Monday, January 31, 2011

Is God Simple-Minded? (Swinburne Pt. 2)

Swinburne spends pages and pages arguing for the existence of God, but most of his discussion boils down to one claim:  God is simple. He argues that when the background evidence is taken to be purely trivial logical knowledge, the probability of a hypothesis is determined mainly by its simplicity. It is clear that the universe itself is quite complex. If we have a choice, then, between taking the universe itself as our fundamental postulate and taking God as our fundamental postulate we should (the argument goes) prefer the simpler hypothesis.

The idea that God is simple has a long history in theology. Usually it is taken to mean that God has no moving parts: he is a unity, not something that can be decomposed into sub-units.

Considering how central it is to his whole program, Swinburne spends remarkably little time defending this claim. He only gives one argument to support it, that goes like this: If God had any finite amount of power, then that amount of power would require some sort of explanation. So an infinite amount of power - omnipotence - is a simpler hypothesis than any finite amount of power. He argues similarly for infinite knowledge and infinite freedom for God to do as he wills.

Now, I am tempted to question this argument, but even if we grant it, how does it follow that God is a simple entity? Maybe the God hypothesis is simple in this one (or these three) respects - it need not be true that he is simple in other respects. As an analogy, consider the spatial extent of the universe. It might be true that the hypothesis of an infinite universe is simpler than a finite universe (I'm not convinced that it is, but let's allow it). But the universe itself remains a very complex thing.

On the contrary, we have very good reasons to believe that an intelligent entity must be complex. An electron is simple: it can be described by its mass, spin, charge, and state of motion. But it isn't intelligent. An amoeba has a certain amount of intelligence: it is able to respond in a rudimentary way to external inputs. But it is already a very complicated entity. It has organelles that convert energy, transcribe DNA into RNA, and RNA into proteins, and so forth. An insect is far more complex again, yet has very limited intelligence and often very rigid behavior.

It is only when we get to organisms with highly complex nervous systems - birds and mammals - that we find problem-solving abilities and other aspects of true intelligence.And humans have, pound for pound, more brain than any other animal.

Likewise with non-living things: a crystal is simple, but it is not intelligent. A computer can beat me at chess and perform other "intelligent" tasks - but it requires a very complex internal structure to do so. Computers do not yet have anything like human-level intelligence, but if some day they do, I'm pretty sure they will be still more complex than today's computers.

So we have very good reasons to think that the higher the intelligence, the more complex the entity. It seems logical, then, that infinite intelligence would require infinite complexity.

But if God is highly complex, then, by Swinburne's criterion, God is highly unlikely.

Tuesday, January 25, 2011

God vs. the Tooth Fairy (Swinburne, Pt. 1)

One of the complaints leveled agains the New Atheists is that they are unaware of the more sophisticated theological arguments about God. So as not to fall prey to this myself, I decided to read The Existence of God by Richard Swinburne. I could spend months blogging my way through his arguments, but others more competent than I have already been there, so I'm going to limit myself to a few comments.

Swinburne baldly states that there are no good deductive arguments for the existence of God. Kudos to him for the honesty to admit that.

He does think that there are good inductive (that is, probabilistic) arguments for God, and he thinks that collectively they make the case that the existence if God is more likely than his non-existence. But for each argument individually, he only makes the much weaker claim that the argument makes God's existence more likely than it would be without the argument.

He calls the latter type of argument a good C-inductive argument, and with a bit of Baysian analysis he shows that what you need in order to have  a good C-inductive argument is
P(e/h,k) > P(e/~h,k),
e = the evidence under consideration,
h = the hypothesis, and
k = general background knowledge.

It is easy to come up with a good C-inductive argument for something that clearly isn't true. Take the tooth fairy, for instance. Let's let e  be the evidence in favor of the tooth fairy's existence: all those coins that kids find under their pillows in place of teeth. And let's let h be the hypothesis that an invisible, non-human being exists who goes around replacing teeth with coins at night. And let's take k to be "mere tautological background evidence." (This is what Swinburne typically chooses for k.)

Now, it is clear that P(e/h,k) = 1. Because if the tooth fairy exists, then we will necessarily see the evidence e, for that is built into the very definition of the hypothesis h. And if the tooth fairy doesn't exist, well, then it might be true that kids will still find coins under their pillows (because their parents put them there), but it's not true of strict logical necessity, so we will have P(e/~h,k) < 1. So Swinburne's condition P(e/h,k) > P(e/~h,k) is fulfilled, and this is a good C-inductive argument for the tooth fairy.

None of this is to say that there's anything wrong with what Swinburne is saying here. It's just to point out what an extremely weak form of argument he's taking as the basis for his arguments for God.

A final comment on Swinburne's practice of taking k to be "mere tautological background evidence." By this he means only things that are tautologically true, like facts of logic and mathematics. By choosing this k, Swinburne makes it illegitimate to bring in any facts from our own experience about what sorts of entities actually exist in the world. In this way Swinburne turns what is usually an uncontroversial choice into a powerful tool in his favor.

To see how he employs this tool, let's jump to Appendix A where he replies to Mackie's critique. Mackie writes that

All our knowledge of intention-fulfillment is of embodied intentions....

and so "there is nothing in our background knowledge that makes it comprehensible" that God should be able to act directly in the universe to fulfill his intentions, as Swinburne claims he does.

Swinburne responds

Mackie has not taken seriously my intention ... to start without any factual background knowledge ... and so to judge the prior probability of theism solely by a priori considerations, namely, in effect, simplicity.

Now, if I were trying to convince someone that the Tooth Fairy doesn't exist, a large part of my argument would revolve around the complete lack of evidence that invisible, intelligent creatures exist. After all, arguing on the basis of past experience is the foundation of inductive reasoning. And how else to go about proving a negative?

According to Swinburne, we can't use this argument against (his argument for) God - simply because Swinburne has chosen a different set of background knowledge. Hmmm....

Tuesday, January 18, 2011

Who Discovered Universal Gravitation?

Isaac Newton, duh.... That's what Westfall says:
The discovery [of universal gravitation] was Newton's, and no informed person seriously questions it.
Oddly, though, Westfall's own presentation doesn't appear to provide much support for such a strong statement. Let me explain.

When Hooke wrote to Newton in 1679, he referred to his (Hooke's) system of the world that he had published in 1674, and asked for Newton's opinion of his hypothesis that orbital motions are compounded of a tangential movement and an attraction toward the center. This letter seems to have been an important impetus in reviving Newton's interest in the motion of the planets.

Hooke's 1674 work contained a remarkable paragraph:

This depends on three Suppositions. First, That all Coelestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the earth to do,but that they do also attract all other Coelestial Bodies that are within the sphere of their activity ... The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers.

Westfall makes a couple of points about this passage. First, he claims that Hooke "did not truly hold a concept of universal gravitation, although it is obvious that he was beginning to break through the limitations of earlier ideas of particular gravities specific to each planet." Even if Westfall is right about this not yet being a thoroughgoing concept of universal gravitation, it is still a remarkable passage, because the comet incident proves that as late as 1680 Newton was still not thinking in terms of universal gravitation.

But Westfall goes on to say that "the most remarkable aspect" of the passage is that "For the first time, it correctly defined the dynamic elements of orbital motion." In fact, it proclaims both "Newton's First Law of Motion": "all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line" and, in some form, "Newton's Second Law of Motion": "till they are by some other effectual powers deflected."

It's hard for me as a physicist to read this, and Westfall's acknowledgment that Hooke had it first, and not think that Hooke deserved rather more credit than he has gotten for setting Newton down the right path. It is not until after this time that Newton begins to talk of a centripetal (rather than centrifugal) force. And it is only after this time that he began to ask his astronomer friend, Flamsteed, whether the motion of Jupiter sped up as it approached Saturn and slowed down as it passed beyond (as it would if Jupiter were affected by Saturn's gravity as well as the Sun's). And it is only after this time, in the Principia itself, that he finally applied the same laws of gravitation and orbital motion to comets that he developed for planets (reversing himself on Flamsteed's comet theory).

On some points I find Westfall convincing. Hooke's own complaint missed the mark: he claimed that Newton had learned of the inverse-square law from him, but Westfall demonstrates that Newton had already considered an inverse-square law of some sort back around 1666 or so. And it's clear that, whatever grasp of gravitation and laws of motion Hooke had, he didn't have the mathematical tools necessary to prove, e.g., that the inverse-square law results in elliptical orbits. Newton, with his (still unpublished) calculus techniques, could plunge right in and solve all sorts of mechanics problems, once he correctly identified the key laws.

So it seems to me that Newton owed a lot more to Hooke, both for the concept of universal gravitation (even if Hooke hadn't completely grasped it himself) and for the "dynamic elements" of the laws of motion, than he ever acknowledged.

Of course, I'm probably wrong about this, since I'm not informed and Westfall is. I guess I'll have to read Westfall's other book, Force in Newton's physics, when I'm done with this bio, and see if I can figure out what he means.

Saturday, January 15, 2011

Blackford on Harris

Russell Blackford points out what's right, and what's wrong, with Sam Harris's The Moral Landscape.

Sometimes Harris seems to think that the course of conduct which maximizes global well-being is the morally right one because “morally right” just means something like “such as to maximize global well-being.” But this won’t do. It’s no use telling somebody (we’ll call her Alice) to act so as to maximize global well-being on the ground that this is the morally right thing to do, while also telling her that “morally right” just means “such as to maximize global well-being”: the upshot is that Alice is told to act to maximize global well-being because this will maximize global well-being! That’s circular. If she is more committed to a goal such as maximizing her own well-being, or that of her loved ones, than to maximizing global well-being, she is not thereby making a mistake about anything in the world. Nor is she doing anything self-defeating, if she maximizes her own well-being, or that of her loved ones, whenever these conflict with maximizing global well-being.

Thursday, January 6, 2011

Newton's Mistakes

As Newton attempted to escape from problems of mathematics and mechanics, others kept calling him back. Hooke, who had continued to work on the problem of orbital motion, wrote to Newton in 1679 to encourage him to send something to the Royal Society. In his reply, Newton discussed an experiment to detect the rotation of the earth by dropping an object from a tower. Since the top of the tower is moving faster than the surface of the earth (because it is moving in a larger circle), the falling object should land to the east, in the direction of rotation.

This much is correct. But Newton went on to sketch the path the object would follow if it could penetrate the earth, showing it as a spiral toward the center of the earth. Hooke caught the mistake, and suggested instead that it would follow an elliptical path.

Newton, annoyed that he had been caught, admitted the error, but then claimed (correctly) that, if the gravitational force were taken as constant, the path would not be an ellipse but rather a cloverleaf shape, in which the points of minimum and maximum distance from the center are about 120 degrees apart. Hooke agreed, but said he had not been thinking of a constant gravity, but of an inverse-square law. This correspondence would be the basis for Hooke's later charge of plagiary against Newton.

In November of 1680, a comet appeared, heading toward the sun. In mid-December, another comet appeared, moving away from the sun. The Royal Astronomer, John Flamsteed, suggested that the two were the same comet. Here Newton made his biggest blunder of all. He wrote to Flamsteed and argued that Flamsteed was wrong about the two comets. Amazingly, although Newton had solved the problem of orbital mechanics a year before, he made no attempt to apply his equations of planetary motion to the comet's path.

Flamsteed had suggested that some sort of magnetic force deflected the comet as it passed the sun, and Newton made a similar assumption in his reply. Both men assumed that comets obeyed different laws than planets: planets were permanent members of the solar system, while comets were strange visitors with a dynamics all their own.

This shows beyond a doubt that Newton was not yet thinking in terms of universal gravitation in 1680. But Hooke's letters and the discussions surrounding the comet(s) had re-invigorated his interest in problems of mechanics. He plunged back into the study of problems of motion, and, for once, managed to complete the project he had begun. That project produced the most amazing scientific treatise that the world had ever seen, the Principia.