William M. Briggs

Statistician to the Stars!

Author: Briggs (page 151 of 423)

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.

Stressed Men Prefer Chubby Chicks

Here’s a title for you, “BMI Not WHR Modulates BOLD fMRI Responses in a Sub-Cortical Reward Network When Participants Judge the Attractiveness of Human Female Bodies.” How about that? I had my money on WHR.

What? Waist-to-hip ratio, of course. The preferred marker of attractiveness for many men. I myself like to reward my sub-cortical network with larger WHR and not higher BMI. But that’s just me, and I’ve been under a lot of stress.

Which makes my proclivity even stranger when you consider that one of the same authors of this paper, Martin J Tov&eactue;e, also wrote this one: “The Impact of Psychological Stress on Men’s Judgements of Female Body Size.” It says that men under stress reach for more.

Men just shy of freaking out rate “significantly heavier female body size as maximally attractive”, while fellows who swim in more placid waters like ‘em thin. This is what science says, this is therefore what is so.

What happened was that Swami and Tov&eactue;e gathered 81 British white WEIRD men and split them asunder, half-plus-one (rounding down) undergoing a stressful trial, and half allowed not to fret. WEIRD equals “Western, Educated, Industrialized, Rich, and Democratic.” I.e., college students; white ones here to acknowledge that different races like different kinds of womenfolk.

The stress group got the TSST (say it) “a 15-minute laboratory stressor that has been reliably shown to increase levels of acute psychological stress.” Apparently this is 10 minutes of chatting followed by an abrupt requirement to “serially subtract the number 13 from 1,022 as fast and accurately as possible.” Watch them free cortisol levels soar! At least it wasn’t adding fractions.

After allowing the math challenged students—no calculators!—to cool their heels for twenty minutes, they ushered them aside and asked them questions about pretty girls. The control group just had to sit in a room “where they waited quietly” and then had to answer the same questions. All 81 men had their weight and height measured. “[W]ithout shoes and in light clothing.” Naturally.

The men then ogled “10 photographic and standardized images of women in front view. The women depicted in the PFRS represent the full range of established BMI categories, from emaciated to obese.” Then they “rated each of the 10 images for physical attractiveness on a 9-point Likert-type scale (1 = Very unattractive, 9 = Very attractive).”

I bet that not one of those men, before they came to this experiment, knew they were employing the scientifically validated Likert-scale when they previously engaged in the very popular hobby of rating looks. Here, however, we must wonder how the men dealt with the rescaling; I mean the missing “10”.

Oh yes, then the men were asked whether they agreed with statements like “I have never been more hungry.”

Turns out that the stressed and calm men liked the Emaciated and Obese pictures least (the labels are so given in the paper). Both groups thought the same about the Underweight, but the stressed gave slightly higher mean marks to Normal and Overweight pictures. The variance of the marks of the stressed men was almost everywhere higher (except for the Emaciated group).

From this they conclude “that participants experiencing psychological stress selected a significantly heavier female body size as maximally attractive compared to the control group.” The “significantly” meant statistically significantly (thank you p-values!) and not in size because, as the authors admit, “the shift in preferences may appear small from a practical point-of-view,” but they still got a paper out of it.

They were however able to theorize that “human mate choice preferences are likely context-specific and recalibrate as local conditions and experiences change, the end result being mate preferences that remain adaptive regardless of the environmental landscape.” Also, some men “may idealise larger body sizes because such body types are associated with better ability to handle environmental threat.” Get a big one in case a famine hits!

The real good news is that “future work” is needed, figuring whether or how “the experience of stress impacted on state self-esteem, empathy, or related constructs…may have impacted on body size perceptions.”


Thanks to Al Perrella for the tip.

Psychic Cleaners, Emails, & Dialogue

No starch on the auras, please

This is a somewhat famous sign on the royal road in Mountain View, California. To economize, the sign is shared by a gypsy and a dry cleaners. I passed by and saw the sign but did not see any mountains. Which is fair enough. My folks live in a town called Mt. Pleasant, which is flatter than an EEG of an audience member at an Al Gore speech. When it comes to cities, you can’t go by names.

Regulars will have noticed a diminution of posts and answers to comments these past two weeks. I’m traveling and particularly busy and I haven’t had the time to keep up. I anticipate this frenzied state will last about another week.

I also have a few hundred emails from you (yes, the word is hundreds); story tips, comments, requests to read this or that, and so forth. I appreciate these very much. But I do apologize that I cannot answer each email personally. I have not yet even been able to read them all.

It’s kind of curious. There are many regulars here, people whom we all know by their comments. There are also many who come but who never leave a comment. And many more who come and who prefer to comment via email. Earlier this week, a habitué sent a charming missive which stated, “You are a liar.” Another said, “Small-minded People like you are doomed to be miserable.” And then I got one that fixated on my growing lack of hair (“A bald head is not an indication that you have matured.”).

As far as emails go, I have noticed a distinct correlation between the sex of the sender and the level of vituperation. I’ll let you guess what this is.

Finally, dialogue. Have you ever remarked that a person or group asking for dialogue is interested in anything but? That instead it is a code word for, “You change your ways, because I’m not changing mine.”

Back to work! Oh, I was able to do a post this morning despite being busy by the simple expedient of arising at 4 am to a trilling car alarm. I went into the motel office at 6 for coffee and said to the clerk, “Aren’t car alarms great?” He replied, “Oh, I’m sorry. That’s actually my car. My battery died on my remote and I’m not allowed to leave the property until somebody relieves me.”

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

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

Act and Potential

TLS is not a complete work of theology or philosophy, nor is it intended to be. The answers to All Questions are not found in its pages. Every distinction with a difference is not parsed, every depth is not plumbed. Feser did not, and did not intend to, build a complete theory of anything; he provided just enough material to show his central argument was true and then signed off.

Nor is this a book of religion. You won’t discover why Catholicism is to be preferred to Methodism. There is no discourse on the valuable insights on the nature of God given to us by Buddhists and Muslims. The festival of Obon never makes an appearance. There isn’t the slightest attempt to proselytize. Thus any rebuttal focusing on some Christian in history who has acted badly, or information on another who has acted saintly, is irrelevant.1 The first person to wield these themes in an effort to dispatch Feser has admitted losing the argument.

The argument is this: that there is no dispute between science and classical metaphysics, that you cannot have science without this philosophy, that it is possible to come to a knowledge of God purely through reason and here are some irrefutable arguments, that the universe is not a giant machine nor are the things in it (including us) small machines, that the charges of “wishful thinking”, “rank ignorance”, “pastafarianism”, “believers are stupid (and I’m smart!)” flung about by New Atheists are not just false, not just the opposite of the truth, but self-rebounding.

And so to work.

Realism is the “view that universals, numbers and/or propositions exist objectively, apart from the human mind and distinct from any material or physical features of the world.” Plato’s Theory of Forms is one such view, though not the only, nor the best. For that we turn to Aristotle—“The Philosopher,” as he was known to the Schoolmen—as so many have in the past, and as an increasing number are today, after a long period of shocking neglect.

On the historical slight ushered in by Bacon and others, Feser says, “Abandoning Aristotelianism, as the founders of modern philosophy did, was the single greatest mistake ever made in the entire history of Western thought” (emphasis original).

Just what have we left behind? Much.

Feser is fond of rubber balls: he is forever bouncing or abusing one. In TLS his ball is blue, in Aquinas he changes it to red. This is useful in itself, because it is obvious that a blue rubber ball is potentially a red one because, of course, a blue one could be painted or dyed red. A blue ball is just as obviously actually blue.

In this simple example are two concepts central to understanding Aristotle’s metaphysics: actuality and potentiality. The actual rubber ball may potentially be a gooey mess, but it is not this potential to be gooey which causes the ball to melt; something external (like heat) to the potential must act on the ball and turn the potential into a new actuality. Act turns potential to actuality.

From these observations is derived Aristotle’s dictum that whatever is moved is moved by another, which in modern phraseology is better put as whatever is changed is changed by another, a slicker way to say that a potential cannot act. A potential has to be a potential for something actual, too; only something actual can be something else potentially. There cannot be a thing which is purely potential and is nothing actually. But there can be things which are actual and which have potentialities. And it even so that there is a thing which is purely actual with no potentiality.

Other examples, more well known: a statue is potentially in a block of marble, but it takes the act of a sculptor to bring it out. A block of wood is potentially a table, but it takes the act of a carpenter to make it so. But I think it wise Feser did not emphasize these old saws because they too quickly bring to mind the idea of a designing intelligence which is rarely needed, especially in the case of rubber balls. Too see this: a blue rubber ball dropped from a soaring aeroplane at 10,000 feet is potentially at 0 feet, but it is not the potentially 0 feet which acts on the ball, it is something external.

What else can the ball potentially be? Well, it can’t be a walrus. For one thing, there isn’t enough mass or energy in a blue rubber ball that can, through the physical means known to us, be changed into a walrus. We can of course imagine the ball morphing into a living, two-ton tusked beat, say via a magical spell, but then we have left reality for the world of fantasy. It is also not that something cannot be added to the ball, like in the case of red paint turning a blue ball red, but that there is no way even adding the right amount of mass or energy the ball can change.

So far there is nothing controversial, very little which could act on your potential belief in God and make it into an actual belief in God. But that’s coming.

Note I am sorry for the brevity of this installment, which probably has more than its usual share of typos. But I am traveling and staying in a motel which has lost its internet connection, and so I’m finishing this post on my portable radiophone. My cell abuts the 24-hour laundry room and so I’m also operating on less sleep.

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, “Feser’s 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 “Rob” at the top illustrates this technique.

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

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