernism. The modernist aesthetic, which dominates our age, takes a variety of forms in the respective arts — in architecture, a lack of scale and ornamentation combined with the overwhelming deployment of materials like glass, steel, and brutalist concrete; in the plastic arts, a rejection of natural forms mixed with an unmistakable tendency towards the repulsive or meretricious; in literature, non-linear narrative, esoteric imagery, and an almost perfect lack of poetic form and diction.

Yet common now to the practice of all these arts are certain primal impulses which may be said to form the core of the modernist aesthetic — a hostility and defiance towards all traditional standards of excellence, discovered over millennia of craftsmanship and reflection; a notion of the artist’s freedom as absolute, and entirely divorced from the ends of his art; and, as Roger Scruton has so clearly demonstrated, a refusal to apply the category of beauty to either the creation or the estimation of artwork.

the dominant impetus behind the advent of modernism was the rejection of tradition.

We see, for example, that contemporary prize-winning architects slavishly copy the same industrial aesthetic originally approved by the Bauhaus, whose members were working for the German industry to sell the industrial products of that time: steel, plate glass, and concrete.

Those buildings perform terribly in all climates and are dysfunctional for most human activities inside and in their immediate external vicinity, yet so-called “starchitects” continue to emulate the rules embodied in those failed examples.

Amen, amen, amen.

[m]odern art attempts to “nauseate” or “brutalize” an audience…

{W]ill I respect and celebrate the life-affirming aspects of human nature (as traditional artists do), or will I reject and condemn human nature, and celebrate its most destructive traits (as modernists and their derivatives do)?

The constant pursuit of beauty in classical art evinces the similarly profound conviction that the human soul is a thing capable of edification, of being drawn more constantly and more thoroughly towards harmony, and that the making of art is unrivaled in its capacity to further such edification.

The level of stylistic violence implicit in modernist architecture is extraordinary: overhangs without obvious supports, leaning buildings, extremely sharp edges sticking out to threaten us, glass floors over heights leading to vertigo, tilted interior walls also leading to vertigo and nausea.

[A] violence against the tactile environment, often falsely excused as being “honest” rather than a sadistic architectural expression.

And behind it all is nothing but despair, betrayed by the total absence of beauty, which signifies these artists’ complete inability to imagine any reality transcending the calamitous ugliness of the modern world.

But enough! We have only reached the half-way point to this most depressing, and entirely accurate, damnation of modernism. Go and read.

Update Just one more!

This is how the farce of modernism ends, with the anti-bourgeois rebel revealed to be a money-grubbing little fraud.

A Peculiar Prevalence Of P Values Just Below .05

Today’s title is lifted directly from the paper of E. J. Masicampo & Daniel R. Lalande, published in The Quarterly Journal of Experimental Psychology. The paper is here, and is free to download. The abstract says it all:

In null hypothesis significance testing (NHST), p values are judged relative to an arbitrary threshold for significance (.05). The present work examined whether that standard influences the distribution of p values reported in the psychology literature. We examined a large subset of papers from three highly regarded journals. Distributions of p were found to be similar across the different journals. Moreover, p values were much more common immediately below .05 than would be expected based on the number of p values occurring in other ranges. This prevalence of p values just below the arbitrary criterion for significance was observed in all three journals. We discuss potential sources of this pattern, including publication bias and researcher degrees of freedom.

File our reaction under “Captain Renault, Shocked.” Regular readers will know that the cult of the p-value practically guarantees Masicampo & Lalande’s result (Pp<0.0001). We will not be surprised if this finding is duplicated in other journals.

Here’s what happened: Our stalwart pair thumbed through back issues of several psychology journals and tabulated the appearance of 3,627 p-values, then plotted them:

A significant bump in p-values (Pp<0.0001)

Perhaps hard to see in this snapshot, there are unexpected bumps in the distribution of p-values at the magic value, the value below which life is grand, the number above which consists of weeping and gnashing of teeth. Understand that these are the p-values that are scattered throughout papers and not just “the” p-values which “prove” that the authors’ preconceptions are “true,” i.e. the p-valus of the main hypotheses.

Masicampo and Lalande rightly conclude:

This anomaly is consistent with the proposal that researchers, reviewers, and editors may place undue emphasis on statistical significance to determine the value of scientific results. Biases linked to achieving statistical significance appear to have a measurable impact on the research publication process.

The only thing wrong with the first sentence is the word “may”, which can be deleted; the deletion of the second sentence is “appear.”

Why p-values? Why are they so beloved? Why, given their known flaws and their ease of abuse, are they tolerated? Well, they are a form of freedom. P-values make the decision for you: thinking is not necessary. A number less than the magic threshold is seen as conclusive, end of story. Plug your data into automatic software and out pops the answer, ready for publishing.

But this reliance “exposes an overemphasis on statistical significance, which statisticians have long argued is hurtful to the field (Cohen, 1994; Schmidt, 1996) due in part because p values fail to convey such useful information as effect size and likelihood of replication (Clark, 1963; Cumming, 2008; Killeen, 2005; Kline, 2009; Rozeboom, 1960).”

I left those references in so you can see that it is not just Yours Truly who despairs over the use of p-values. One of these references is “Cohen, J. (1994). The earth is round (p<.05). American Psychologist, 49, 997–1003.” This is a well-known paper, written by a non-statistician, which I encourage you to see out and read.

The real finding is the subtle confirmation bias that seeps into peer-reviewed papers. The, conscious or not shading of results in the direction the of authors’ hope. Everybody thinks confirmation bias happens to the other guy. Nobody can see his own fingers slip.

Everybody also assumes that the other fellows publishing papers are “basically honest.” And they are, basically. More or less.

Update Reader Koene Van Dijk notes the paper is no longer available free, but gives us the email address of the authors: masicaej@wfu.edu or lalande.danielr@gmail.com.


Thanks to the many readers who sent this one in, including Dean Dardno, Bob Ludwick, Gary Boden; plus @medskep at Twitter from whom I first learnt of this paper.

Reasoning To Belief: Feser’s The Last Superstition: A Refutation of the New Atheism — Interlude: Empiricism Is False

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

In going through Feser’s book, many in the comments profess to be confused about what truth means, and about the difference from there being one overall (or foundational) Truth, and many individual truths. I believe one of us even took up Pilate’s speech and asked, without irony, “Quid est veritas?” (To even ask the question presupposes its existence.)

Several other readers also claimed to be empiricists, which are those who believe in truth but say that all truths are discovered solely by observation. Empiricism is false: all truths cannot be discovered by observation. Quite simply, even its defining statement is self-contradictory. I asked yesterday how do we know, since we have not observed them, that there are an infinity of numbers. Answer came there none. This small example proves empiricism false.

But since those who wish to hold to empiricism (for fear of what abandoning it implies?) will not be satisfied by so telegraphic a proof, here is a longer one, given by the (non-theist) philosopher David Stove. I find it exceptionally lovely. We’ve seen this before, but today we’re seeing it again.

Stove shows each of us must come equipped with knowledge which cannot be learned. Stuff that is only known to be true only through introspection, via what we call intuition or faith, or what yesterday we called revelation; philosophers usually settle on the technical term a priori (or on phrases more technical still).

David StoveThis is just one (of many) proofs given by David Stove in his The Rationality of Induction1 He made this argument in the support of revealed knowledge in his larger work showing induction is reasonable2. A man named Bolzano is named in the proof: all you need know about that gentleman is that he disputed the idea that we all of us come with built-in knowledge.

Reading this passage, as with reading any proof, requires some sophistication. This cannot be avoided. The formula numbers are as they appeared in Stove’s book. The unseen formula “(149)” is here equivalent to “(166)” below.

First, as to our knowledge of validity. Bolzano says that the validity of barbara, or rather, that the barbara schema always preserves truth, is a hypothesis reasonably believed by us, just because of the extensive experience we have had of never finding a counter-example to it. That is, our grounds for believing (149), or rather, for believing

     (166) For all x, all F, all G, either ‘x is F and all F are G is false’, or ‘x is G‘ is true,

consist just of observations we have made, such as

     (151) Abe is black and Abe is a person now in this room and all persons now in this room are black.

That is putting it starkly; still it is, in essence, what Bolzano believes. We learn deductive logic by inductive inference.

But now, this is tacitly to concede, to certain propositions of non-deductive logic, precisely the intuitive status which Bolzano expressly denies to any proposition of deductive logic. Our putative logic learner is supposed to be devoid of all intuitive logical knowledge. Yet Bolzano is evidently crediting him with knowing, straight off, at least this much: that

     (167): (151) confirms (149).

Of course, he need not be supposed to know that he knows (167); still, he is evidently being supposed to know it. But to know (167) is to have some logical knowledge, even is only non-deductive logical knowledge.

And Bolzano must suppose that (167) is known by our logic learner intuitively. Otherwise he would have to have learnt it, as he is supposed to be learning (166), by experience. And how would he accomplish this?

It must at any rate be from some observation-statements. I do not know what kind of observation-statements Bolzano would regard as confirming (167): let us just call these observation-statements

     (167) O1.

But even if our logic learner has found by experience that O1 he will be no further advanced. To learn (167), he needs to know, not only that O1, but that

     (169): (168) confirms (167).

But this is a proposition of logic too. If he does not know (169) intuitively, as by hypothesis he does not, then he will have to learn it, too, from experience. No doubt from some observations

     (170) O2.

But that is not enough. He will also need to know that

     (171): (170) confirms (169);

and so on.

Obviously, he is never going to make it. Experience is not enough.

As a sketch: to even know that an observation confirms some statement is to use the knowledge that “observations confirms this statement”, and the knowledge of that could not have been discovered observationally, or empirically. We must already know (at least) this before we begin. Just as we must know the axioms before we begin mathematics. Axioms by definition are truths which cannot be proved.

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.


1p. 162-163. This book, especially the second half, is a treasure that all statisticians, probabilists, and logicians should read.

2Yes, some people think it isn’t. Bolazno was not one of these: he thought all (as in all) knowledge was known empirically.

Reasoning To Belief: Feser’s The Last Superstition: A Refutation of the New Atheism — Part III

First Things First

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

There is only one truth, and everybody must operate by its implications. You needn’t (yet) believe this Truth is God, nor must you even know that this Truth exists. But you’re stuck with it all the same. A man jumping from a tall building need not know it is gravity which grips him, nor need he have any idea what is about to happen to him. Another man may believe he can fly. A third fellow, a physicist, may spout his controversial theory that gravity is a fiction. But all will reenact the flight of Newton’s apple.

Parmenides will walk from town to town lecturing that all movement is impossible. Zeno will hear of Parmenides’s approach and will claim, even as he sees him cresting the horizon, that Parmenides will never make it. Berkeley will follow Johnson and stub his toe, and then deny the swelling. A solipsist will lecture earnestly how wonderful the world would be if only everybody believed as he did that nobody else existed. A materialist will lecture earnestly how wonderful the world would be if only everybody acknowledged as he did that other people existed, but that they were all fictions of their own imaginations.

A relativist will argue that it is certain that there are no truths. A scientist will claim it is certain that only observation can tell us that there are certainties. A socialist will—but enough insanity!

It is clear enough, to most of us, that we must operate by the “laws” of physics. Ignorance of these laws is no excuse. Unlike human laws, it is impossible to break the dictates of physics. Even if one claims that one can or has. Exceptions are only apparent, the result of lack of knowledge. And so it is will all Truth, even metaphysical truth. We must follows its laws, even when we’re unaware of them, or claim to be.

Observation cannot tell us all truth. This is proved simply: we cannot observe that only observations can tell us all truth. We can and do—must—use reason to deduce that which cannot be observed. It then follows that we must come built with (or are at some point given) the revelations necessary to carry out these operations. The three paths to truth are: revelation, reason, and observation. Scoffing? You shouldn’t. This is how all mathematics works. Axioms are revealed, reason carries them forward, observations prove the application. It is is not through reason or observation that we know the axioms. It is not through revelation or observation that we know there are an infinity of numbers. It is not through reason or revelation that we learn which equation fits a set of numbers best.

Now given all this, it behooves us to sit and to think and to figure out just what the truth is. The first question is: what can we know? The first result is that we cannot know all of Truth. The proof is trivial: most, including the living and dead, people didn’t or don’t. Consider a scene from Hannah and Her Sisters, in which Woody Allen’s character is telling his aged parents of his (temporary) conversion to Catholicism. His mother is distressed and somehow the conversation turns to history. The mother shouts to the father to explain to Woody why there were Nazis. “How the hell do I know why there were Nazis,” the father says, “I don’t know even how the can opener works!” “We” don’t know anything; only an individual can know. Plus, there is no proof that all can be known; the universe and reality are far too complex for most of us, perhaps for any of us. Observations—history is saturated with examples—shows that mistakes are easy and common.

Obversely, there is plenty we do know, including philosophical and metaphysical truths. Feser says scientists begin with the metaphysical truths that

[T]here is a physical world existing independently of our minds; this world is characterized by various objective patterns and regularities; our senses are at least partially reliable sources of information about this world; there are objective laws of logic and mathematics that apply to the objective world outside our mind; our cognitive powers—of concept-formation, reasoning from premises to conclusion, and so forth—afford us a grasp of these laws and can reliably take use form evidence derived from the sense to conclusions about the physical world; the language we use can adequately express truths about these laws and about the external world; and so on and on.

But it is only recently, in the last few minutes of intellectual thought, that some scientists would deny not just these metaphysical truths, but all of metaphysics. These scientists are, however, no different than the man who denies gravity. Feser quotes from E.A. Burtt: “even the attempt to escape metaphysics is no sooner put in the form of a propositions than it is seen to involve highly significant metaphysical postulates.” You can deny truth, but you cannot escape it: “…your metaphysics will be held uncritically because it is unconscious; moreover…it will be propagated by insinuation rather than by direct argument.” The scientist who disbelieves in metaphysics “must have a method, and he will be under a strong and constant temptation to make a metaphysics out of his method, that is, to suppose the universe ultimately of such a sort that his method must be appropriate and successful.”

Very well: we must have a metaphysics, and as we have seen above—to quote from The Highlander, a source which never stops giving—there can be only one. Next time we start with Feser’s recounting of Aquinas’s First Way.

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.


1Note: all comments about Feser’s tone or about the personalities of the New Atheists will be removed to Part I of this series. A related dodge—which is always obvious—is to say, “These arguments stink” and then to leave without saying exactly, precisely, logically why. However, you’re welcome to use this ploy if you think that, just this once, it will work. The comment by “Cole” at the top illustrates this technique.

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