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Category: Philosophy

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

April 19, 2018 | 11 Comments

A Society Run By Atheist Scientists Would Be Horrible

Skeptic Michael Shermer is pleased the number of folks with no religious affiliation is growing, and will likely continue to grow.

One estimate is that “there are more than 64 million American atheists, a staggering number that no politician can afford to ignore.” There are about 358 million people in the USA, making about 18% who are effectively atheist. That’s on the low end. The same estimate suggests the number may be as high as 26%, or 93 million.

He says, “This shift away from the dominance of any one religion is good for a secular society whose government is structured to discourage catch basins of power from building up and spilling over into people’s private lives.”

This is not only not true, it is willfully blind. The catch basin of power known as the State has not only spilled over into people’s lives, but it is overtaking them. Each day the State discovers a new area which it can control, regulate, manipulate, “nudge”, or direct. Religion and the family were able to hold the State at bay, at least to some extent. Which is why it is not surprising these institutions are under attack by the State.

An Unreasonable Suggestion

Moreover, if these trends continue, we should be thinking about the deeper implications for how people will find meaning as the traditional source of it wanes in influence. And we should continue working on grounding our morals and values on viable secular sources such as reason and science.

This is wrong. And also frightening. We cannot ground our morals on reason and science. Reason may assist but science is as silent as Hell is not on which morals and values a society should favor. Science is in the measurement and not the judgement business. It can tell us, say, how many heads are lopped off the world over, including those in would-be mothers’ wombs, but it cannot say whether lopping itself is good or bad. Reason should have told Shermer that.

Maybe it did but he wasn’t listening. The message isn’t one he’d like to hear. But it’s as simple dropping a piece of toast buttered side down.

The Silence of Science

Science cannot say if murder is right or wrong. That is a moral judgement and moral judgments are not scientific. Science can describe where and when murders take place, and under what circumstances, and it might even be able to predict with varying accuracy where murders are going to take place, or possibly even who might commit them.

These activities involve measurement, modeling, and prediction. That is what science does, and only what science does.

A scientist can say, “Click here to read the rest.

April 15, 2018 | No comments

Summary Against Modern Thought: How Things Are Ordered To Their Ends

Summary Against Modern Thought: How Things Imitate Divine Goodness

Previous post.

Question: What is the final cause? Answer: Yes.

How Things Are Ordered To Their Ends In Their Various Ways

1 It can be shown from the foregoing that the last thing through which any real being is ordered to its end is its operation. Yet this is done in various ways, depending on the diversity of operations.

2 One kind of operation pertains to a thing as the mover of another, as in the actions of heating or sawing. Another is the operation of a thing that is moved by another, as in the case of being heated or being sawed. Still another operation is the perfection of an actually existing agent which does not tend to produce a change in another thing. And these last differ, first of all, from passion and motion, and secondly from action transitively productive of change in exterior matter.

Examples of operations in this third sense are understanding, sensing, and willing. Hence, it is clear that the things which are moved, or passively worked on only, without actively moving or doing anything, tend to the divine likeness by being perfected within themselves; while the things that actively make and move, by virtue of their character, tend toward the divine likeness by being the causes of others. Finally, the things that move as a result of being moved tend toward the divine likeness in both ways.

Notes An example of the perfection of an actually existing agent is you reading St Thomas. I.e. not all change is movement. Which is a (minor) proof the world is not entirely physical.

3 Lower bodies, inasmuch as they are moved in their natural motions, are considered as moved things only, and not as movers, except in the accidental sense, for it may happen that a falling stone will put in motion a thing that gets in its way. And the same applies to alteration and the other kinds of change. Hence, the end of their motion is to achieve the divine likeness by being perfected in themselves; for instance, by possessing their proper form and being in their proper place.

4 On the other hand, celestial bodies move because they are moved. Hence, the end of their motion is to attain the divine likeness in both ways. In regard to the way which involves its own perfection, the celestial body comes to be in a certain place actually, to which place it was previously in potency. Nor does it achieve its perfection any less because it now stands in potency to the place in which it was previously. For, in the same way, prime matter tends toward its perfection by actually acquiring a form to which it was previously in potency, even though it then ceases to have the other form which it actually possessed before, for this is the way that matter may receive in succession all the forms to which it is potential, so that its entire potentiality may be successively reduced to act, which could not be done all at once. Hence, since a celestial body is in potency to place in the same way that prime matter is to form, it achieves its perfection through the fact that its entire potency to place is successively reduced to act, which could not be done all at once.

5 In regard to the way which involves movers that actively move, the end of their motion is to attain the divine likeness by being the causes of others. Now, they are the causes of others by the fact that they cause generation and corruption and other changes in these lower things. So, the motions of the celestial bodies, as actively moving, are ordered to the generation and corruption which take place in these lower bodies. Nor is it unfitting that celestial bodies should move for the sake of the generation and corruption of these lower things, even though lower bodies are of less value than celestial bodies, while, of course, the end should be more important than what is for the sake of the end.

Indeed, the generating agent acts for the sake of the form of the product of generation, yet this product is not more valuable than the agent; rather, in the case of univocal agents it is of the same species as the agent. In fact, the generating agent intends as its ultimate end, not the form of the product generated, which is the end of the process of generation, but the likeness of divine being in the perpetuation of the species and in the diffusion of its goodness, through the act of handing on its specific form to others, and of being the cause of others. Similarly, then, celestial bodies, although they are of greater value than lower bodies, tend toward the generation of these latter, and through their motions to the actual eduction of the forms of the products of generation, not as an ultimate end but as thereby intending the divine likeness as an ultimate end, inasmuch as they exist as the causes of other things.

Notes Eduction = to bring out or deduce; here the former usage. Contrast induct for the latter.

6 Now, we should keep in mind that a thing participates in the likeness of the divine will, through which things are brought into being and preserved, to the extent that it participates in the likeness of divine goodness which is the object of His will. Higher things participate more simply and more universally in the likeness of divine goodness, while lower things do so more particularly and more in detail. Hence, between celestial and lower bodies the likeness is not observed according to complete equivalence, as it is in the case of things of one kind. Rather, it is like the similarity of a universal agent to a particular effect. Therefore, just as in the order of lower bodies the intention of a particular agent is focused on the good of this species or that, so is the intention of a celestial body directed to the common good of corporeal substance which is preserved, and multiplied, and increased through generation.

7 As we said, since any moved thing, inasmuch as it is moved, tends to the divine likeness so that it may be perfected in itself, and since a thing is perfect in so far as it is actualized, the intention of everything existing in potency must be to tend through motion toward actuality. And so, the more posterior and more perfect an act is, the more fundamentally is the inclination of matter directed toward it. Hence, in regard to the last and most perfect act that matter can attain, the inclination of matter whereby it desires form must be inclined as toward the ultimate end of generation.

Now, among the acts pertaining to forms, certain gradations are found. Thus, prime matter is in potency, first of all, to the form of an element. When it is existing under the form of an element it is in potency to the form of a mixed body; that is why the elements are matter for the mixed body. Considered under the form of a mixed body, it is in potency to a vegetative soul, for this sort of soul is the act of a body.

In turn, the vegetative soul is in potency to a sensitive soul, and a sensitive one to an intellectual one. This the process of generation shows: at the start of generation there is the embryo living with plant life, later with animal life, and finally with human life. After this last type of form, no later and more noble form is found in the order of generable and corruptible things. Therefore, the ultimate end of the whole process of generation is the human soul, and matter tends toward it as toward an ultimate form. So, elements exist for the sake of mixed bodies; these latter exist for the sake of living bodies, among which plants exist for animals, and animals for men. Therefore, man is the end of the whole order of generation.

Notes And, of course, angels are not generable and corruptible, and are of a nobler form than we.

8 And since a thing is generated and preserved in being by the same reality, there is also an order in the preservation of things, which parallels the foregoing order of generation. Thus we see that mixed bodies are sustained by the appropriate qualities of the elements; Plants, in turn, are nourished by mixed bodies; animals get their nourishment from plants: so, those that are more perfect and more powerful from those that are more imperfect and weaker.

In fact, man uses all kinds of things for his own advantage: some for food, others for clothing. That is why he was created nude by nature, since he is able to make clothes for, himself from other things; just as nature also provided him with no appropriate nourishment, except milk, because he can obtain food for himself from a variety of things. Other things he uses for transportation, since we find man the inferior of many animals in quickness of movement, and in the strength to do work; other animals being provided, as it were, for his assistance.

And, in addition to this, man uses all sense objects for the perfection of intellectual knowledge. Hence it is said of man in the Psalms (8:8) in a statement directed to God: “You have subjected all things under his feet,” And Aristotle says, in the Politics I [5: 1254b 9], that man has natural dominion over all animals.

Notes Evidently this includes blogs.

9 So, if the motion of the heavens is ordered to generation, and if the whole of generation is ordered to man as a last end within this genus, it is clear that the end of celestial motion is ordered to man, as to an ultimate end in the genus of generable and mobile beings. Hence the statement in Deuteronomy (4:19) that God made celestial bodies “for the service of all peoples”.

April 8, 2018 | 5 Comments

Summary Against Modern Thought: Become More Godlike

Previous post.

Review! We skipped a week because of Easter, and memories are short.

That things naturally tend to become like God inasmuch as He is a cause

1 As a result, it is evident that things also tend toward the divine likeness by the fact that they are the cause of other things.

2 In fact, a created thing tends toward the divine likeness through its operation. Now, through its operation, one thing becomes the cause of another. Therefore, in this way, also, do things tend toward the divine likeness, in that they are the causes of other things.

Notes Don’t get cocky. You become “like” God because you can cause things, and God is cause itself. But animals also cause things, and so do bags of rocks.

3 Again, things tend toward the divine likeness inasmuch as He is good, as we said above. Now, it is as a result of the goodness of God that He confers being on all things, for a being acts by virtue of the fact that it is actually perfect. So, things generally desire to become like God in this respect, by being the causes of other things.

4 Besides, an orderly relation toward the good has the formal character of a good thing, as is clear from what we have said. Now, by the fact that it is the cause of another, a thing is ordered toward the good, for only the good is directly caused in itself; evil is merely caused accidentally, as we have shown. Therefore, to be the cause of other things is good. Now, a thing tends toward the divine likeness according to each good to which it inclines, since any created thing is good through participation in divine goodness. And so, things tend toward the divine likeness by the fact that they are causes of others.

5 Moreover, it is for the same reason that the effect tends to the likeness of the agent, and that the agent makes the effect like to itself, for the effect tends toward the end to which it is directed by the agent.

The agent tends to make the patient like the agent, not only in regard to its act of being, but also in regard to causality. For instance, just as the principles by which a natural agent subsists are conferred by the agent, so are the principles by which the effect is the cause of others. Thus, an animal receives from the generating agent, at the time of its generation, the nutritive power and also the generative power.

So, the effect does tend to be like the agent, not only in its species, but also in this characteristic of being the cause of others. Now, things tend to the likeness of God in the same way that effects tend to the likeness of the agent, as we have shown. Therefore, things naturally tend to become like God by the fact that they are the causes of others.

6 Furthermore, everything is at its peak perfection when it is able to make another thing like itself; thus, a thing is a perfect source of light when it can enlighten other things. Now, everything tending to its own perfection tends toward the divine likeness. So, a thing tends to the divine likeness by tending to be the cause of other things.

Notes And this is why our saint can teach us so well.

7 And since a cause, as such, is superior to the thing caused, it is evident that to tend toward the divine likeness in the manner of something that causes others is appropriate to higher types of beings.

8 Again, a thing must first be perfect in itself before it can cause another thing, as we have said already. So, this final perfection comes to a thing in order that it may exist as the cause of others. Therefore, since a created thing tends to the divine likeness in many ways, this one whereby it seeks the divine likeness by being the cause of others takes the ultimate place. Hence Dionysius says, in the third chapter of On the Celestial Hierarchy, that “of all things, it is more divine to become a co-worker with God”; in accord with the statement of the Apostle: “we are God’s coadjutors” (1 Cor, 3:9).

Notes Do God’s will.

April 5, 2018 | 20 Comments

The Gremlins Of MCMC: Or, Computer Simulations Are Not What You Think

I don’t think we’re clear on what simulation is NOT. RANDOMNESS IS NOT NECESSARY, for the simple reason randomness is merely a state of knowledge. Hence this classic post from 12 June 2017.

“Let me get this straight. You said what makes your car go?”

“You heard me. Gremlins.”

“Grelims make your car go.”

“Look, it’s obvious. The cars runs, doesn’t it? It has to run for some reason, right? Everybody says that reason is gremlins. So it’s gremlins. No, wait. I know what you’re going to say. You’re going to say I don’t know why gremlins make it go, and you’re right, I don’t. Nobody does. But it’s gremlins.”

“And if I told you instead your car runs by a purely mechanical process, the result of internal combustion causing movement through a complex but straightforward process, would that interest you at all?”

“No. Look, I don’t care. It runs and that it’s gremlins is enough explanation for me. I get where I want to go, don’t I? What’s the difference if it’s gremlins or whatever it is you said?”

MCMC

That form of reasoning is used by defenders of simulations, a.k.a. Monte Carlo or MCMC methods (the other MC is for Markov Chain), in which gremlins are replaced by “randomness” and “draws from distributions.” Like the car run by gremlins, MCMC methods get you where you want to go, so why bother looking under the hood for more complicated explanations? Besides, doesn’t everybody agree simulations work by gremlins—I mean, “randomness” and “draws”?

Here is an abbreviated example from Uncertainty which proves it’s a mechanical process and not gremlins or randomness that accounts for the succeess of MCMC methods.

First let’s use gremlin language to describe a simple MCMC example. Z, I say, is “distributed” as a standard normal, and I want to know the probability Z is less than -1. Now the normal distribution is not an analytic equation, meaning I cannot just plug in numbers and calculate an answer. There are, however, many excellent approximations to do the job near enough, meaning I can with ease calculate this probability to reasonable accuracy. The R software does so by typing pnorm(-1), and which gives -0.1586553. This gives us something to compare our simulations to.

I could also get at the answer using MCMC. To do so I randomly—recall we’re using gremlin language—simulate a large number of draws from a standard normal, and count how many of these simulations are less than -1. Divide that number by the total number of simulations, and there is my approximation to the probability. Look into the literature and you will discover all kinds of niceties to this procedure (such as computing how accurate the approximation is, etc.), but this is close enough for us here. Use the following self-explanatory R code:


n = 10000
z = rnorm(n)
sum(z < -1)/n

I get 0.158, which is for applications not requiring accuracy beyond the third digit peachy keen. Play around with the size of n: e.g., with n = 10, I get for one simulation 0.2, which is not so hot. In gremlin language, the larger the number of draws the closer will the approximation "converge" to the right answer.

All MCMC methods are the same as this one in spirit. Some can grow to enormous complexity, of course, but the base idea, the philosophy, is all right here. The approximation is seen as legitimate not just because we can match it against an near-analytic answer, because we can't do that for any situation of real interest (if we could, we wouldn't need simulations!). It is seen as legitimate because of the way the answer was produced. Random draws imbued the structure of the MCMC "process" with a kind of mystical life. If the draws weren't random---and never mind defining what random really means---the approximation would be off, somehow, like in a pagan ceremony where somebody forgot to light the black randomness candle.

Of course, nobody speaks in this way. Few speak of the process at all, except to say it was gremlins; or rather, "randomness" and "draws". It's stranger still because the "randomness" is all computer-generated, and it is known computer-generated numbers aren't "truly" random. But, somehow, the whole thing still works, like the randomness candle has been swapped for a (safer!) electric version, and whatever entities were watching over the ceremony were satisfied the form has been met.

Mechanics

Now let's do the whole thing over in mechanical language and see what the differences are. By assumption, we want to quantify our uncertainty in Z using a standard normal distribution. We seek Pr(Z < -1 | assumption). We do not say Z "is normally distributed", which is gremlin talk. We say our uncertainty in Z is represented using this equation by assumption.

One popular way of "generating normals" (in gremlin language) is to use what's called a Box-Muller transformation. Any algorithm which needs "normals" can use this procedure. It starts by "generating" two "random independent uniform" numbers U_1 and U_2 and then calculating this creature:

Z = \sqrt{-2 \ln U_1} \cos(2 \pi U_2),

where Z is now said to be "standard normally distributed." We don't need to worry about the math, except to notice that it is written as a causal, or rather determinative, proposition: ``If U_1 is this and U_2 is that, Z is this with certainty." No uncertainty enters here; U_1 and U_2 determine Z. There is no life to this equation; it is (in effect) just an equation which translates a two-dimensional straight line on the interval 0 to 1 (in 2-D) to a line with a certain shape which runs from negative infinity to positive infinity.

To get the transformation, we simply write down all the numbers in the paired sequence (0.01, 0.01), (0.01, 0.02), ..., (0.99, 0.99). The decision to use two-digit accuracy was mine, just as I had to decide n above. This results in a sequence of pairs of numbers (U_1, U_2) of length 9801. For each pair, we apply the determinative mapping of (U_1, U_2) to produce Z as above, which gives (3.028866, 3.010924, ..., 1.414971e-01). Here is the R code (not written for efficiency, but transparency):


ep = 0.01 # the (st)ep
u1 = seq(ep, 1-ep, by = ep) # gives 0.01, 0.02, ..., 0.99
u2 = u1

z = NA # start with an empty vector
k = 0 # just a counter
for (i in u1){
for (j in u2){
k = k + 1
z[k] = sqrt(-2*log(i))*cos(2*pi*j) # the transformation
}
}
z[1:10] # shows the first 10 numbers of z

The first 10 numbers of Z map to the pairs (0.01, 0.01), (0.02, 0.01), (0.03, 0.01), ..., (0.10, 0.01). There is nothing at all special about the order in which the (U_1, U_2) pairs are input. In the end, as long as the "grid" of numbers implied by the loop are fed into the formula, we'll have our Z. We do not say U_1 and U_2 are "independent". That's gremlin talk. We speak of Z is purely causal terms. If you like, try this:

plot(z)

We have not "drawn" from any distribution here, neither uniform or normal. All that has happened is some perfectly simple math. And there is nothing "random". Everything is determined, as shown. The mechanical approximation is got the same way:

sum(z < -1)/length(z) # the denominator counts the size of z

which gives 0.1608677, which is a tad high. Try lowering ep, which is to say, try increasing the step resolution and see what that does. It is important to recognize the mechanical method will always give the same answer (with same inputs) regardless of how many times we compute it. Whereas the MCMC method above gives different numbers. Why?

Gremlins slain

Here is the gremlin R code, which first "draws" from "uniforms", and then applies the transformation. The ".s" are to indicate simulation.

n = 10000
u1.s = runif(n)
u2.s = runif(n)
z.s = sqrt(-2*log(u1.s))*cos(2*pi*u2.s)
sum(z.s < -1)/n

The first time I ran this, I got 0.1623, which is much worse than the mechanical, but the second I got 0.1589 which is good. Even in the gremlin approach, though, there is no "draw" from a normal. Our Z is still absolutely determined from the values of (u1.s, u2.s). That is, even in the gremlin approach, there is at least one mechanical process: calculating Z. So what can we say about (u1.s, u2.s)?

Here is where it gets interesting. Here is a plot of the empirical cumulative distribution of U_1 values from the mechanical procedure, overlaid with the ECDF of u1.s in red. It should be obvious the plots for U_2 and u2.s will be similar (but try!). Generate this yourself with the following code:


plot(ecdf(u1),xlab="U_1 values", ylab="Probability of U1 < value", xlim=c(0,1),pch='.') lines(ecdf(u1.s), col=2) abline(0,1,lty=2)

The values of U_1 are a rough step function; after all, there are only 99 values, while u1.s is of length n = 10000.

Do you see it yet? The gremlins have almost disappeared! If you don't see it---and do try and figure it out before reading further---try this code:

sort(u1.s)[1:20]

This gives the first 20 values of the "random" u1.s sorted from low to high. The values of U_1 were 0.01, 0.02, ... automatically sorted from low to high.

Do you see it yet? All u1.s is is a series of ordered numbers on the interval from 1-e6 to 1 - 1e-6. And the same for u2.s. (The 1e-6 is R's native display resolution for this problem; this can be adjusted.) And the same for U_1 and U_2, except the interval is a mite shorter! What we have are nothing but ordinary sequences of numbers from (roughly) 0 to 1! Do you have it?

The answer is: The gremlin procedure is identical to the mechanical!

Everything in the MCMC method was just as fixed and determined as the other mechanical method. There was nothing random, there were no draws. Everything was simple calculation, relying on an analytic formula somebody found that mapped two straight lines to one crooked one. But the MCMC method hides what's under the hood. Look at this plot (with the plot screen maximized; again, this is for transparency not efficiency):

plot(u1.s,u2.s, col=2, xlab='U 1 values',ylab='U 2 values')
u1.v = NA; u2.v = NA
k = 0
for (i in u1){
for (j in u2){
k = k + 1
u1.v[k] = i
u2.v[k] = j
}
}
points(u1.v,u2.v,pch=20) # these are (U_1, U_2) as one long vector of each

The black dots are the (U_1, U_2) pairs and the red the (u1.s, u2.s) pairs fed into the Z calculation. The mechanical is a regular gird and the MCMC-mechanical is also a (rougher) grid. So it's no wonder they give the same (or similar) answers: they are doing the same things.

The key is that the u1.s and u2.s themselves were produced by a purely mechanical process as well. R uses a formula no different in spirit for Z above, which if fed the same numbers always produces the same output (stick in known W which determines u1.s, etc.). The formula is called a "pseudorandom number generator", whereby "pseudorandom" they mean not random; purely mechanical. Everybody knows this, and everybody knows this, too: there is no point at which "randomness" or "draws" ever comes into the picture. There are no gremlins anywhere.

Now I do not and in no way claim that this grunt-mechanical, rigorous-grid approach is the way to handle all problems or that it is the most efficient. And I do not say the MCMC car doesn't get us where we are going. I am saying, and it is true, there are no gremlins. Everything is a determinate, mechanical process.

So what does that mean? I'm glad you asked. Let's let the late-great ET Jaynes give the answer. "It appears to be a quite general principle that, whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought."

We can believe in gremlins if we like, but we can do better if we understand how the engine really works.

There's lots more details, like the error of approximation and so forth, which I'll leave to Uncertainty (which does not have any code).

Bonus code

The value of -1 was nothing special. We can see the mechanical and MCMC procedures produce normal distributions which match almost everywhere. To see that, try this code:

plot(ecdf(z),xlab="Possible values of Z", ylab="Probability of Z < value", main="A standard normal") s = seq(-4,4,by=ep) lines(s,pnorm(s),lty=2,col=2) lines(ecdf(z.s),lty=3,col=3)

This is the (e)cdf of the distributions: mechanical Z (black solid), gremlin (green dot-dashed), analytic approximation (red dashed). The step in the middle is from the crude step in the mechanical. Play with the limits of the axis to "blow up" certain sections of the picture, like this:

plot(ecdf(z),xlab="Possible values of Z", ylab="Probability of Z < value", main="A standard normal", xlim=c(-1,1)) s = seq(-4,4,by=ep) lines(s,pnorm(s),lty=2,col=2) lines(ecdf(z.s),lty=3,col=3)

Try xlim=c(-4,-3) too.

Homework

Find the values of U_1 and U_2 that correspond to Z = -1. Using the modern language, what can you say about these values in relation to the (conditional!) probability Z < -1? Think about the probabilities of the Us.

What other simple transforms can you find that correspond to other common distributions? Try out your own code for these transforms.