What Good is an Explanation? (Part 2)

Tweet

The post in the second in a series on Peter Lipton's article "What good is an Explanation?". The article tries to ascertain what the intrinsic and instrumental good of an explanation actually is. Lipton identifies "understanding" as being the intrinsic good of explanation.

The problem is that "understanding" can sustain at least five distinct conceptual interpretations. In part one, we went through each of these interpretations and tested them against three key features of an explanation. Through this process we learned that the causal-conception of understanding is the strongest.

According to this conception, we understand why something is the case when we identify what caused it to be the case.

In this part, we will do two things. First, we will follow Lipton as he tries to discover why it is that the identification of causes satisfies our explanatory lust. Second, with the discussion of the intrinsic good of explanation under our belts, we turn to consider the instrumental good(s) of explanation.



1. Is there a Question?
Before we answer the question "why do causes explain?", we must consider whether the question makes any sense. After all, we have just defined explanation in terms of cause and so there may be a suspicion that the question is akin to asking "why are bachelors unmarried?".

Despite this suspicion, Lipton thinks that the question can make sense. Particularly if we reformulate it as "why do causes explain rather than effects?". This seems to be non-trivial question as is illustrated by an example.

At the Mt. Wilson Observatory, Edwin Hubble famously observed the red shift of galaxies. This red-shift was explained by the fact that these galaxies were receding away from us. By contrast, the red-shift did not explain the recession of the galaxies.

Why the asymmetry?

That seems like a question worth asking.


2. So, Why Do Causes Explain?
Answering it proves to be quite tricky. Lipton starts off by saying that the cause (C) of an event (E) explains E because C is what brings about E. The problem with this reply is that "brings about" sounds suspiciously like "causes", so we haven't really answered the question.

An alternative definition, and the one preferred by Lipton, is that causes explain because they make a difference. That is to say, they show why E occurred instead of not occurring. Lipton's approach here is similar to the counterfactual approach to causation being discussed in my series on Steve Sloman's book Causal Models.


Lipton lists four attractive features of the "making a difference"-view.

The first is that our ability to manipulate causes in order to alter effects is what gives us control. And since control is of enormous practical value, the making a difference-view accounts for our fascination and preoccupation with explanation.

The second is that it accounts for our ambivalence about certain causes. After all, not all causes are explanatory. For example, if we were told that a rabbit has been killed and were asked to explain why, we could give two answers. First, we could describe the behaviour of one particular fox who was seen in the area at the time. Second, we could cite the high numbers of foxes who live in the area.

Lipton suggests that the high population was what really "made a difference". Why? Because it would seem like if only one fox was in the locality, the rabbit could probably escape and survive. However, given a high population, the rabbit seems to be doomed.

The third attractive feature concerns its importance in constrastive explanations. Again, an example will help to illustrate the idea. Suppose we are wondering why Martin got paresis (a form of partial paralysis). You claim that syphilis was the cause. We might be satisfied with this if we are contrasting Martin with an ordinary healthy member of society. But suppose we are contrasting Martin with Bill, who also has syphilis. In those circumstances, we would be less satisfied with the proffered explanation.

Lipton argues that "making a difference" accounts for the discrepancy between the two cases: the syphilis makes a difference in the first case, but not in the second.

The fourth, and final, attractive feature concerns its ability to draw out the distinction between descriptions of causes that are explanatory and those that are not. The example Lipton uses is a fire in a university department. A report into the incident cites the lack of appropriate insulation of high voltage power lines as the cause of the fire.

If we asked for an explanation of the fire we would be displeased if a colleague said "the fire was caused by the problem cited on pg. 17 of the incident-report". It may well be that pg. 17 contains a description of the lack of insulation, but citing a page reference does not explain the incident.

This is because a truly explanatory description should cite the features of an incident which made the difference between the incident's occurrence and non-occurrence. Pg. 17 of the report, however accurate, did not make a difference.


3. Instrumental Goods
It is obvious enough that explanation has many practical and instrumental benefits. If we can identify and manipulate causes, our ability to pursue our non-explanatory goals will be greatly enhanced.

However, there is another, less obvious, instrumental good associated with explanation. This is that explanations allow us to make inferences. And the making of inferences lies at the heart of many inductive and intellectual practices. For example, scientists must infer which hypothesis is true or false; historians must infer which events are most likely to have taken place.

By constraining these inferential practices so that they must offer the best available explanation of the relevant phenomena, we are helping these researchers in their studies.

What Good is an Explanation? (Part 1)

Tweet

Peter Lipton's death in 2007 was a great loss to the philosophy of science. He was probably the foremost explicator and defender of the explanatory method which I find most congenial: inference to best explanation.

In this brief series, I am going to take a look at one of his articles. The following one to be precise:

"What Good is an Explanation?" in Cornwell, J. (ed) Understanding Explanation (Oxford University Press, 2004)

It will no doubt come as a shock to learn that in this article Lipton attempts to answer a meta-question about the good of explanations. In other words, instead of asking "what makes for a good explanation?" he asks "why should we even bother explaining something?".

The answer to this meta-question is hardly earth-shattering. We explain things for instrumental reasons, i.e. to help us achieve some other goal, and also to achieve the intrinsic good of "understanding".

The majority of the article is taken up with trying to determine what this intrinsic good of understanding really consists in. Only at the end does Lipton return to the instrumental good of explanation.

In this post we will do two things. First, we will identify three key features of an explanation, features that must be accounted for in any formal definition of "understanding". Second, we will consider five possible definitions of understanding.


1. Three Key Features of an Explanation
Lipton begins his article by highlighting three uncontroversial and yet key features that are shared by most explanations. These features serve as diagnostic tests for any sound conception of understanding.

The first of these features is the distinction between knowing that something is true and understanding why it is true. Suppose you and I have just received our exam results. We both did badly. Staring askance at our grades, we are both inclined to ask the "why" question: why did I do so badly? In this scenario, we both already know that we did badly. We now want something more: we want to understand.

The second of these features is the benign nature of the why-regress. We all know the irritating manner in which every possible answer to a why-question can be followed up by another why question. As follows:

Why did I fail my exam?
Because you didn't study properly.
Why didn't I study properly?
Because you're easily distracted.
Why am I easily distracted?
etc. etc.

The important point here is that explanations are not worthless just because there is a potentially infinite regress of why-questions. Genuine understanding can be gained at each link in the question-and-answer chain.

The third feature of explanations is that they are sometimes self-evidencing. What this means is that the data they are intended to explain can, at least partially, justify us in accepting them. So for example, my lack of study can explain why I failed the exam; and my failing the exam can provide evidence for my lack of study. There is a kind of circularity here (H explains E; E justifies H), but it is not vicious.

With these three features in place, we can proceed to consider five possible conceptions of understanding. They are: (i) the reason conception; (ii) the familiarity conception; (iii) the unification conception; (iv) the necessity conception; and (v) the causal conception.

The first two of these make understanding an epistemic matter; the last two make it an ontological matter; the middle one can go either way. This will make more sense once we have gone through them, which is what we are now going to do.

2. The Reason-Conception of Understanding
According to this conception, what we really want from an explanation of a particular fact is a reason to believe in that fact. So questions of the form "why P?" need to be restated in the form "why should we believe that P?". Bayesian evidentialists are fond of this idea.

There are two main attractions to this conception. First, it doesn't distinguish between reason-seeking why-questions and explanation-seeking why-questions. So it reduces the size of the set of epistemological questions we need to ask. Second, it does not rely on somewhat dubious metaphysical concepts, such as causation and necessity.

There is, however, one significant problem with it: it fails to account for any of the three features of explanation outlined above.

• It does not account for the distinction between knowing and understanding because, for example, your doctor's expert opinion about the state of your health may give you a reason to believe that you are sick, but it would not help you to understand why you are sick.

• It does not account for the benign nature of the why-regress because, according to one approach, in order to have a reason to believe that H explains E, we would also need a reason to believe H. This approach would have to fall foul of the why-regress.

• It does not account for self-evidencing explanations because if E is reason to believe in H, H cannot be a reason to believe in E. This would be a vicious circle.

3. The Familiarity-Conception of Understanding

According to this conception, an explanation works when it reduces the unfamiliar to the familiar. So the goal of all explanations should be to build analogies (or other logical bridges) between the known and the unknown. For example, Charles Darwin explained the "design" exhibited in the natural world by building an analogy between the processes of artificial and natural selection.

This conception fits well with the typical context in which explanations are sought, namely: the context of epistemic surprise. In other words, we tend to seek explanations when something seems unfamiliar or surprising and this tendency is captured by this conception. Also, this conception does account for the gap between knowing and understanding: something is understood when it is rendered familiar; something is known when we have reasons to believe in it.

Despite these good points, the familiarity-conception does poorly when dealing with the other two features of explanations. 

• It cannot deal with the why-regress because in order to be familiar, something must be understood, and so only what it already understood can count as an explanation. Thus, it is impossible to derive satisfaction from an explanation that is itself unexplained.

• It cannot deal with the self-evidencing nature of some explanations for the following reason. If an explanations works only to the extent that it reduces unfamiliar facts (E) to a familiar hypothesis (H), it unclear how those same unfamiliar facts could give us reason to believe in the truth of H.

4. The Unification-Conception of Understanding

According to this conception, something is understood once we can see its place within a broader, more unified, conception of reality.

This unification-conception accounts for two of the key features of explanation outlined above. First, it accounts for the gap between knowledge and understanding: we can know that a fact is true without necessarily knowing where it fits in the broader conception of reality. 

Second, it accounts for the self-evidencing nature of explanation. Lipton uses an analogy to make this point: a single piece of a broader pattern can provide evidence for that broader pattern, while at the same time the broader pattern can help us to understand the role of function of the single piece.

It may also account for the why-regress, although Lipton thinks this is less clear. It would do so by showing how E is explained by the wider pattern of H, while leaving the place of H within a still wider pattern unclear.

5. The Necessity-Conception of Understanding

According to this conception, something is understood once it has been shown that it had to occur; that there was no other way things could have turned out. This brings us face-to-face with the principle of sufficient reason, a metaphysical concept beloved by theists and atheists, which is used to argue for the existence of a necessary being.

This necessity-conception can account for the gap between knowledge and understanding. After all, something can be known to be true without being known to be necessarily true. There would also appear to be no problem with self-evidencing necessary explanations.

Where the conception appears to fall down is with the why-regress. It would seem that in order for an explanation (H) to confer necessity on a set of facts (E), the explanation would itself need to be shown to be necessary. This would rule out the possibility of being satisfied with an explanation that was not itself shown to be necessary.

6. The Causal-Conception of Understanding

According to this conception, something is understood once we have information concerning its causes. This is the conception of understanding that Lipton himself prefers.

The causal-conception can easily account for the three key features of explanation that we have been discussing: 

• Something can be known to occur, without knowing what caused it to occur (knowledge v. understanding); 
• We can know that C was the cause of E without also needing to know what caused C (why regress); 
• There is no reason why C cannot be the cause of E, while at the same time E can provide evidence for C (self-evidencing).

Despite these powerful attractions, there are, of course, challenges facing the causal conception. Lipton identifies three important ones.

• There is no completely adequate concept of causation. (See section 2 of this post for some of the different approaches)
• Some explanations, such as mathematical explanations, seem to be clearly non-causal.
• Not all causes are explanatory. Even though there is a long chain of causes linking my present actions to the origin of the universe, it would be odd to explain my behaviour by referring to the Big Bang.

Acknowledging these challenges, Lipton's goal for the remainder the article is to offer a more detailed defence of the causal conception of understanding. I will outline that defence in part two.

Successful Theistic Explanations (Part 4) - Informativeness

Tweet

This post is part of my series on Chapter 7 of Gregory Dawes's book Theism and Explanation. In this chapter, Dawes considers the merits of theistic explanations in light of six explanatory virtues.

Part one introduced the topic and looked at the explanatory virtue of testability. Part two focused on the explanatory virtues of consistency with background knowledge and past explanatory success. And part three dealt with the virtues of simplicity and ontological economy.

In this final entry in the series, we will consider theism in light of the virtue of informativeness, and we will also summarise the conclusions reached in this chapter.

1. What is Informativeness?
In defining informativeness, Dawes relies on Peter Lipton's definition of a "lovely" explanation. This definition has two aspects to it. First, the explanation must specify some causal mechanism. Second, it must allow us to deduce precise effects that would arise from this mechanism.

Earlier in the book, Dawes argued that theistic explanations are unlikely to be able to specify a causal mechanism, but that this is not necessarily a fatal objection to them. Still, it is worth seeing how well theism does in terms of the second aspect of informativeness, i.e. our ability to deduce precise effects from it.

It will no doubt shock you to learn that theism is not very informative in this regard. Let's see why that is.


2. Quantifiable Predictions and Intentional Explanations
The first, somewhat spurious, objection to theism is that we cannot deduce precise quantifiable predictions from it. This is something that we can do in the case of the most successful scientific explanation: we can specify a causal mechanism and specify what the measurable effects of this mechanism would be (see my posts on neuroscientific explanations for more).

But the fact that theism fails in this regard is not a serious charge. Theistic explanations are a species of intentional explanation. As such they explain events and states of affairs in terms of the goals and intentions of an agent. We employ such explanations all the time, e.g. when trying to make sense of the behaviour of our family and friends.

None of these everyday intentional explanations yield precise quantifiable predictions, so we shouldn't expect theism to do so either.


3. The Problem of Mysteriousness
There is, however, a problem with theistic explanations that is not shared by typical intentional explanations. In dealing with human behaviour and social interaction, we know what to expect.

For instance, we know the type of conduct to expect from someone if they are feeling hungry, or if they have just learned that their husband/wife are cheating on them, or if they have a desire to become a doctor and so on. In this sense, everyday intentional explanations are informative.

Theistic explanations are not. We are not able to generate similar expectations when applying mental or action predicates to God because the nature of his agency is "wholly other". The mental and actions predicates that are applied to human beings are tailored to their finite, temporal and physical properties. What would it mean to apply the same predicates to an infinite, eternal and non-physical being.

Theists have ways out of this problem. They can argue that there is a core meaning to the predicates that does depend on the properties of human beings. For example, they could argue that the action predicate "creates" has a core meaning of "uses imagination to bring into being". This core meaning does not rely on temporal, finite or physical properties.

This may be true. But in extracting the core meaning, we take away all the things that make these predicates informative (in the sense defined above). We do not really know what to expect from a creation that emanates from an infinite, eternal and non-physical being.


4. The Problem of Accommodation
This leads to a final problem for theistic explanations. Because they have a tendency to be uninformative, they also have a tendency for accommodationism. That is: they tend to make the evidence fit with the hypothesis, rather than predicting what the evidence should be given the hypothesis.

The example that Dawes uses to illustrate this point is quite interesting. He imagines a believer who has a powerful experience of confidence and joy when reading passages of scripture. The believer is told that he has experienced what is known as the "internal testimony of the Holy Spirit".

This explains his experience and also serves to corroborate religious claims concerning the authority of the scripture.

But there is a huge problem with this explanation of the experience. Since theism is uninformative, we have no idea what it would mean to receive testimony from an incorporeal being. And it is because theism is uninformative that it is all too easy for the believer to offer spurious explanations of this sort.

Dawes concludes by noting that uninformativeness is a serious problem for theists. Indeed, it is so serious that it means non-theistic, natural explanations that yield precise predictions will almost always be preferable.


5. Summary
In this series we have investigated the explanatory merits of theism in light of six explanatory virtues. The results of this investigation are summarised in the image below (click to embiggen).

Successful Theistic Explanations (Part 3) - Simplicity and Ontological Economy

Tweet

This post is part of my series on chapter 7 of Gregory Dawes's book Theism and Explanation. In this chapter, Dawes assesses the strength of theistic explanations against a list of six explanatory virtues.

Part one, provided an introduction to this topic and also considered the explanatory virtue of testability. Part two considered the explanatory virtues of consistency with background knowledge and past explanatory success. In neither case did theism fare well.

In this post we will look at theism in light of the explanatory virtues of simplicity and ontological economy.


1. What is Simplicity?
The simpler the hypothesis, the more inclined we are to accept it. But which is the simpler hypothesis? It is usually understood as being the hypothesis that posits the fewest number of distinct entities and properties. That, at least, is Richard Swinburne's approach to simplicity.

But this is not what Dawes means by simplicity. He defines simplicity in terms of falsifiability and auxiliary hypotheses. He takes this definition from the work of Karl Popper and Paul Thagard. According to this definition, a hypothesis is simple if it is readily falsifiable and relies on as few a number of auxiliary hypotheses as possible.

This might be a little opaque, so let's consider an example. Suppose you have recently developed a plant fertiliser. You are adamant that it will dramatically increase the rate at which my plants grow. I decide to put it to the test. I set up a rudimentary controlled experiment in which I give some plants your fertiliser, some plants a standard fertiliser and some plants nothing at all. I try to hold constant other relevant factors such as access to sunlight and water.

Much to my chagrin, after several weeks there is no discernible difference in growth rates. I come back to you with these disappointing results. You respond by saying that I wasn't using the fertiliser properly. It must be administered in the dark and at a temperature below 5 degrees celsius.

I take this new information on board and initiate a new test. After several weeks of the new regime there is still no discernible difference in growth rates. Feeling slightly aggrieved at having wasted so much time, I return to you once more with my results. You respond again by suggesting that I am not using it properly. I must also talk to my plants while administering the fertiliser and then play classical music to them when I am not around.

At each stage in this process, you are introducing auxiliary hypotheses that make it more and more difficult for your original hypothesis to be falsified. And so you are making your hypothesis less and less simple.


2. Is Theism Simple?
How well do theistic explanations fare in terms of simplicity? To answer this question, it will be instructive to consider a debate between Peter Van Inwagen and Paul Draper.

Back in 1989, Draper presented an argument suggesting that certain observations we have made concerning the biological utility of pain are more surprising on the hypothesis of theism than they are on the hypothesis of indifference. I will be covering this argument over at commonsenseatheism.com soon so I will not explain it here. All that needs to be said here is that Draper's argument is an evidentialist form of the problem of evil.

Van Inwagen responds to Draper's argument by introducing a series of auxiliary hypotheses that account for the presence of pain. These auxiliary hypotheses posit a set of possible reasons God might have for allowing pain to exist. These auxiliary hypotheses are usually called "theodicies". Van Inwagen doesn't claim that these are in fact true, he just thinks they could be true "for all we know". And this is enough to save the hypothesis of theism.

This is not a promising approach. If it is accepted, then theism will score low in terms of simplicity. To retain any explanatory merit, these auxiliary hypotheses will need to score highly in terms of the other explanatory virtues.

It is interesting to note that one reason why Van Inwagen does not find the idea of positing auxiliary hypotheses to be problematic is that he is not an evidentialist. He follows Plantinga in thinking that we know of God's existence in a properly basic manner. Because of this, evidence is to be treated in terms of damage control: what do we need to deny and what can be explained away?

Van Inwagen's approach might be shared by many theists. They will not typically believe in God because he happens to be the best explanation for a set of facts. They will believe for psychological and emotional reasons. So when challenged with events and states of affairs that seem to be inconsistent with their idea of God, they will be happy to invent a plethora auxiliary hypotheses.

The obvious question is the following: once you have added-on all these auxiliary hypotheses, are you left with something worth believing in?


3. Ontological Economy
So much for simplicity, now we have to consider the virtue of ontological economy. What Dawes means by this comes close to what Swinburne means by simplicity, but it is slightly different. What he means is that when explaining something we should not introduce new kinds (types) of ontological entity (or process) unless we have sufficient reason to do so.

Dawes cites two examples suggesting that this is an acceptable restriction to place on successful explanations. The first comes from the work of Charles Lyell, one of the founders of modern geology. Lyell argued that when we are explaining how the earth got to be the way it is, we should do so in terms of processes that we can still observe today.

We should be wary about suggesting that there were different ontological processes in the past because that would open the door to "the utmost license of conjecture in speculating on the causes of geological phenomena."

The second of Dawes's examples comes from the work of Thomas Aquinas. Dawes notes that in considering arguments for the existence of God, Aquinas accepted the virtue of ontological economy. So the point here is that we shouldn't be apologetic about using this explanatory virtue since it is something that theists can accept.

Now, it should be borne in mind that this virtue is not intended to be an explanatory straitjacket: we can posit new ontological entities and processes if there is sufficient reason to do so. "Sufficient reason" would mean satisfying the other explanatory virtues such as testability, simplicity, informativeness and so on.

Of course, it should not come as a surprise to learn that theism does not fare well on the ontological-economy-front.

Okay, that's it for this post. In the next part of this series we will consider theism in light of the final explanatory virtue: informativeness.

Successful Theistic Explanations (Part 2) - Background Knowledge and Past Success

Tweet

This post is part of my series on Chapter 7 of Gregory Dawes's book Theism and Explanation. In this chapter, Dawes's assesses the merits of theistic explanations in light of a series of six explanatory virtues.

In part 1, I covered the general background to chapter 7 and looked at the first of the explanatory virtues (testability). In this part, I will cover the next two explanatory virtues: consistency with background knowledge and past explanatory success.

To better appreciate this discussion it is worth remembering two things. First, a potential explanation is one that fits into an abductive schema. Second, a potential theistic explanation is one that appeals to divine intentions. In other words, it is an explanation that attributes events and states of affairs in the world to the goals of a divine agent.


1. What is Background Knowledge?
The first question we need to ask is: what is background knowledge? The answer is straightforward: background knowledge is any fact or theory, excluding the fact(s) we are currently trying to explain, of which we already have knowledge.

All things being equal, consistency with background knowledge is an explanatory virtue. As we shall see in a moment, some argue that in the case of theism things are not equal. For now, let's assume that they are.

One good illustration of the virtue of consistency with background knowledge is Darwin's theory of natural selection. When Darwin proposed his theory we had no way of observing the process of natural selection in action. So Darwin illustrated how his theory was consistent with another well-known process, namely: artificial selection.

The fact that Darwin's theory was consistent with artificial selection counted in its favour.


2. Is Theism Consistent with Background Knowledge?
Now we need to ask whether theistic explanations are consistent with background knowledge. On the one hand, given that we employ intentional explanations all the time, there is reason to think they are consistent. On the other hand, the nature of the divine agent is so completely different to the intentional agents with which we normally deal that the consistency is more apparent than real.

The main problem is that God is a non-physical, eternal, omniscient agent. The idea that such an agent could will into existence the physical, non-eternal universe is completely alien from our background knowledge.

Note that this is true even if you embrace some form of dualism about the human mind. J.L. Mackie made this point well when he criticised Swinburne's cosmological argument. He said:

All our knowledge of intention-fulfillment is of embodied intentions being fulfilled indirectly by way of bodily changes and movements which are causally related to the intended result, and where the ability thus to fulfil intentions itself has a causal history, either of evolutionary development or of learning or of both. (From The Miracle of Theism, p. 100)

Mackie's statements are consistent with the idea of a non-physical human mind, and they signal how alien the divine mind really is.


3. Is Background Knowledge Relevant?
Given the inconsistency of theism with background knowledge, theists might be inclined to argue that this particular explanatory virtue is not relevant when considering the explanatory merits of theism. Indeed, this is precisely what Richard Swinburne does and his argument is worthy of our attention.

Swinburne thinks that consistency with background knowledge is usually a relevant consideration but that it becomes less and less relevant as the scope (or breadth) of the explanation increases. The reason for this is that as an explanation explains more and more facts, there is less and less independent background knowledge. And since some theistic explanations are extremely broad in scope, it follows that there is practically no background knowledge with which they can be consistent. The only exception is logical knowledge (and some theists think god explains that as well!).

At first glance this seems like a sound objection, but it falls apart on closer inspection. What Swinburne is saying here is that theistic explanations are so broad that they can explain all true propositions (P1, P2....Pn) about the world. But the reality is that no theist does, or even could, offer such a broad explanation.

This is best illustrated by taking a look at cosmological arguments. These are the potential theistic explanations with the broadest scope. But even then they only cover general propositions about the world and not the set of all true propositions (P1...Pn). They cover propositions like "there cannot be an infinite set of contingent entities", "there cannot be an infinite sequence of causes", "there cannot be an infinite sequence of temporal events" and so on. Each of these propositions is only part of the set of all true propositions.

So, it is always going to be possible to distinguish between what is being explained by theism, and background knowledge that is being taken for granted. And given that it is possible to do this, theism should be consistent with background knowledge (if it wants to be taken seriously as an explanatory hypothesis).


4. Past Explanatory Success
This brings us to the question of past explanatory success. In some ways this is similar to the question of consistency with background knowledge, but Dawes thinks it is significant enough to be considered a separate explanatory virtue.

Past explanatory success refers to the track record of a particular explanatory hypothesis. For example, the reason why so many people have found evolutionary theories of human psychology to be appealing is that evolutionary explanations have a good track record outside of human psychology. There may, of course, be other reasons to discount evolutionary psychology (lack or failure of testability for example).

The point can be generalised: the past explanatory success of naturalistic scientific explanations is a reason to favour them over supernatural explanations (such as theism). This is not simply an illegitimate attempt to stack the deck against theistic explanations. The successes of naturalism are numerous and real. We are aware of them every time we take an antibiotic or turn on a laptop.

Until theistic or supernatural explanations have had similarly productive explanatory successes, there will always be reason to be sceptical of them.


That's it for now. In the next part of this series we will look at the explanatory virtues of simplicity and ontological economy.

Successful Theistic Explanations (Part 1) - Testability

Tweet

I previously covered chapter 5 of Gregory Dawes's book Theism and Explanation. I am now going to cover chapter 7 of the same book.

Before we get into the meat of this chapter, a quick summary of Dawes's basic thesis is in order. Dawes argues throughout his book that theism can be a genuine explanatory hypothesis. To be precise, it can be an abductive intentional explanation. This means that it will explain events and states of affairs by appealing to divine intentions. Any posited intentions will be constrained by the rationality and optimality principles. These were covered when discussing chapter 5.

Up to this point in the book, Dawes feels he has established the explanatory potential of theism. The final consideration is whether theism can be a successful explanation. This will require an assessment of a potential theistic explanation against a list of explanatory virtues.

In chapter 7, Dawes assesses potential theistic explanations against six explanatory virtues: (i) testability; (ii) consistency with background knowledge; (iii) past explanatory success; (iv) simplicity; (v) ontological economy and (vi) informativeness.

Some of these are more important than others. In this first post, we will deal with the testability of theistic explanations. There is quite a lot of ground to cover here so I hope you are sitting comfortably.


1. Testability and Corroboration
Testability is often singled out as the hallmark of scientific explanations. This may seem to make its application to theism questionable. We'll get to that in a moment.

The first thing to note is that an explanation is testable only if it makes predictions about facts other than those it purports to explain. Another way of putting this is to say that a testable explanation will be able to exclude at least one possible state of affairs. This avoids the "explains everything, therefore nothing" objection.

An example might be my claim that my car won't start because the engine is flooded. This explanation is testable because it predicts that if the engine were not flooded, the car would start. It thus excludes the "not flooded" state of affairs from its scope.

The second thing to note is that mere testability is not enough. An explanation must actually pass the test in order to merit our consideration. When an explanation passes a test we refer to it as being corroborated.

2. Are Theistic Explanations Testable?
The problem facing theistic explanations is that they tend to fall into the "explains everything, therefore nothing"-category. After all, theists tend to believe that everything is ultimately attributable to god (except, perhaps, the freely willed actions of humans), even if the road to that attribution is unclear.

Nonetheless, Dawes argues that theistic explanations could be testable if they were more specific. They would need to identify some divine goal and show how a particular state of affairs served as a means to that goal. They could then be corroborated by showing how this divine goal explains other states of affairs.

The example Dawes uses to make this point is the 2004 Indian Ocean Tsunami. In the aftermath of this incident, at least some religious commentators attributed it to God's desire to stamp out sexual immorality. These commentators are making a specific claim about God's goals, and this claim can be tested. How? By seeing whether other natural disasters target regions known for breaching the sex code.

Of course, as Dawes notes, no reputable religious philosopher is willing to do this because the explanatory merit of the specific goals tend to unravel. For instance, Richard Swinburne has offered probably the most sophisticated defence of merits of theistic explanation. But in doing so he strategically avoids specifying what God's intentions are and how creating this world helps him to realise those intentions.

In sum, theistic explanations in their most sophisticated form tend to be untestable, and in their least sophisticated form they tend to be uncorroborated.


3. Predictions and Retrodictions
After critiquing Swinburne's lack of specificity, Dawes takes a more detailed look at how theistic explanations could make predictions.

The strict understanding of predictions comes from Karl Popper. He argued that in order to make a prediction, a scientific theory must predict wholly new events that can subsequently be verified (or, rather, falsified) by observation.

This Popperian view is unreasonable given the history of scientific practice. For example, one factor counting in favour of Einsteinian relativity over Newtonian mechanics was its ability to account for the long-known peculiarities in the orbit of Mercury. This was not a novel prediction, but it seemed reasonable to accept it as corroboration nonetheless.

But when rejecting the restrictiveness of Popper's view, we must be careful not fall prey to correlative vice of permissiveness. We do this, according to Dawes, by making sure we consider alternative explanations during the corroboration process.

This is referred to as the historical approach. Why? Because the alternative explanations are usually predecessors to the proposed explanation, as in the Einstein-Newton example given above. The new explanation is corroborated if it accounts for something that the old explanation does not account for (and should have been able to account for).

This could be an issue when looking at theistic explanations because there is often no competing explanation. For example, Richard Swinburne claims that God can explain the laws of nature. There is no predecessor theory that attempts to do the same. Does theism then win the explanatory battle because it is the only competitor?

To answer that question, we must take a detour into some of Elliot Sober's arguments against Swinburne.


4. The Solitary Explanatory Hypothesis
Sober objects to Swinburne's thesis on the grounds that it is an untestable, solitary explanatory hypothesis. Sober, like Swinburne, couches his arguments in terms of confirmation theory so his specific claim is that meaningful probabilities cannot be assigned to the solitary hypothesis.

We can see this if we consider Swinburne's argument more carefully. Swinburne is claiming that the probability of there being laws of nature (O) is high on the hypothesis of theism (T) and low in the absence of an explanation. This gives us the following:

• Pr (O | T) > Pr (O)

Sober's point is that Swinburne has no right to assign a low probability to O and a high probability to O|T. And the main reason that he has no right to do so is that there is no competitor theory.

If Sober is right, then Swinburne's philosophical programme is severely damaged. But is he right? Dawes offers two reasons for rejecting Sober's argument.

First, it might be possible for the theistic explanation to be compared with a "null hypothesis". This is routinely done in scientific investigations. For example, when testing the effectiveness of a drug. The proponents of the drug predict that it will lead to measurable differences between two groups of experimental subjects (those who are given the drug and those who are not). The null hypothesis predicts that any differences between the groups will be attributable to chance.

Something similar could be done in Swinburne's case. In this instance, the null hypothesis would be that the laws of nature got to be the way they are by chance. This would involve defining the relevant probability space (i.e. the range of values or forms that the laws of nature could take). Something that could be difficult to do.

The second response to Sober is more interesting. Sober's argument is, surprisingly, being generous to Swinburne. It accepts the vague form of theism that Swinburne adopts. Dawes would argue that Swinburne should step up to the plate and posit a specific divine intention as the explanation for the laws of nature.

If Swinburne does this, then there will usually be some clear-cut implications that follow. In other words, additional facts that would be explained by that same intention. We could then go out and see whether those facts actually obtain. In this manner, the solitary hypothesis could become testable.

It is, perhaps, telling that Swinburne does not do this.

Okay, that's it for now. In the next part of this series we will consider how well theistic explanations fare when measured against the explanatory virtues of consistency with background knowledge and past explanatory success.

Potential Theistic Explanations: Optimality and its Discontents

Tweet

This post is part of my discussion of Chapter 5 of Gregory Dawes's book Theism and Explanation that began here and, much to everyone's surprise, continued here.

Dawes's basic goal is to show that there are no good in principle objections to theistic explanations. They can be genuine intentional explanations. It just so happens that they aren't very good explanations.

Chapter 5 of Dawes's book deals with some of the in principle objections. Since the argument is that divine explanations are types of intentional explanation, the proponent must posit a specific divine intention as the explanation of a given state of affairs.

The theological sceptic thinks this is untenable: we cannot know the mind of God. So we cannot offer divine intentional explanations. We saw this last time when looking at Elliot Sober's objection to intelligent design.

Dawes responded to Sober by claiming that we can put some constraints on theistic explanations. We do so by employing the rationality and optimality principles. The optimality principle states that God, because of his divine nature, would always choose the most optimal means to an end.

Dawes thinks this helps to constrain potential theistic explanations. If the theist wants to claim God (G) is the best explanation for something (X), then they have a double burden: (i) they must posit a specific divine goal that would require X; and (ii) they must show that X is the most optimal means to achieving the divine goal.

This is potentially devastating for the theist since it seems obvious to many that the world is imbued with sub-optimality. This would seem to imply that God could not be a good explanation for what we observe.

Thus, some will be inclined to object to this optimality principle. Dawes considers four such objections.


1. God is not Obliged to act Optimally
The first objection derives from certain assumptions about God's agency. It is argued that since God is omnipotent and perfectly free, he is under no obligation to act in an optimal way.

Dawes argues that this objection is misplaced. The optimality principle places a constraint on potential theistic explanations; it does not place a constraint on God. It is an epistemological claim; not a metaphysical or theological claim.

If theism wants to enter the explanatory market, then it has to play by the rules. It has to offer itself up for rational scrutiny along with other explanations. If the response to that scrutiny is that God can do whatever he likes, then theism is inscrutable and cannot be a explanatory thesis.


2. There is no Optimal Action
The second objection begins with some parallels between the idea of the best possible world and the optimal realisation of a divine intention. Surely if we are to claim that X is optimal, we are implying that X is a feature of the best possible world?

The problem with this parallel, according to the objectors, is that the concept of the best possible world is incoherent. Two reasons are offered for this (i) there is no single scale of value and (ii) value is potentially infinite.

These are problems with which utilitarians have long contended. For instance, classical hedonic utilitarians argued that conscious pleasure was the sole measure of value. "Piffle!" replied John Stuart Mill. There is a range of higher pleasures that are not commensurable with the lower pleasures. But if there is no single scale of value, then we cannot establish which is the best possible world.

Likewise, if value comes in units (e.g. utiles) then it is something that you can repeatedly add to (like an infinite set). And if it is infinite, there is no best possible world.

Dawes agrees that these are forceful criticisms but identifies three possible responses.

First, this objection may simply prove the incoherence of theism. After all, the optimality principle seems plausible: if God is omniscient, omnipotent and omnibenevolent, then it seems right to expect him to act optimally. So maybe the problem is not with the acceptability of the optimality principle, but with the very idea of God. Perhaps to speak of perfect goodness is to land ourselves in a conceptual muddle.

Second, Dawes thinks it is possible to reject the parallel between the optimal realisation and the best possible world. The idea here is that optimal realisation is only concerned with specific features of the actual world and not with general features of all possible worlds.

Third, it may be that a comparative judgement is all that is required. In other words, even if we cannot talk about a best possible world, we can talk about a better world. This line of thought is attributed to William Rowe. If Rowe is right, then comparing the merit of different realisations of a divine plan should be a doddle.


3. We Cannot Make Such Judgements
The third objection to the optimality principle stems from modal scepticism. This is something I alluded to in the first post on Dawes's book. The idea is that in proposing an intentional explanation, we assume knowledge of the options that were available to the intentional agent.

So in explaining why you chose chocolate ice-cream, I can imagine the options that were open to you and make certain guesses about why you chose as you did. The problem is that we can't do this when considering God as an intentional agent. We have no idea what options were available to him.

This type of modal scepticism is promoted by Peter van Inwagen, who uses it in responding to the problem of evil. (He rejects the idea that God explains anything; we do not come to know of God's existence through evidence and observation.)

Dawes has a couple of responses to this. First, he argues that a complete modal scepticism is unwarranted. We may not be able to comment on all the options available to God, but we may be able to make some decent comparative assessments.

Second, modal scepticism has devastating implications for the doctrine of divine omnipotence. Omnipotence is usually defined in terms of being able to do what is logically possible. But modal scepticisms implies that we cannot even know what is logically possible. Hence we cannot appeal to divine omnipotence.


4. Intelligent Design is not Optimal Design.
The final objection comes from the intelligent design theorist William Dembski. The official ID-position is that the designer is intelligent, not necessarily divine. So ID is not committed to optimality. Of course, Dembski is a theist, but he thinks that sub-optimality arguments must be dealt with from a theological perspective not a scientific one.

Suppose the theist is challenged by an atheist claiming that the wasteful suffering in the natural world provides evidence against the existence of a theistic designer. Dembski would respond by trying to reconcile God's nature with what we observe. In other words, by constructing a theodicy. This would still not affect our ability to infer design simpliciter.

Dawes thinks that this underestimates the problem. Sure, it is possible to reconcile God's existence with wasteful suffering, but this only works on the presupposition of God. It is not possible to infer the existence of God from a sub-optimal natural world.

In other words, unless we specify the divine intention and adopt the optimality constraint, we must concede that theism is not in the explanatory game.

Potential Theistic Explanations: Sober Scepticism

Tweet

(Series Index)

This post continues the discussion of Chapter 5 of Gregory Dawes's book Theism and Explanation that began here.

As noted last time, Dawes is trying to argue that theistic explanations cannot be a priori wiped from the explanatory menu. They can be genuine intentional explanations: they can explain events and states of affairs by relating them to a set of beliefs, desires and intentions.

It may turn out that these intentional explanations aren't any good in practice (Dawes makes this case), but they are, nonetheless, worthy of consideration.

Chapter 5 deals with some in principle objections to theistic explanations. These in principle objections come in two forms: theological scepticism and modal scepticism.

In this entry, we will take a look at one variety of theological scepticism that is attributable to philosopher of science Elliot Sober. We will also look at Dawes's response to Sober's scepticism.

1. Sober Scepticism Described
Sober's theological scepticism begins with his consideration of the design argument. Sober analyses this argument in accordance with what he calls the "likelihood principle". This uses concepts from confirmation theory.

The likelihood principle is a way of testing the strength of a potential explanation by comparing its probability with the probability of an alternative explanation. As follows:

• Observation O supports hypothesis H1 more than it supports hypothesis H2 if and only if Pr(O|H1) > Pr(O|H2)

Restating this last part in plain English we get: "if and only if the probability of O given H1 is greater than the probability of O given H2". So we are concerned with the entailment relationship between a hypothesis and an observation: how likely does the hypothesis render the observation?

Looking at the arguments of intelligent design theorists,* Sober points out that they try to compare the likelihood of two hypotheses, design (D) and chance (C), given certain observed features of the natural world (O). 

They are aware of Darwinian explanations but think these are insufficient. So the contest is between chance and design. And, of course, they think this is no contest at all: design wins hands down. In other words:

• Pr(O|D) > Pr(O|C)

Sober thinks they are wrong to jump to this conclusion, not because chance is a good explanation, but because the design hypothesis is incapable of yielding any probability judgements whatsoever.

His reasoning is as follows. He concedes that we often do make inferences to design (or, more appropriately, intention) in the sciences. For example, archaeologists do it when they discover artifacts. But the reason they can do this is that they already know something about the beliefs, desires and intentions of human beings. Using this background knowledge, they can specify how human beings might be expected to act and makes guesses about the artifacts they might be inclined to create.

There is no analogous background knowledge when it comes to God. The theist can of course look at structure of the vertebrate eye and exclaim "how clever of God to include a blindspot! A permanent reminder of our limitations and his transcendence." But to do so merely begs the question: is the vertebrate eye actually attributable to a divine intention?

We can postulate divine goal-ability pairs til the cows come home, but this is ad-hocery, pure and simple. It has no explanatory merit.

Hence, Sober concludes, putative theistic explanations are D.O.A.

2. Rationality and Optimality
Dawes actually thinks Sober is correct in some of his criticisms. It is surely unacceptable to dream up ad-hoc divine intentions on the basis of what we observe. We need to impose some independent constraints upon theistic explanations.

Where Dawes differs from Sober is in thinking that there are two plausible independent constraints on theistic explanations. The first of these comes from looking at intentional explanations as a whole; the second from looking at the specific nature of the divine agent.


a. Rationality
The first constraint comes from the "rationality principle". Whenever we use an intentional explanation we must assume that the agent is acting rationally. This means that we assume their actions flow from their beliefs, desires and intentions (BDIs).

To be more precise, we assume that the action they have chosen to perform is: (a) consistent with their BDI-complex; (b) efficacious, i.e. likely to attain their goal; and (c) efficient, i.e. requires the least expenditure of time and effort (given their beliefs).

To illustrate what this might mean in practice, Dawes uses Gould's example of the panda's thumb. The panda has five regular digits (like all mammals) and one strange bony protuberance that it uses to strip bamboo.

Gould famously argued that the Panda's thumb, and other functional oddities like it, were good arguments for the truth of evolution. Why? Because they were clearly cobbled-together solutions to selective pressures  necessitated by the Panda's convoluted ancestry. They were not the kind of solutions you would expect from an intelligent designer.

Sober disagrees with Gould's argument. Gould, he argues, is presuming we know what God would be inclined to do if he built pandas. We cannot make that presumption.

Dawes thinks Gould was right to argue as he did because in doing so he employed the rationality constraint. If we posit a particular goal such as "creating a panda that can strip leaves from bamboo", then we are surely right to point out that the means chosen was inefficient.

There are problems with Gould's approach. Foremost among them is that he never actually specifies what the relevant divine intention is. Why would God want to create a panda in the first place?

This is a weakness in theistic explanations: posited divine intentions will always be open to challenge. But this is the price you pay if you want to offer theistic explanations. You cannot offer vague generalisations about a divine "plan"; you have to identify a specific intention.


b. Optimality
The second constraint on theistic explanations arises from a the nature of the divine agent. God is no ordinary rational agent. He is omniscient, omnipotent and morally perfect. Consequently, he would adopt the most optimal means for achieving his goals.

To make this more explicit, Dawes lists the following qualities of divine agency, qualities that are missing for ordinary agents:

1. God cannot act on false beliefs. You might open the fridge on the mistaken belief that the last slice of chocolate cake still resides within. Unbeknownst to you, I have taken it. God, being omniscient, cannot act on false beliefs like this (although, note, there are theologies in which he may lack knowledge of what free agents).
2. God has unlimited logically possible options open to him. You might be limited in your choices by time and physical capabilities; God faces none of those restrictions.
3. God would not suffer from weakness of will. You might resolve to give up alcohol and then find yourself falling off the wagon. This could not happen to God.
4. God could directly will whatever he likes. Just as you can raise your arm merely by thinking about it, God could create the world.

Taken together, Dawes argues that these qualities imply optimality.

The optimality principle gives us another constraint with which proposed theistic explanations can be assessed. To withstand scrutiny, the proposed theistic explanation will have to fend off sub-optimality arguments. These are arguments that show how the means chosen to achieve some divine goal are wasteful and inefficient.

In the next entry we will look at the objections to this optimality principle.

* Note: I hope to be covering Sober's arguments in more depth on this blog at a later time. 

Potential Theistic Explanations: Introduction

Tweet

Gregory Dawes's book Theism and Explanation is one of the more careful treatments of the question: can God be an explanation of anything?

I have no intention of going through the entire book, but I was recently reading through Chapter 5 on "Potential Theistic Explanations" and thought it merited a blog series (why waste all that effort reading it, right?).


1. The Story so Far...
In Chapter 5, Dawes deals with the position of theological scepticism. This is the claim that God cannot be an explanation of anything because we do not know enough about him. Interestingly, this position is defended by atheists, such as Elliot Sober, and by theists, such as Peter van Inwagen.

You might wonder why theists defend this position, but the answer is straightforward: they think we come to know of God's existence in a manner distinct from how we come to know the truth of ordinary explanatory hypotheses. They may also be conscious of the fact that bringing God into the explanatory arena is not necessarily a boon to theism.

To get the most out of the discussion of Chapter 5, I need to offer a quick background sketch of what Dawes tries to establish in the preceding chapters. I am not going to cover everything he says, just the essentials. Nor am I going to defend any of the claims presented in this sketch. Dawes does this, but for present purposes they will need to be taken as given.

The first important point relates to the purpose of Dawes's book. He is trying to argue that there are no in principle objections to theistic explanations; that theistic explanations cannot be wiped from the explanatory menu.

There may, however, be good de facto objections to theistic explanations. Indeed, the final chapter of Dawes's book presents several of these de facto objections.

Having established the purpose of the book, Dawes proceeds in chapters 2, 3 and 4 to the general topic of explanation and the specific topic of theistic explanation. He makes two important claims. First, that any purported explanation must satisfy the requirements of Peirce's schema for abductive inference. This schema is the following:

• The surprising fact E has been observed.
• H, if true, would entail E.
• Therefore, there is reason to suspect H is true.

As he points out at length elsewhere, it does not take much to satisfy this schema. The real test of an explanation is how well is measures up against a list of explanatory virtues. I have discussed this previously. 

The second important claim is that theistic explanations are a brand of intentional explanation. What does this mean? Well, an intentional explanation is one that explains something in terms of the beliefs, desires and intentions of rational agents. 

So I explain your opening of the fridge door, in terms of (a) your intention to open the door which arises from (b) your desire to retrieve the milk and (c) your belief that the milk is in the fridge.

To add some formalistic dressing to this relatively simple idea, Dawes presents the following practical syllogism. All intentional explanations must fit with this syllogism:

• There exists a rational agent A with intended goal G.

• A has beliefs B1, B2, .... Bn relating to the attainment of G.

• If B1, B2, .... Bn were true, E would be the best way of achieving G.

• Rational agents always choose the best way of achieving their goals.

• Therefore A will do E.

This practical syllogism incorporates what Dawes calls the "rationality principle". I will talk about this in more detail later.

2. Theological Scepticism

Now that we have some appreciation for the backdrop to Chapter 5, we can proceed to its actual contents. In this chapter, Dawes tries to counter some in principle objections to theistic explanations. As mentioned at the outset, these objections come in the shape of theological scepticism.

Dawes distinguishes between two varieties of theological scepticism. Remember, the idea is that God could be an explanation of certain states of affair because they are attributable to a divine intention. This is analogous with how we explain the behaviour of other intentional agents.

The first type of theological sceptic thinks that the analogy cannot hold water. The divine agent is wholly distinct from the human and animal agents we have to contend with on a daily basis. We have no idea what God's beliefs and desires really are, so we have no juice to put into the divine explanatory engine.

The second type of sceptic focuses more on our inability to make modal judgements about God. Modality is, very roughly, a bit of jargon for propositions that are qualified by terms such as "possible", "necessary", "contingent" etc. It is most often brought up when discussing possible worlds. I mentioned this in one of my posts about causation.

Applying this to the present debate, we cannot have a theistic explanation because we simply do not know what options (possible worlds) were open to God when he is trying to implement his intentions. Are there innumerable options or is he restricted in some way?

Dawes responds to these criticisms by saying that we can make certain assumptions about God and so can actually place certain constraints on a theistic explanation. Two of these constraints are central to this chapter: (i) the rationality principle and (ii) the optimality principle.

We will take a look at these constraints and take a more detailed look at the arguments of the sceptics in future entries.

Explanations: Breadth and Depth

Tweet

It's been awhile but I am finally writing about explanations again.

In this post I'll examine two basic explanatory qualities: breadth and depth. It is often said that a good explanation should have breadth and depth, but what does this mean? And is it really a good thing?


1. Explanations vs. Arguments
Before addressing the nature of these two concepts, let's backtrack for a moment and consider the differences between explanations and arguments.

An argument is an attempt to demonstrate or establish the truth of a particular proposition. It works from a set of premises to a conclusion. For example, let's say that you and I disagree about whether the best way to tackle an recession is through increased government expenditure (in the form of a "stimulus package") or cuts in government spending.

Let's say I'm in favour of the stimulus package. I want to get you to agree with the proposition "The stimulus package is the way to get the country out of recession". How can I do this? Well, I might present the following argument:

• (1) The recession has been caused by a collapse in consumer confidence. People are afraid to spend money because they worry about further deepening of our economic woes. 

• (2) The collapse in confidence creates a vicious cycle: less money is being spent which reduces output in the economy, and the reduction in output adds to people's lack of confidence.

• (3) To break this vicious cycle, we need to do something to restore consumer confidence.

• (4) A stimulus package, by pumping money into the economy and encouraging spending, will increase output and increase confidence.

• (5) Therefore, the stimulus package is the way to get the country out of recession.

Now this may be a good or a bad argument. It does not matter. What does matter is that the argument is about establishing the truth of the concluding proposition.

This is to be contrasted with an explanation. An explanation begins with the truth of a proposition and then tries to identify the factors that account for the truth of that proposition.

Let's imagine that you and I are arguing once more about the economic woes of our country. Except this time our argument takes place a few years later and the country has indeed exited recession. We both agree on this fact. We now want to know: what accounts for this?

Suppose that in the interim period the government has in fact passed a stimulus package. I think that the stimulus package is the obvious explanation of our increasing prosperity. How could I convince you of this? Well, I would in fact present the exact same argument as I did when we were in recession. You will challenge this by presenting alternative explanations and we will assess these explanations in terms of their explanatory virtues.

In sum, an explanation works from an accepted proposition to a set of premises that would, if true, entail that proposition.

That is, roughly, the formal distinction between an explanation and an argument. In practice, the distinction counts for little. For example, although an explanation may be introduced in order to explain a particular proposition, the strength of the explanation may be established because it makes successful predictions about other propositions. 

The predictions work a little bit like arguments, i.e. we accept the truthfulness of the explanation and try to see what would follow (deductively) from its truth.

2. Breadth and Depth

All of the above was an extended introduction to what I really wanted to talk about, which is the concepts of breadth and depth. I am going to use the relationship between the work of three giants of the scientific revolution to illustrate these concepts. They are Isaac Newton, Johannes Kepler and Galileo Galilei.

First, let's look at the concept of depth. Kepler, using the data gathered and compiled by Tycho Brahe, noticed something odd about the motions of the planets. He explained these oddities in terms of three laws of planetary motion. These laws suggested that the planets followed elliptical orbits around the sun.

Some years later, the deeply unpleasant Isaac Newton came along an showed how Kepler's elliptical orbits were themselves accounted for by his law of gravitational attraction. Newton laws were deeper than Kepler's.

You can think of depth in terms of the unending string of "why" questions: 

• "Why is X true?" 
• "Because of Y. "
• "Why is Y true?" 
• "Because of Z."
• "Why is Z true?"
• "Stop asking these silly questions."

The deeper the explanation, the more of these questions it can answer.

To look at the concept of breadth we need only add to the picture Galileo's laws concerning falling bodies here on earth. Again, Galileo took the behaviour of falling objects as his data and developed a set of laws that accounted for this behaviour. And again, Newton came along and showed how Galileo's laws were accounted for by his law of gravitation.

Thus, Newton's laws have breadth as well as depth: they explain both the motions of the planets and the motions of falling bodies. 

Breadth is a function of how much data is covered by an explanation. It is linked to depth. As an explanation becomes deeper and more abstract, it covers more and more facts.

We can represent the breadth and depth of Newton's laws schematically as follows.

Although breadth and depth are counted as explanatory virtues, some caution is warranted. An explanation can be broad and deep and still be trivial; explaining everything and nothing.

We need more criteria.

Explanations: A Gentle Introduction

Tweet

Welcome to yet another series! This time out I am going to be covering explanations. The series is going to be quite wide-ranging but will have one question at its core: what makes for a good explanation?

There is a danger here. The form of this question could tempt us into an arcane and esoteric exercise in academic self-indulgence. You know the kind. If we are not careful, we could well spend all our time with sentences like the following: "x is a good expanation iff it has P, Q, and R, and has no S, T or U."

I want to avoid this kind of dry treatment. Explanations are the glue that hold together the fragile and disparate territories of the intellectual commonwealth: understanding their complexities and their simplicities, and their successes and their failures, is essential.

So, in order to give the topic the treatment it deserves, I want to avoid abstract analyses and use instead the medium of practical illustration. In other words, I want to compare and contrast several types of explanations across several different domains: philosophical, historical, scientific and religious.

This introductory post has two goals. First, it gets the necessary abstractions out of the way by considering the form that a good explanation should take. Second, it offers a simple example of explanation-in-action by going over one of Sherlock Holmes's fictional cases.

1. Abductive Inference and Explanatory Virtues

When I speak about explanation, I speak in particular about explanations that are arrived at through abductive inference. This was a method first formalised by Charles Sanders Pierce, one of the three great American pragmatists.

An abductive inference looks like this:

D is some collection of data (includes facts, observations, and givens)

H is some hypothesis that would, if true, explain D

No other hypothesis explains D as well as H

Therefore, H is probably true

As can be seen, abductive inference reaches probabilistic conclusions, not definitive conclusions. It also involves the comparison of different hypothesis: weighing their respective merits against one another. Human inquiry always begins in the middle, i.e. with the contradictions and tensions in our present worldview, we must always consider different ways of resolving these tensions and contradiction. We cannot consider one hypothesis in isolation from everything else that we know.

But how can we weigh one explanation against another? How can we know when one explanation is stronger? This is where the idea of explanatory virtues becomes important. The virtues are a set of criteria that can be used to assess explanations. Luke over at commonsenseatheism provides a good list of these virtues here. I can't improve upon it.

The image below summarises the formal aspects of abductive inference and includes a list of the explanatory virtues.

2. Explanation in action: Sherlock Holmes and the Adventure of the Three Students

To ease our way into future practical examples, it will be useful to consider something frothy, frivolous and yet instructive.

Everybody's favourite fictional detective, Sherlock Holmes, is often thought to be the embodiment of abductive reasoning. In solving the cases presented to him by the troubled citizens of London he marshals the evidence, considers the different hypotheses, eliminates the impossible ones and accepts the remaining one, however improbable it may at first appear to be. (This is a paraphrase of one of Holmes's famous sayings, but it is questionable, see here - an improbable answer is more likely to be the result of an improper question).

To show how Holmes uses abduction, I will look at how he solves the case presented in the story "The Adventure of the Three Students". It is one of the more forgettable of Conan Doyle's efforts, but its academic setting appeals to the student in me.

The Problem

The story begins with Holmes and Watson firmly ensconced in one of England's famous university towns (the precise location is never divulged). They are interrupted by one of the professors, a man named Soames, who presents Holmes with a problem befitting his intellect.

Earlier that afternoon, Soames was going over the proofs for the Greek scholarship exams, which are being held the following morning. He had to visit a colleague and so left the proofs on the desk in his room.

When he returned he found that the proofs had been disturbed. They were left in various positions around the room, including one left by the window overlooking the quad. There were other notable disturbances: strange globules of mud were deposited in various locations, and a broken pencil had been left behind. The latter was presumably used by the intruder to copy the proof.

Soames alerted his servant, named Bannister, as soon as he suspected that there had been an intruder. Bannister became quite upset upon hearing this and collapsed into one the chairs in Soames's room. After calming him, Soames walked straight over to Holmes to seek his help.

Soames informs Holmes that the intruder is likely to be one of the three students with whom he shares the building in which he lives. All three are due to sit the exam, so all three have an incentive to cheat.

The student living on the ground floor is a hard-working, scholarly and athletic but disadvantaged youth named Gilchrist. His father had once been rich, but had lost all his money in that all too common vice of the English gent: gambling.

The second floor is occupied by an Indian student named Daulat Ras. He is quiet and intelligent, although Greek is his weakest subject.

The third floor is inhabited by Miles McLaren. He is brilliant but intemperate, wild, and morally circumspect. He has had previous run-ins with the college authorities and was almost expelled on one occasion.

Holmes goes over Soames's room with his usual care, interviews the servant Bannister and visits each of the student's rooms, with the exception of McLaren's who wouldn't let them in. Satisfied with his efforts, he promises Soames that he will resolve the case first thing the following morning (just before the exam is due to start).

The following morning Holmes delivers the goods: Gilchrist is revealed to be the guilty party and, what's more, the servant Bannister is implicated in the events. Gilchrist confesses, withdraws from university and all is right in the world.

How did Holmes manage to correctly identify the intruder?

The Explanation

As noted, all three students had an incentive to cheat on the exam. So we are weighing three hypotheses (i.e. potential explanations of the events) against each other: (i) Gilchrist did it; (ii) Ras did it; or (iii) McLaren.

For the most part, the available data is equally well accounted for by each hypotheses. But there are three crucial points at which the Ras- and McLaren-hypotheses break down:

• Holmes reasons that the intruder was likely to have seen the proofs on Soames's desk as they passed his window - to have simply stumbled into the room and find them was too much to ask. Neither Ras, nor McLaren were tall enough to see in the window.
• The strange balls of mud found in the room came from the sandpit over on the long jump practice ground. Gilchrist was a long jumper and had been practicing that afternoon. That's almost a QED right there.
• The other puzzling fact was the behaviour of Bannister. His collapsing into the chair on being told that there may have been an intruder seemed over-the-top to Holmes. He reckoned Bannister was trying to cover up for Gilchrist because Gilchrist was still hiding in the room. After Soames left to see Holmes, Bannister could sneak Gilchrist out. This is revealed to have been true. Indeed, Bannister and Gilchrist were connected because Bannister used to work for his father.

What we have then is a classic example of an abductive inference: three hypotheses are on the table, they are compared on the basis of their explanatory virtues, and one is left standing.

The diagram below illustrates the form and virtue of Holmes's explanation. It fills in some details missing from the summary to this point.

Alas, that brings this post to a close. In future contributions to this series I will look at various scientific, philosophic and religious explanations. All the time adhering to the abductive method.