William M. Briggs

Statistician to the Stars!

Category: Philosophy (page 1 of 148)

The philosophy of science, empiricism, a priori reasoning, epistemology, and so on.

Don’t Use Statistics Unless You Have To

It's catching.

It’s catching. (Image source.)

We’re finally getting it, as evinced by the responses to the article “Netherlands Temperature Controversy: Or, Yet Again, How Not To Do Time Series.

Let’s return to the Screaming Willies. Quoting myself (more or less):

You’re a doctor (your mother is proud) and have invented a new pill, profitizol, said to cure the screaming willies. You give this pill to 100 volunteer sufferers, and to another 100 you give an identically looking placebo.

Here are the facts, doc: 72 folks in the profitizol group got better, whereas only 58 in the placebo group did.

Now here is what I swear is not a trick question. If you can answer it, you’ll have grasped the true essence of statistical modeling. In what group were there a greater proportion of recoverers?

This is the same question that was asked [before], but with respect to…temperature values. Once we decided what was meant by a “trend”—itself no easy task—the question was: Was there a trend?

May I have a drum roll, please! The answer to today’s question is—isn’t the tension unbearable?—more people in the profitizol group got better.

Probability models aren’t needed: the result is unambiguously 100% certain sure.

As before, I asked, what caused the difference in rates? I don’t know and neither do you. It might have been the differences due to profitizol or it might be due to many other things about which we have no evidence. All we measured was who took what substance and who got better.

What caused the temperature to do what it did? I don’t know that either. Strike that. I do know that it wasn’t time. Time is not a cause. Fitting any standard time series model is thus admitting that we don’t know what the cause was or causes were. This is another reason only to use these models in a predictive manner: because we don’t know the causes. And because we don’t know the causes, it does not follow that the lone sole only cause was, say, strictly linear forcing. Or some weird force that just happened to match what some smoother (running means, say) produced.

Probability isn’t needed to say what happened. We can look and see that for ourselves. Probability is only needed to say what might yet happen (or rather, to say things about that which we haven’t yet observed, even though the observations took place in the past).

Probability does not say why something happened.

I pray that you will memorize that statement. If everybody who used probability models recited that statement while standing at attention before writing a paper, the world would be spared much grief.

In our case, is there any evidence profitizol was the cause of some of the “extra” cures? Well, sure. The difference itself is that evidence. But there’s no proof. What is there proof of?

That it cannot be that profitizol “works” in the sense that everybody who gets it is cured. The proof is the observation that not everybody who got the drug was cured. There is thus similar proof that the placebo doesn’t “work” either. We also know for sure that some thing or things caused each person who got better to get better, and other causes that made people who were sick to stay sick. Different causes.

Another thing we know with certainty: that “chance” didn’t cause the observed difference. Chance like time is not a cause. That is why we do not need probability models to say what happened! Nothing is ever “due” to chance!

This is why hypothesis testing must go, must be purged, must be repulsed, must be shunned, must be abandoned, must be left behind like an 18-year-old purges her commonsense when she matriculates at Smith.

Amusingly for this set of data a test of proportions gives a p-value of 0.054, so a researcher who used that test would write the baseless headline, “No Link Between Profitizol And The Screaming Willies!” But if the researcher had used logistic regression, the p-value would have been 0.039, which would have seen the baseless headline “Profitizol Linked To Screaming Willies Cure!”

Both researchers would falsely think in terms of cause, and both would be sure that cause was or wasn’t present. Like I said, time for hypothesis testing to die the death it deserves. Bring out the guillotine.

Since this is the week of Thanksgiving, that’s enough for now.

Summary Against Modern Thought: God Is Not A Body

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.

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Chapter 27: That God Is Not In The Form Of A Body

1 ACCORDINGLY, having shown that God is not the being of all,i it can be proved in like manner that God is not the form of any thing.

2 For the divine being cannot be the being of a quiddity that is not it own being, as shown above.[1] Now that which is the divine being itself is no other than God. Therefore it is impossible for God to be the form of any other thing.ii

3 Further. The form of a body is not its very being but the principle of its being. But God is being itself. Therefore God is not the form of a body.

4 Again. The union of form and matter results in a composite, and this is a whole in respect of form and matter. Now the parts are in potentiality with respect to the whole: but in God there is no potentiality.[2] Therefore it is impossible for God to be the form united to any thing.

5 Again. That which has being per se, is more excellent than what has being in another. Now every form of a body has being in another. Since then God is the most excellent being, as the first cause of being,[3] He cannot be the form of any thing.iii

6 Moreover, this can also be proved from the eternity of movement, as follows.[4] If God were the form of a movable thing, since He is the first mover, the composite will be its own mover. But that which moves itself can be moved and not moved. Therefore it is in it to be either. Now a thing of this kind has not of itself indefectibility of movement. Therefore above that which moves itself we must place something else as first mover, which confers on it perpetuity of movement. And thus God Who is the first mover is not the form of a body that moves itself.iv

7 This argument avails for those who hold the eternity of movement. Yet if this be not granted the same conclusion may be drawn from the regularity of the heavenly movement. For just as that which moves itself can both be at rest and be moved, so can it be moved with greater or less velocity. Wherefore the necessity of uniformity in the heavenly movement depends on some higher principle that is altogether immovable, and that is not the part, through being the form, of a body which moves itself.v

8 The authority of Scripture is in agreement with this truth. For it is written in the psalm:[5] Thy magnificence is elevated above the heavens; and (Job xi. 8, 9): He is higher than heaven, and what wilt thou do?…the measure of Him is longer than the earth, and deeper[6] than the sea.vi

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iGod is not the universe. Pantheism is out.

iiAs proved before, God’s existence and essence are the same; existence itself is not a body; a body is partly in act, partly in potential, but in God there is no potential; just as God is not made of material stuff; thus God is not a body. These same (now proven) premises are picked up in arguments 3 and 4.

iiiThe thing to recall here is that objects, like bodies, are composites of form and matter. The same matter under the “influence” of other forms is a different object; i.e. objects are instantiated forms. Ed Feser’s favorite example (now forever stuck in my head) is rubber balls and erasers: two objects made of the same matter, but with different forms. But God is not made of matter, and God’s form is His existence, therefore He is not a body.

ivWe ever come back to Chapter 13, which is best to review. So much flows from the demonstration that God is Unmoved Mover, the Uncaused Cause, and other nicknames, that it is astonishing. The proof here flows directly (and easily).

vIt’s as well here as anywhere to remind us of the kind of movement Aquinas spoke of in his proof of God being the First Cause. He was not talking about the kind of movement like dominoes, where one pushes another and so on. He meant the here-and-now bottom-down ultimate cause of all movement. If you can’t remember this distinction, do the review before commenting.

viI normally leave the scriptural arguments out because they are not convincing to modern audiences. However in this case, since the question has often arise that since Jesus was in the form of a body, and in the Eucharistic species, and that Jesus is part of the Trinity, i.e. is God, does it not follow that God is a body? It does not. Jesus is God, and had a fully divine nature. But he was also a man and had a human nature, a nature that required a body. That part of him was not divine; it was human flesh, just like ours. The Eucharistic is likewise of two natures, divine and mundane. The bread is there, but do is the divine. Now how are these miracles brought about? I haven’t the slightest idea.

Likewise, when scripture uses figurative or metaphorical language (“Seated a the right hand of God…”), it is just that: figurative or metaphorical. Avoid the atheist temptation to read all of the Bible literally.

[1] Ch. xxii.
[2] Ch. xvi.
[3] Ch. xiii.
[4] Cf. chs. xiii., xx.
[5] Ps. viii. 2.
[6] Vulg., broader.
[7] Sum. Th. P. I., Q. iii., A. 8.

Pascal’s Pensées, A Tour: I

PascalSince our walk through Summa Contra Gentiles is going so well, why not let’s do the same with Pascal’s sketchbook on what we can now call Thinking Thursdays. We’ll use the Dutton Edition, freely available at Project Gutenberg. (I’m removing that edition’s footnotes.)

Update Comments fixed.

1

The difference between the mathematical and the intuitive mind1.—In the one the principles are palpable, but removed from ordinary use; so that for want of habit it is difficult to turn one’s mind in that direction: but if one turns it thither ever so little, one sees the principles fully, and one must have a quite inaccurate mind who reasons wrongly from principles so plain that it is almost impossible they should escape notice.

But in the intuitive mind the principles are found in common use, and are before the eyes of everybody. One has only to look, and no effort is necessary; it is only a question of good eyesight, but it must be good, for the principles are so subtle and so numerous, that it is almost impossible but that some escape notice. Now the omission of one principle leads to error; thus one must have very clear sight to see all the principles, and in the next place an accurate mind not to draw false deductions from known principles.

All mathematicians would then be intuitive if they had clear sight, for they do not reason incorrectly from principles known to them; and intuitive minds would be mathematical if they could turn their eyes to the principles of mathematics to which they are unused.2

The reason, therefore, that some intuitive minds are not mathematical is that they cannot at all turn their attention to the principles of mathematics. But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those[Pg 2] who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics; because the principles are not known to us in the same way, and because it would be an endless matter to undertake it. We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree. And thus it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it.3

Intuitive minds, on the contrary, being thus accustomed to judge at a single glance, are so astonished when they are presented with propositions of which they understand nothing, and the way to which is through definitions and axioms so sterile, and which they are not accustomed to see thus in detail, that they are repelled and disheartened.

But dull minds are never either intuitive or mathematical.

Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate and insufferable, for they are only right when the principles are quite clear.

And men of intuition who are only intuitive cannot have the patience to reach to first principles of things speculative and conceptual, which they have never seen in the world, and which are altogether out of the common.4

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1From Allan Bloom The Closing of the American Mind: How Higher Education Has Failed Democracy and Impoverished the Souls of Today’s Students (p. 52):

Every Frenchman is born, or at least early on becomes, Cartesian [the mathematician above] or Pascalian [the intuitive]…Descartes and Pascal represent a choice between reason and revelation, science and piety, the choice from which everything else follows…These great opponents whom no snythesis can unite—the opposition between bon sens and faith against all odds—set in motion a dualism…

It was, therefore, very French of Toucqueville to say that the Americans’ method of thought was Cartesian…

2The great fallacy is to suppose we can do with only one of these types (even inside one body). American and British thought plunges headlong into the mathematical—we are all Cartesians here. This isn’t a new observation. Tocqueville said “each American appeals to the individual exercise of his own understanding alone. America is therefore one of the countries in the world where philosophy is least studied, and where the precepts of Descartes are best applied…they follow his maxims because this very social condition naturally disposes their understanding to adopt them.”

Strict Cartesianism leads to scientism and the worship of rationality and reason as if these could live without intellection, what Pascal called intuition. No mathematician could even begin to think without intellection. Intuition, used in this special sense, is necessary and prior to logic, mathematics, and ratio. Axioms, for instance, are not provided by rationality. Pure rationality is always incomplete. I’ll have much more to say about this in the coming weeks.

3It is well to put it here the fallacy that says that because sometimes our intuitions fail us that they always do. Sometimes our mathematical reason also fails us, but nobody would claim that therefore all of mathematics should be tossed or is suspect (except radical skeptics; paradoxically, personages only found in Western universities).

4Relying only on one leads to rank pedantry, sterility, and blind alleys.

The Scientific Ethicist: Mathematics & Logic Edition

The Scientific Ethicist, PhD

The Scientific Ethicist, PhD

This week, three letters from concerned readers.

Can I Skip College?

Dear Scientific Ethicist,

I am a junior in high school and will graduate in the first semester of my senior year. Someday I would like to be a stay-at-home mom. I have no interest in going to college. I feel it would be a waste of money for me to go when I don’t intend to use my degree.

To say my parents are disappointed in me over this is putting it mildly. They have a life planned for me that includes college. I would also like to move away to somewhere where it’s warm year-round, and they don’t like that idea either.

How do I make them understand that this is MY life and everything will be OK?

Uninterested in Idaho

Dear Uninterested,

This is obviously related to the Fundamental Theorem of Calculus. Let me quote Wikipedia, “The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that an indefinite integral of a function[1] can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.

The second part, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.”

As you can see, the rest follows easily. That’s the power of mathematics!

The Scientific Ethicist

P.S. See also the first, second, and third laws of thermodynamics in reference to your comment about heat.

Dating Woes

Dear Scientific Ethicist,

The school year has started and many high school girls like me are faced with a similar problem: how to politely decline when a boy asks you to a dance.

Whether it be homecoming, winter formal or prom, some boys go all out and ask girls in elaborate and creative ways. I don’t know what to do in these situations if I don’t want to go with the boy who is asking me. I feel bad saying “no” because of all the work they put into it, and also sometimes there is an audience watching. Should I just go anyway?

Saratoga Teen

Dear Saratoga,

Meta logic is the answer here, especially formal systems. A formal system must have a finite alphabet, a listing of the strict rules of grammar (exceptions aren’t allowed), a specified list of inference rules, and finally a set of indubitable axioms. The latter may be made up because, of course, science has no way of externally checking the validity of any set of axioms.

The point for you, and I’m sure you already see it, is that since you can create this formal system any way you like, the next time to you attend a formal you can act any way you like. Logic guarantees this.

Truly there is nothing more logical than logic!

The Scientific Ethicist

Social Media Prayers

Dear Scientific Ethicist,

I frequently receive requests via Facebook and other social media sites asking for prayers for people who are ill or suffering a loss. I’m not a religious person, but I would like to acknowledge their pain and extend my sympathy. Any suggestions?

Challenged in Tucson

Dear Challenged,

Have you considered that e is irrational? Every schoolgirl ethicist knows that

e = \sum_{n = 0}^{\infty} \frac{1}{n!}\cdot .

Now if e were rational, it would have the form a/b where the two numbers are integers, and where obviously b does not equal 1. Then

\frac{1}{1}\ + \frac{1}{1}\ < e = \frac{1}{1}\ + \frac{1}{1}\ + \frac{1}{1\cdot2}\ + \frac{1}{1\cdot2\cdot3}\ + ...  < \frac{1}{1}\ + \frac{1}{1}\ + \frac{1}{1\cdot2}\ + \frac{1}{1\cdot2\cdot2}\ + ... = 3.

Well, we repeat a procedure like this, working with infinite series, manipulating this way and that, and we finally conclude that e cannot be rational.

But you can be, using math, logic, and science!

The Scientific Ethicist

Be sure not to miss other penetrating installments of The Scientific Ethicist. Or send in your questions today!

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