Enoch on The Epistemological Challenge to Metanormative Realism (Part 1)

David Enoch, on the left

I recently put together a series of posts on the constructivist metaethics of Sharon Street. Constructivism, as we learned, maintains that moral truths are made, not found. Indeed, that they are constructed out of the attitudes and dispositions of rational agents. This places constructivism in conflict with a metaethical position known as moral realism.

Moral realism comes in a couple of versions but one version, which has been undergoing something of a resurgence in recent years, is non-natural moral realism. According to this, moral properties are part of the basic metaphysical scaffolding of reality. They do not depend for their existence on the attitudes or dispositions of rational agents. And they are not reducible to the causal or physical entities studied by the sciences.

As Street pointed out, this brand of realism seems to face an epistemological challenge. It seems to owe us some account of how human beings, with their evolved cognitive faculties could possibly come to know of the existence of these mind-independent, non-causal, non-natural properties.

David Enoch's article "The Epistemological Challenge to Metanormative Realism" is an attempt to confront this challenge from a realist perspective. In the course of the article, Enoch does two things. First, he tries to develop the strongest possible formulation of the epistemological challenge. And second, he shows how the realist can deal with the challenge.

Before giving the strongest possible formulation of the challenge, Enoch tries to show how not to think about the challenge. That provides the subject matter for this post.


1. Is it about Epistemic Access?
Some people think that realists need to show how we can gain epistemic access to the non-natural moral domain. Enoch says there are problems with this.

The main one is that the notion of "epistemic access" is poorly defined. It is not clear that it means anything above and beyond other epistemic concepts such as justification, reliability and knowledge. Since these are discussed below, Enoch sees no reason to dwell on "access".

Perhaps, someone can develop an understanding of "access" that is distinct from these other concepts. If so, there may be an additional problem facing moral realism. But this has not been done to date.



2. Is it about Justification?
Maybe the realist owes us an account of how their normative beliefs are justified? That is, how they know that their beliefs are true or accurate. Certainly, an account of justification would be an important part of a completed metaethical theory.

Although this is correct, Enoch thinks that there are three reasons for not conceiving of the epistemological challenge in terms of justification:

• Normative beliefs are no more difficult to justify than non-normative beliefs. Theories of justification such as foundationalism or coherentism have problems across all domains of cognition, not just in the moral domain.
• Even within the normative domain, it is not clear that realism faces any justificatory problem that is distinct from the justificatory problems faced by other metaethical positions, including constructivism.
• Since no theory of epistemic justification is satisfactory on its own terms, other desiderata must play a role in picking the best theory of justification. One of those desiderata would surely be "consistency with intuitive beliefs". Since, realism provides room for strong moral intuitions, it would score well on this desideratum. An alternative theory of justification would have to have other virtues before it could dislodge a commitment to moral realism. 

3. Is it about reliability?
Reliable belief-formation may be thought a precondition for other epistemic qualities such as justification and knowledge. Thus, reliability of moral belief-formation would be an important foundation from which to build a theory of moral realism. But perhaps realism faces noteworthy hurdles when it comes to the reliability of its constituent beliefs?

Enoch thinks there is something to this objection and will return to it later in the article. However, he does make one observation. He thinks that truth opens up the possibility of reliability. So, if the realist conception of moral properties is true, it is at least possible for moral beliefs to be reliable.


4. Is it about Knowledge?
Perhaps the problem is that realism cannot give us an adequate account of moral knowledge? To see whether this is right, Enoch asks us to consider what we would expect from an account of knowledge.

The classical position is that knowledge is justified true belief. However, as Enoch notes, realism could satisfy these three demands: (i) there is no obvious problem of moral belief on the realist account; (ii) there is no non-question begging reason to doubt that realism could be true; and (iii) there is no reason to single out realism when it comes to the problem of justification.

But the thing is, the classical view of knowledge is no longer accepted. As Gettier pointed out back in the 1960s, there are some situations in which all three conditions are satisfied but, due to luck or coincidence, we could not say that knowledge has been obtained. As a result, epistemologists have been searching for a fourth condition to plug the gap between true belief and knowledge. (See this post for more)

Some accounts of this fourth condition rely on the causal and counterfactual properties of beliefs. These accounts may well be incompatible with realism since the moral properties proposed by realists are causally inert.

However, Enoch thinks that the case for these conditions is not watertight and that, again, realism has other strengths that should be considered before picking an epistemology that rules out strongly intuitive moral beliefs.

As a result, Enoch does not think the challenge is best thought of in terms of knowledge.



5. Is it about General Epistemic Scepticism?
It could be that the challenge to realism is just a particular instance of epistemological scepticism. That is, of the scepticism invoked by Descartes in his famous thought experiment on the deceptive demon, or of the scepticism invoked by the brain-in-the-vat thought experiment.

But in that case the challenge is not specifically directed at moral realism. It is directed at all beliefs.


6. So what is it about?
Going through the possibilities in this systematic manner can actually help us to figure out what a good version of the epistemological challenge should look like. It seems like it should have the following features:

• It should be peculiar to normative beliefs;
• It should be hard for moral realism as opposed to other metaethical positions;
• It should not beg the question against realism (i.e. it should not presume that realism is false);
• It should not rely on highly contested epistemological notions such as "knowledge" and "justification".

In the next part, we will see how Enoch develops a version of the challenge that has these features.

Podcast on iTunes

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For some reason it's down as "philosophical disquisitions" as opposed to "discursions". Must have something to do with how I filled out the form.

Gwiazda on Swinburne: God's Properties

This post is part of my series on Jeremy Gwiazda's criticisms of Richard Swinburne's argument for the existence of God. For the necessary introduction and background, see here.

To recap, Swinburne's argument takes a Bayesian form. He says that the probability of God's existence (h) given certain empirical evidence (e), as well as background tautological evidence (k), is high. Or, at least, higher than any alternative explanations of the same empirical evidence. The requisite probability is derived using Bayes' theorem, as follows:

• Pr(h|e&k) = Pr(e|h&k) Pr(h|k) \ Pr(e|k)

In previous entries we saw that one of Swinburne's key claims is that the intrinsic probability of theism, Pr(h|k), is high because God is the simplest possible being. And the reason for God's simplicity, according to Swinburne, is that he possesses certain properties in infinite quantities. The properties in question are freedom, knowledge and power.

We have already seen how Gwiazda challenges Swinburne's claim that infinite values are necessarily simpler, but for the purposes of this post we will accept it. Our focus instead will be on the problems that stem from Swinburne's seemingly contradictory assertions about God's properties.

1. Restricted Knowledge and Power?

Swinburne sees the properties of freedom, knowledge and power as being central to the person of God. Furthermore, in his most famous work, The Existence of God, Swinburne asserts (p. 7) that God has perfect freedom, omniscience and omnipotence. That is to say, he has the maximal* or infinite amount of these properties.

And yet, in The Coherence of Theism, Swinburne claims (p. 177) that it is impossible for a being to be perfectly free and omniscient; that God must be perfectly free; and, consequently, that God's knowledge must be curtailed or restricted.

As it happens, there is a reasonably compelling argument for this conclusion. Roughly:

• Perfect freedom entails the absence of sufficient causal predetermination of your actions. In other words, it entails that your decisions are exempt from ordinary causal laws.
• If your decisions are exempt from ordinary causal laws, it is impossible to predict or know what they would be in advance.
• If a being had perfect knowledge of the future, it would have to have knowledge of its future decisions.
• But this would mean that its future decisions were not perfectly free.
• Therefore, a being cannot be both perfectly free and omniscient.

The same reasoning could apply to God's power, which should not be able to affect future decisions.

This strikes me as being about right, but it would seem to contradict Swinburne's claim in The Existence of God, and, more importantly, his argument for God's simplicity. The latter depending entirely on the claim that infinite values of properties are the simplest.

Gwiazda identifies two possible lines of response for Swinburne.


2. The Relativity of Simplicity
First, Swinburne could argue that God has the maximal amount of knowledge and power that is consistent with his perfect freedom. In other words, God has as much knowledge and power as it is possible to have, relative to perfect freedom. And that this makes it as simple as it could be.

Gwiazda argues that this response can do nothing to rehabilitate Swinburne's argument for God's simplicity. Once you accept that power (or any other property) can be simple provided it is maximal relative to a constraint, you open up the possibility of simplicity being claimed for much lower levels of power.

To see this, imagine the following two cases. In the first, we have two supernatural beings: God and Schmod. God has perfect freedom and constrained power. Schmod has perfect power and constrained freedom. Swinburne would be claiming that God is simple even though his power is less than what it could be. But why could the same reasoning not be applied to Schmod? Is freedom somehow more important? We will return to this question at the end.

In the second case, we have God and a regular mortal human named Alex. We assume that Alex has as much power as it is possible for a human being with mental and physical limitations to have. In other words, that his power is maximal relative to other constraints. Can we now claim that Alex's power is simple? If not, why not?

If simplicity can be defined as maximality relative to a constraint, and if all levels of a property are maximal relative to some constraint or other, it is difficult to see how simplicity has any distinguishing features.


3. One Simple Property
The other response open to Swinburne is to pin the claim of simplicity on one of God's properties and not on the collection of freedom, knowledge and power.

Gwiazda detects two places in Swinburne's writings where this seems to be done. The first is in The Christian God where he claims that God possesses 'pure, limitless intentional power' and that this property is simple. The second is in an article entitled "Can There be More than One God?"** where he discusses God's almightiness and argues that it is simple.

Gwiazda thinks there are problems with these single-property arguments. First, it is difficult to see how intentional power and almightiness are not ultimately constituted by freedom, knowledge and power. Second, the actual argument to God's simplicity in The Existence of God only talks about freedom, knowledge and power, not these other single properties.

Thus, Swinburne would need to reformulate his argument for God's simplicity.


4. A Question of Priority
The final question mark hanging over Swinburne's understanding of God's properties is his prioritisation of freedom over knowledge and power. For some reason, Swinburne thinks that this prioritisation gives rise to the simplest possible being. Gwiazda is not convinced. He thinks there is another, even simpler being.

To see what this might be, let's first represent God's three properties -- freedom, knowledge and power, as an ordered triple. "R" stands for a restricted property and "∞" stands for an infinite property. The simplest being would be (∞, ∞, ∞), but since perfect freedom is not compatible with omniscience and omnipotence, Swinburne's god is (∞, R, R).

Now, we saw in the previous part  how Swinburne thinks that zero is probably as simple as infinity and definitely more simple than any finite value. But wouldn't this imply that a being with no freedom, but infinite power and knowledge (0, ∞, ∞) would be simpler than Swinburne's god?

It is hard then to see why priority is given to freedom.





* "Maximal" is understood here to cover infinite values, but leaves the door open to the possible of some logical or absolutely necessary limits.
** (1988) 5 Faith and Philosophy 225

The Podcast (Index)

This will serve as an index to all the episodes of the podcast. You can subscribe on itunes, if you wish.


1. Sceptical Theism and Divine Lies
Description: Discusses Erik Wielenberg's argument that sceptical theists cannot rule out the possibility that God is lying to them in sacred texts. This, it is suggested, can have devastating consequences for our understanding of revelation and religious experience.


2. Cosmic Fine-Tuning and the Goodness of Life
Description: Discusses Neil Manson's argument that those who think fine-tuning demands an explanation must be doing so on the assumption that life is an intrinsic good.


3. A Semantic Attack on Divine Command Metaethics
Description: Discusses Steve Maitzen's argument that a Divine Command Metaethics is tautologous and theologically vacuous.


4. Theology and Falsification
Description: Discusses Antony Flew's classic symposium piece "Theology and Falsification" as well as the various responses to it. I conclude that Flew's piece remains a significant challenge to the cogency of religious belief.


5. Transcendence Without God
Description: Discusses Anthony Simon Laden paper on "Transcendence without God" from the collection of papers Philosophers without Gods.


6. The Absurd
Description: Compares and contrasts the views of William Lane Craig and Thomas Nagel on the absurd. Craig argues that life without God is without ultimate meaning or significance; Nagel argues that the very concept of ultimate meaning is incoherent.


7. A Simple Argument against Design
Description: Discusses Dan Moller's paper "A Simple Argument Against Design". As the name suggests, Moller offers a simple, likelihood-based objection to design arguments.


8. Foundations of Religious Liberty
Description: Discusses Brian Leiter's paper "Foundations of Religious Liberty: Toleration or Respect?". Leiter argues that, when properly understood, there are no good grounds for (legally) respecting religion.


9. Divine Evil
Description: Discusses David Lewis' paper "Divine Evil" from the collection Philosophers without Gods. Lewis argues that one of the most disturbing aspects of traditional theistic belief is the evil it attributes to God.

10. The Open Society and the Doctrine of Hell
Description: Discusses Popper's Open Society argument and its implications for the toleration of religious beliefs and practices.

11. The Future Like Ours Argument
Description: Discusses Don Marquis's famous "Future like ours"-argument and David Boonin's critique of it. Marquis' argument is one of the best known secular arguments against abortion.

Gwiazda on Swinburne (Index)

This is an index for my recent series on Jeremy Gwiazda's criticisms of Richard Swinburne's argument for the existence of God.


1. Introduction

2. Complexity Quotients and God's Simplicity

3. Alternatives to God

4. The Principle P

5. God's Properties

The Podcast - Episode 2: Cosmic Fine-tuning and the Goodness of Life

Episode Two of the podcast is available for download here. In this episode I cover a short paper by Neil Manson entitled "Cosmic Fine-tuning, Many Universe Theories and the Goodness of Life". You can download a copy of the paper at Neil's webpage.

I received some feedback for my previous effort. Most was positive and no doubt the naysayers kept quiet. One person suggested that my voice was a little dry, and I would have to agree. I've tried to liven things up in this episode and I personally think it is an improvement. Let me know if you disagree.

I'd be happy to receive comments or suggestions, particularly suggestions for topics or papers you would like me to cover in the future. My only ground rule is that the papers must be short enough to cover in about 20 mins.

Enjoy.

Gwiazda on Swinburne: The Principle P

This post is part of my series on Jeremy Gwiazda's criticisms of Richard Swinburne's argument for the existence of God. For the essential introduction and background to Swinburne's argument, see here.

To briefly recap, Swinburne claims that the probability of God (h) given certain empirical evidence (e) and background tautological evidence (k) is high. Or, at least, higher than any of the alternatives. This argument makes use of Bayes' theorem:

• Pr(h|e&k) = Pr(e|h&k) Pr(h|k) / Pr(e|k)

We have seen in previous entries that one of the things Swinburne relies upon to support his claim that Pr(h|e&k) is high is the argument that intrinsic probability of theism, or Pr(h|k), is high due to God's simplicity.

To support the argument for God's simplicity, Swinburne appeals to something he calls the Principle P:

Hypotheses attributing infinite values to properties of objects are simpler than ones attributing large finite values.

God's three key properties are his knowledge, freedom and power, and according to orthodox theism these properties are infinite in their values. On principle P, this would make God the simplest possible being.

Principle P does a lot of heavy lifting for Swinburne. It allows him to rule out, as profoundly unlikely, any explanation that appeals to a finite or limited god. This undercuts some of Hume's classic objections to theistic explanations. Given the heavy lifting that P is doing, it is essential to investigate whether or not it is justified. That is what Gwiazda does and that is what we will do in this post.


Four Arguments for P
Gwiazda identifies four justifications of P, sprinkled throughout Swinburne's oeuvre. We will respond to each in sequence.


i. Mathematical Simplicity
The first justification comes from the mathematical understanding of simplicity. Swinburne argues that "a  law is mathematically simpler than another in so far as the latter uses terms defined by the terms used in the former but not vice versa". So, for example, addition is said to be simpler than multiplication because the latter operation depends on the concept of addition.

Applying this to infinity, Swinburne argues that we can understand what the idea of an infinite quantity (or quantity without limit) is without needing to understand the specific large numbers, such as a googolplex, that are part of that infinite quantity.

This, as Gwiazda points out, is a rather silly argument. For we can also understand what a googolplex is without understanding what infinity is. Neither is simpler than the other, even if we accept Swinburne's definition of mathematical simplicity.


ii. Scientific Practice
The second justification of the principle P comes from the history of scientific practice. Swinburne uses one example over-and-over again. It is the example of the speed of light.

Swinburne argues that scientists -- or natural philosophers as they were then known -- originally preferred to posit an infinite velocity for the speed of light. It was only later, when other considerations came into play, that the finite value was arrived at. This, he thinks, is suggestive of the simplicity of an infinite value.

Gwiazda points out that Swinburne is being selective in his treatment of scientific history. Although it is true that figures like Aristotle and Descartes preferred the infinite value for the speed of light, it is equally true that Empedocles, Francis Bacon and Galileo preferred a finite value. Furthermore, it is surely not an insignificant point that those preferring the infinite value turned out to be wrong.

There are a few more points to be made here. First, Swinburne would need a much broader survey of scientific history to justify his claim -- one example won't cut it. Second, Gwiazda thinks that there might be psychological reasons why we prefer infinite values over finite values. For instance, it might be due to an unwillingness to admit to imprecision in our measurements; or it might be due to a primacy-recency effect in which the limits or endpoints of a sequence are remembered with greater felicity than the intermediate points.

I wouldn't overemphasis those psychological observations myself.


iii. Finite Limitations Need Explanation
On occasion, Swinburne appeals to the notion that a finite limitation is begging for explanation, in a way that limitlessness does not. Gwiazda thinks that this would need to be developed into an actual argument if it is to succeed. There is no further detail given in Swinburne's work (according to Gwiazda anyway).


iv. Zero and Infinity are "Neat"
On other occasions, Swinburne appeals to the notion that zero, one and infinity are mathematically neater and simpler quantities than all other finite numbers. The idea here is that 0 and 1 must be understood jointly, because one can't have the concept of zero-ness without also having the concept of one-ness but one could have the concept of one-ness without having the concept of two-ness. Likewise, as discussed earlier, Swinburne thinks that infinity can be understood without needing to understand other finite quantities.

Again, there is little support for this intuition and it could even be developed into an objection to Swinburne's understanding of God. We will do this in a moment.

On the whole, Swinburne's support for P is pretty thin. Next, Gwiazda develops two arguments for the falsity of P.


2. Why P might be false
The first argument against P focuses on the fact that the postulation of infinite values is often a sign of complexity and error in scientific explanations. This is a direct refutation of Swinburne's second argument for P.

Gwiazda uses the example of singularities in cosmology to make his case. A singularity is a point at which some measurement takes on an infinite value. The best-known examples are the points of infinite density found in black holes and at the origin of the universe (Big Bang). Scientists are not particularly happy with these infinite values. Indeed, they usually take them as indications of errors in their present theories.

The second argument against P takes onboard Swinburne's claim about the simplicity or neatness of zero, one and infinity. If Swinburne is right when he makes this claim, it would seem to follow that a God with no freedom (or knowledge or power) would be just as simple as one with infinite freedom. It would also seem to follow that a God with one unit of freedom (or knowledge or power) would be just as simple as an infinite God.

This is surely not something Swinburne would wish to entertain. But if that's the case, he will have to do a lot more work ironing out his definition of simplicity and his arguments in favour of an infinite God.

That's it for this post. In the next entry we will consider Swinburne's understanding of the relationship between God's three key properties (freedom, knowledge and power) and how this understanding further damages his argument for the infinite and simple God. 

Philosophical Disquisitions - The Podcast

In a momentary lapse of my otherwise sound judgment, I decided to record a podcast. The podcast is really just an audio version of what I'm already doing on the blog. It provides a summary and commentary on the various book chapters and articles that I've been reading.

It is intended to complement rather than replace the written summaries that I am already providing. There won't be any overlap between the two and the podcast will only be an occasional addition to the menu here at Philosophical Disquisitions.

The first episode is available for download here. It covers Erik Wielenberg's recently published article "Sceptical Theism and Divine Lies".

This is very much a trial run. I am hoping to improve my style and delivery over time and I would be happy to receive feedback -- constructive or otherwise -- in the comments section. I'm particularly concerned with how easy or difficult it is sustain concentration for the full duration of the podcast (24mins), particularly given my somewhat placid voice.

Anyway, let me know what you think.

Gwiazda on Swinburne: Alternatives to God

This post is part of a series on Jeremy Gwiazda's criticisms of Richard Swinburne's argument for the existence of God. For an introduction to the series, and to Swinburne's argument, see here.

To quickly recap, Swinburne argues that the probability of God's existence (h), given certain empirical evidence (e) and background tautological evidence (k) is high. This is stated in Bayesian form as:

• Pr(h|e&k) = Pr(e|h&k) Pr(h|k) / Pr(e|k)

Obviously, this equation is meaningless without actual numerical values. We saw in part two that problems arise when we combine some of Swinburne's proposed values and with his assumptions about probability. In particular, we saw that if he wants h to confer a high probability on e, he may have to abandon his commitment to God's simplicity.

In this part we will look at another mathematical difficulty. One that arises when Swinburne considers alternatives to theism.


1. What are the Alternatives?
Swinburne is trying to offer an explanation for the evidence we observe in this universe. He thinks theism is the most probable explanation. But he identifies three alternatives:

• h1 = "There are many Gods responsible for the creation of the universe"
• h2 = "There is an eternal physical universe (or multiverse)"
• h3 = "There is no explanation; the universe is just a brute fact"

So we end up with four possible explanations for the observed universe:

2. Putting Figures on the Alternatives

For the purposes of analysing the argument, we can assume that these four possibilities are mutually exclusive and jointly exhaustive. In other words, they amount to a complete carving-up of the available probability space. And since all probabilities have a value between 0 and 1, we must accept the following equation:

• Pr(h|k) + Pr(h1|k) + Pr(h2|k) + Pr(h3|k) = 1

Now we need some estimate of the different probabilities. Interestingly, as Gwiazda points out, Swinburne thinks that the Pr(h|k) could be very small indeed. His reason being that the existence of something rather than nothing is highly improbable. This leads Gwiaza to put a figure of 0.001 on it.

You may think this figure is slightly suspicious (I did) but I think Gwiazda is only using it to make a point about the combination of Swinburne's reluctance to put precise figures into his equation with his philosophical assumptions about what makes something probable or not.

Anyway, if we accept the figure of 0.001 for Pr(h|k) we must also accept that:

• Pr(h1|k) + Pr(h2|k) + Pr(h3|k) = 0.999

3. Muddled Reasoning

Now let's go through Swinburne's thoughts on each of these alternative explanations. He starts off by saying that the probability of there being many gods (h1) must be much lower than the probability of a single God. This would seem to make sense.

He goes on to say that the probability of no explanation (h3) must be "infinitesimally low". I'm not sure how defensible that is. I guess it depends on how we understand probability. If we are working from a subjective or epistemic understanding, then I guess the thought that the universe had no explanation would be pretty surprising. This would then lead to an infinitesimally low figure for Pr(h3|k). Still, I have my doubts.

Nonetheless, if we accept Swinburne's reasoning we must ask: Where does that leave the probability of the eternal physical universe (h2)? In pretty good shape actually. For if Swinburne is correct, h1 and h3 must be less intrinsically probable than h. This means that they must be less than 0.001.

That can mean only one thing: h2 must have a high intrinsic probability. Indeed, it could have a probability of up to 0.998. This would make h2 the most attractive explanation by a mile.

Obviously, Swinburne does not agree. He thinks the physical universe is highly complex and so highly improbable. Now we saw how this assumption was problematic in the previous post, but if its going to work here Swinburne will need to raise his estimate for the intrinsic probability of theism, or consider more alternative explanations.

Either way, he has work to do.

4. Summing up and Moving On

The first two entries in this series have dealt with some technical problems that arise from Swinburne's use of Bayes' theorem. Gwiazda's main argument has been that Swinburne's philosophical assumptions about probability have placed him somewhere between a rock and a hard place when it comes to proving his central thesis that God is a better explanation of complex universe than anything else.

In future entries in this series we will move on from these technical problems to consider Swinburne's understanding of God's simplicity.

Gwiazda on Swinburne: Complexity Quotients and God's Simplicity

This post is the second in a series on Jeremy Gwiazda's criticisms of Richard Swinburne's argument for the existence of God. For an introduction to Swinburne's argument see here.

We saw in the first part that Swinburne's basic argument is Bayesian in form. He claims that the probability of theism (h) given certain empirical evidence (e) and background tautological evidence (k) is high. We derive this probability using Bayes theorem, as follows:

• Pr(h|e&k) = Pr(e|h&k) Pr(h|k) / Pr(e|k)

Swinburne estimates that Pr(e|h&k) is 0.5. He then argues that the intrinsic probability of h, or Pr(h|k), is much higher than the intrinsic probability of e, or Pr(e|k). He does so on the grounds that h is much simpler than e and that the simpler hypothesis must have the higher probability.

Gwiazda thinks that this line of reasoning gets Swinburne into probability theory's version of hot water. We are about to see why.

1. Complexity Quotients

To appreciate the flaws we need to introduce the concept of a complexity quotient. This is a figure that arises from the division of one intrinsic probability by another. It gives some indication of how complex one theory is when compared to another.

In the case at hand, the relevant quotient is derived when we divide the intrinsic probability of theism by the intrinsic probability of the evidence. Before we consider that case, let's consider an instructive example.

Let w be the hypothesis "exactly one wooden block exists". W must have some intrinsic probability based on the background tautological evidence. But when you think about, w is ambiguous: wooden blocks come in a variety of sizes and shapes.

For illustrative purposes we can divide w into four more specific hypotheses. Since we are going purely on background tautological evidence, we can assume that these more specific hypotheses are equiprobable. The hypotheses are as follows:

• w1 = "one small light wooden block exists"
• w2 = "one large light wooden block exists"
• w3 = "one small dark wooden block exists"
• w4 = "one large dark wooden block exists"

Because these are more specific versions of w, and because they are equiprobable, it follows that:

• Pr (w|k) = 4*Pr(w1|k)

Which implies the following complexity quotient:

• Pr (w|k) / Pr(w1|k) = 4

Which means that w is four times more probable than w1. This makes sense since w is the more general, non-specific hypothesis. 

So good, so far.

2. Swinburne's Error

Swinburne's error becomes apparent once we bring the concept of the complexity quotient to bear on his original equation.

• Pr (h|e&k) = Pr(e|h&k) Pr(h|k) / Pr (e|k)

Recall that all probabilities must be greater than 0 but less than 1. This means that the maximum value for each side of this equation is 1. Recall also that Swinburne put a figure of 1/2 or 0.5 on Pr(e|h&k). This would give us:

• 1 ≥ 1/2 * Pr(h|k) / Pr(e|k)

Which we can multiply through by 2 to give us:

• Pr(h|k) / Pr(e|k) ≤ 2

This is an odd result. Whereas the intrinsic probability of one wooden block existing was 4 times greater than the probability of one small light wooden block, we are now forced to conclude that the intrinsic probability of God is only 2 times greater than the intrinsic probability of all the evidence that Swinburne wants to explain.

In other words, despite his claims that the evidence was incredibly complex and so in need of an explanation, Swinburne's own figure for Pr(e|h&k) would force him to accept that the evidence is not that complex when compared with God.

3. Where did he go wrong?

Gwiazda suggests that there is a rational explanation for Swinburne's error. You see, Swinburne wants the posterior probability of God's existence -- that is, Pr(h|e&k) -- to be reasonably high (> 0.5). He wants this because he wants his argument to have some persuasive force. After all, if you were told that the probability that God explains the observable universe was, say, 0.1 you would be relatively unimpressed.

Because he wants the figure to be relatively high, he needs h to confer a relatively high probability on the evidence. This is why he comes up with the figure of 1/2 for Pr(e|h&k). 

But at the same time he is committed to: (i) the idea that simple things are more probable than complex things; and (ii) the idea that God is simple whereas the observable evidence is complex. This commitment implies that a simple thing can never confer a high probability on a complex thing.

Consequently, he would be better off abandoning his claim that God is simple (or that the evidence is complex).

That's it for now. In the next part we will consider an additional mathematical problem that arises when Swinburne addresses alternative explanations for e.

Gwiazda on Swinburne: Introduction

Richard Swinburne is a highly respected contemporary Christian philosopher. In his impressive back-catalogue you will find painstaking evidentialist arguments supporting everything from the existence of God, the truth of the resurrection, to the validity of core Christian doctrines such as the trinity and the incarnation.

Jeremy Gwiazda is a recent CUNY PhD whose scholarly career is only in its spring. And yet, in a series of short papers (and in his PhD thesis), he has had the gall* to take on some of Swinburne's most important arguments.

It has all the makings of a modern day David and Goliath. Will the young upstart come out on top yet again? We'll see.

In this series I will look at Gwiazda's criticisms, using the following three papers as my guide:

• "Richard Swinburne, The Existence of God, and Exact Numerical Values" (2010) 38 Philosophia 357-363
• "Richard Swinburne's Argument to the Simplicity of God via the Infinite" (2009) 45 Religious Studies 487
• "Richard Swinburne, The Existence of God and Principle P" (2009) 48 SOPHIA 393-398

In this introductory post, I will provide some background on Swinburne's argument. Gwiazda focuses on the same basic deficiency in the all three of the articles, so this material will be essential reference as we go through them.

1. Bayes' Theorem

Ours is a Bayesian age. There are a number of excellent guides to Bayes' theorem online. I cannot hope to improve upon them here so I will provide a Spartan summary of the basic details.

Bayes' theorem is a formal result from probability theory. However it has some interesting philosophical implications for our understanding of rationality and induction. How so? Well, Bayes' theorem appears to give a mathematical formula for updating our degree of confidence in a hypothesis or belief based on our encounter with some evidence.

The theorem, along with a description of its basic terms, is given in the diagram below (click to enlarge).

In case you don't want to click on that and read it, the most important terms for the purposes of analysing Swinburne's argument are the likelihood of H and the prior probability of H.

The former represents the probability that a hypothesis confers on a piece of evidence. This tells us nothing about the probability of the hypothesis. Suppose you hear a knocking sound in your attic late at night. You propose that it is a group of gremlins getting rowdy. This hypothesis may confer a high probability on the knocking sound. After all, rowdy gremlins might be inclined to make noise. But this shouldn't encourage us to think that the gremlin hypothesis is itself highly probable. Before we can think that we need to know the values of the other quantities.

The prior probability, unsurprisingly, is the probability of the hypothesis without the evidence. Sometimes this figure is based on prior empirical data. However, in the case of Swinburne's argument there is no prior empirical data. So he is concerned with the intrinsic probability of the hypothesis. That is, the probability of the hypothesis given only certain logical/tautological truths.


2. Swinburne's Argument
Swinburne's central argument for the existence of God -- in the imaginatively titled The Existence of God -- is Bayesian in form. He looks at eleven pieces of evidences and feeds them through Bayes' theorem both individually and collectively. These pieces of evidence include things like purported religious experiences, apparent design, consciousness and so on.

Gwiazda only looks at the scenario in which Swinburne considers the conjunction of all eleven pieces of evidence. In the Bayesian calculus, this conjunction is labelled with an "e". Swinburne considers the probability of the hypothesis "God exists" (labelled h) given e and given a set of background "tautological" evidence (k).

This basic form is illustrated below. Obviously, Swinburne's goal is to show that Pr(h|e&k) is high (or at least higher than any alternative explanation of the evidence).

3. God's Simplicity
Giving the form is all well and good, but to make it meaningful some numerical values are needed. This, according to Gwiazda, is where the argument falls down. Before looking to Gwiazda's criticisms, we'll review what Swinburne actually says.

First, as noted in the diagram, Swinburne estimates that the likelihood of God's existence is about 1/2 or 0.5. This is the probability that God (and the tautological evidence) confers upon the evidence.

Second, Swinburne thinks that Pr(h|k) or the intrinsic probability of God's existence is high, whereas the Pr(e|k) is very low. The reason for this is that a simpler hypothesis is more probable than a complex one. And God is simple, whereas the evidence is complex.

Q.E.D, surely?

In the next part we'll see why Swinburne's approach is mistaken and why he needs to provide more precise figures to make his argument work.

*It has oft been noted that the internet needs a sarcasm-button. I add my voice to the swelling chorus supporting that idea.

Objectivity and Truth: You'd Better Rethink It (Part 4)

This post is part of my series on Sharon Street's article "Objectivity and Truth: You'd Better Rethink It". The article is a response to an earlier article by the legal theorist Ronald Dworkin, as well as a contribution to the realist v. antirealist debate in metaethics.

Part One covered the general background and structure to the realist v. antirealist conflict. Part Two covered Dworkin's own idiosyncratic take on this debate. He tried to dissolve the distinction between metaethics and normative ethics.

Part Two also introduced Street's basic challenge to realists: how do you reconcile your claim that moral values are mind-independent with the fact that our cognitive faculties have a complex and messy evolutionary origin? Part Three covered Dworkin's response to this challenge, along with Street's counter-responses.

In the end, we concluded that Dworkin has no adequate answer to the challenge and that antirealism does. The question then became: is antirealism plausible?

That is the question dealt with in this part.

1. The Repugnancy of Antirealism
Before addressing the question, a quick recap on antirealism and realism. The version of moral realism in the debate-pit is the one that views moral values as abstract, mind-independent metaphysical properties. In contrast to this, antirealism is the view that moral values depend on existence of practical agents with evaluative attitudes.

There are two main classes of antirealism. Kantian antirealism holds that certain moral values (e.g. respect for human dignity) are an inherent or necessary part of being a practical agent. Humean antirealism holds that there are no values that are necessarily shared by all practical agents.

One way of sharpening the nature of the dispute between the Kantians and the Humeans (and the realists) is to consider the hypothetical case of the ideally-coherent Caligula. I've mentioned him before. He is an agent with a consistent and coherent set of values and beliefs, that just happens to include the value of torturing children. Kantians think no such agent could exist; Humeans think he could and so could have a reason to torture; Realists also think he could, but that he would be morally wrong to act upon his values.

The attitudes of the respective parties to the ideally-coherent Caligula is significant when it comes to assessing the plausibility of antirealism. Dworkin holds that realism must be the more plausible view -- even if it fails to meet Street's challenge -- because it is the only one that can support the robust intuition that torture is always and everywhere morally wrong.

In other words, antirealism fails because of its repugnant and counterintuitive implications.


2. Dealing with Repugnancy
This argument places particular strain on Street's brand of antirealist constructivism which is of the Humean variety. So how does the Humean deal with the robust intuition against the possible moral propriety of torture?

Street offers several lines of response:

• First, that a rational agent would endorse torture would involve that agent meeting a strict set of conditions: their beliefs and evaluative attitudes would need to be in perfect harmony. These conditions are unlikely to be met by any actual human beings.

• Second, if we could imagine the ideally-coherent Caligula in full and vivid detail, it is likely that his reasons for valuing the torture of children would become less counterintuitive.

• Third, just because Caligula has an internal reason for endorsing the torture of children does not mean we have any reason to share in it. We can still criticise or condemn him.

• Fourth, if confronted by the ideally-coherent Caligula we would be in our right to prevent him from acting upon his values. 

If these responses are good, Humean antirealism is not as counterintuitive as it first seemed. The burden then shifts back to the realist who must now show that his vision of moral ontology and epistemology is more plausible than the antirealist's. This conclusion is strengthened if we endorse Kantian antirealism.

3. Is Antirealism Self-Defeating?

Street considers one final objection to antirealism. This is the argument that antirealism is ultimately self-defeating. To appreciate this objection we need to address the specific type of antirealism embraced by Street, which she labels constructivism.

I've covered this position before. The (inelegant) definition is the following:

• The fact that X is a reason for me to do Y is constituted by the fact that the judgment that X is a reason to do Y withstands scrutiny from the standpoint of my other judgments about reasons.

For a more comprehensive understanding of this, you'll have to read the other posts in the series. 

Street's constructivism might be thought to be self-defeating in the following way. Imagine a realist like Dworkin making the following normative judgment:

X is a reason for me to do Y, and it would be such a reason even if I judged that it wasn't and even if that judgment withstood scrutiny from the standpoint of my other judgments about reasons.

This, of course, is a straightforward endorsement of realism and rejection of constructivism. But couldn't  this judgment withstand scrutiny from the perspective of Dworkin's other judgments?

That would leave us in a strange position. A constructivist methodology would have been used to establish a realist conclusion. This cannot be right, can it?


4. It is not Self-Defeating
Street responds in the obvious manner: it would actually be impossible for Dworkin's endorsement of realism to withstand scrutiny from the perspective of his other judgments. Her argument for this is the argument that she has been pursuing throughout the paper. We can briefly restate it.

Every agent is capable of viewing themselves from two perspectives: the practical and the theoretical. From the practical perspective they think about their values and their reasons-for-action; from the theoretical perspective they consider how they happened to have the values and reasons-for-action that they do have. This means that every agent can ask questions about the causal origins of their normative judgments.

But when they do this, they must confront Street's challenge: how did their evolved moral faculties stumble upon the mind-independent moral truth? And as we have seen, realists do not seem to have a good answer to this question.

Going through this reasoning process would lead the agent to the following conclusion: constructivism is the only theory that makes sense of moral epistemology. And this would mean that, irrespective of your initial metaethical views, the endorsement of realism could not withstand scrutiny from the perspective of your other judgments.

In other words, only constructivism withstands scrutiny from within the practical point of view.

Psychology of Religion (Index)

There has been some groundbreaking work done in recent years on the psychology of religious belief. This is undoubtedly a topic of perennial fascination. David Hume's work The Natural History of Religion is noteworthy in this respect. 

The contemporary research is different in that it adopts the tools of cognitive and evolutionary science. Using them to explore the mechanisms and origins of religious belief systems.

I hope to cover some of this material on this blog. This will serve as an index.

1. Videos on the Psychology of Religion

2. The Five Features of Fundamentalism

3. Teehan on the Moral Function of God

Objectivity and Truth: You'd Better Rethink It (Part 3)

This post is part of my series on Sharon Street's article "Objectivity and Truth: You'd Better Rethink It". The article is a response to an earlier article by the legal theorist Ronald Dworkin, as well as a contribution to the more general realist/antirealist debate in metaethics.

In Part 1 I provided a general introduction to the realism v. antirealism debate. In Part 2 I covered Dworkin's take on this debate. Dworkin is a realist, but a realist with a bit of a twist.

At the end of Part 2 I presented Street's challenge to realism. She argued that because realists hold to the mind-independence of moral values, they are forced to explain how our evolved cognitive faculties manage to track the truth of moral facts. In other words, on the realist view there is a puzzling coincidence between our messy causal history and moral truth.

Street identified three possible answers to this puzzling coincidence. The first was to reject realism and embrace antirealism. The second was to offer some causal explanation. And the third was simply to accept the coincidence as a brute fact.

The third explanation is the one preferred by Dworkin. In this part we will see why it is unsatisfactory.

1. Winning the Moral Lottery
To justify his brute fact explanation, Dworkin uses the analogy of the lottery. Winning a lottery is highly improbable. But suppose you had been told that your numbers were drawn. Should you then doubt the fact that you had won? Should you ask for some deeper explanation for why you, of all people, happened to be the winner?

Dworkin thinks it obvious that you don't need to do either. And he thinks that the same reasoning applies to our moral beliefs: we don't need to explain why they happen to be true; they just are.

Street points out that this analogy is deeply flawed. It is true to say that no deeper explanation is needed after we learn that our numbers were drawn in the lottery. But it would be insane to think you had won before any numbers were drawn. And this is the position we are in with respect to moral truth. We do not yet know whether we have won the moral lottery.

Street argues that we need a non-trivial non-question-begging reason to think we have hit upon the independent moral truth posited by realists. Dworkin has a possible answer. He says our individual moral judgments can be non-trivially supported by appeal to our other moral judgments. The goal then being to achieve some consistent web of moral judgments.

That's all well and good, but it comes much closer to antirealism than to realism. And another problem arises. There may be many consistent webs of moral judgment. The realist needs to explain why their system happens to coincide with independent moral truths. Indeed, this is the whole point of the ideally-coherent Caligula example discussed earlier.


2. Three Worries and Responses
Three complaints may be made about Street's challenge. She reviews and responds to each of them.

First, it may be argued that she is asking for too much; that she is asking for an external justification of morality. This seems to be implicit in what was just said about the realist needing to explain why their entire system of moral judgments happens to be correct. But we saw in part 2 that Dworkin thinks it is impossible to pass judgment on the entire domain of normativity.

Street responds by saying she is not asking for an external justification. She is accepting Dworkin's argument against external scepticism. However, Dworkin accepts that the claim "moral truths are mind-independent" is a type of internal normative claim. Street is merely asking for a justification of that internal claim.

Second, it might be objected that Street's challenge applies equally well to beliefs about the external world and so says nothing particularly important about moral beliefs. The idea here is that, although it is possible to offer an evolutionary account of how our cognitive faculties give us reliable beliefs about the external world, this account itself depends on beliefs about the external world (i.e. our belief that the theory of evolution is true). If we are allowed to assume what we want to prove, then moral realism is in no trouble.

Street argues that this is mistaken. The evolutionist offers reasons that are internal to their worldview for thinking that their beliefs about the external world are correct. It would be acceptable for the moral realist to do the same. But the Dworkinian moral realist offers no reasons for thinking that their moral beliefs are correct.

Finally, some might worry that Street is assuming that a causal explanation of the coincidence is necessary. And there are enough people who doubt the relevance of causal explanations in the moral domain to make this an issue.

Street counters by saying she is not assuming that a causal explanation is necessary. She herself rejects the need for a causal epistemology when it comes to normative judgments (see other posts on Street's constructivism for this point). However, she thinks that some epistemology is needed and that Dworkin has failed to provide it.

Furthermore, she thinks that her own moral antirealism can answer the challenge she has raised. It holds that there is no puzzling coincidence because moral values are not mind-independent.

This may seem suspect. Has Street simply invented a problem in order to endorse her preferred moral theory? She thinks not because antirealism is plausible for other reasons.

We will take this up in the final part.

Objectivity and Truth: You'd Better Rethink It (Part 2)

This post is part of my series on Sharon Street's article "Objectivity and Truth: You'd Better Rethink It". The article is a response to an earlier article by the legal/political theorist Ronald Dworkin, as well as being a contribution to the realist v. antirealist debate in metaethics.

In part one, I covered Street's characterisation of this debate. Street is a proponent of moral antirealism and tries to defend this from realists such as Dworkin.

In this part, we will sketch Dworkin's version of realism, introduce Street's challenge to realism and consider some responses to this challenge.

1. Normative Realism vs. Metaethical Realism
Dworkin has a somewhat unique approach to moral realism. To get a grasp on it, we need to take a step back and consider the distinction between normative ethics and metaethics.

Normative ethics is concerned primarily with the following types of questions: what is good/bad? What is right/wrong? These questions are at the heart of our ethical lives and they are answered by identifying moral principles or values.*

Metaethics -- as the name implies -- takes a step back from these normative issues and asks about the meaning, ontology and epistemology of the moral principles and values identified by normative ethics.

Dworkin's originality lies in arguing that metaethical questions are actually part of normative ethics. That is, that the distinction I just outlined cannot be sustained. In making this argument, Dworkin takes particular issue with those who claim to be moral sceptics.

Dworkin asks us to consider two types of moral sceptic, the internal sceptic and the external sceptic. The internal sceptic operates within the normative domain and is simply sceptical about some proposed moral values and principles. For example, the internal sceptic might think that maximising conscious pleasure cannot be a moral principle because there are other values and following this principle would compromise those.

We can live with the internal sceptic. In fact, we need the internal sceptic. After all, thrashing out which principles are acceptable and which are not is the central task of ethics. Provided that the internal sceptic explains his thinking, we can appreciate his contribution to ethical debate.

Dworkin is less happy about the external sceptic. Unlike the internalist, the externalist tries to pass judgment on the entire domain of normative ethics. He will say things like "There are no moral truths", "Everything is relative", "Morality is just an expression of the emotions". We all know the type.

Dworkin's key argument is that it is impossible to be an external sceptic. He takes it that one cannot step outside the prescriptive or normative domain and analyse it from some Archimedean point. Why does he think this? Well, because to Dworkin the claims of the external sceptic are, for all their huffing and puffing to the contrary, re-statable as normative claims.

For example, the claims about relativity and nihilism can be plausibly reconstrued as calls for toleration of others and humility about one's own judgments, respectively. And since these calls have normative force, the external sceptic must be wrong.


2. A Puzzling Coincidence
Dworkin's dismissal of the external sceptic has some important implications for how we think about typical metaethical statements.

The realist vs. antirealist debate was characterised in part one as being concerned with the relationship between the mind and the system of moral values. According to the realist, moral values are mind-independent metaphysical states of affairs; according to the anti-realist, moral values are mind-dependent.

To sharpen the nature of their dispute, the realists and anti-realists try to imagine intelligent hypothetical agents (e.g. the ideally-coherent Caligula) who might be favourably disposed to torture. Realists argue that even if such an agent existed, torture would be morally wrong. Anti-realists think that the wrongness of torture depends on the preferences of agents, but they are split down the middle on the possibility of an ideally-coherent Caligula. Kantian anti-realists think that such an agent could not exist; Humean anti-realists think he could, but that his hypothetical existence is not relevant to current moral debates.

Dworkin argues that this debate takes place within, not outside, the domain of normative ethics. It is simply a normative dispute where special attention is paid to counterfactual cases involving agents with evaluative attitudes that are quite different from our own. As it happens, Dworkin thinks that the realists get it right.

Street is willing to grant Dworkin his idiosyncratic views on metaethics. But she is not willing to grant him his defence of realism. She thinks that realism fails as an internal normative claim.

She does so because of the practical/theoretical puzzle outlined in part one. Briefly, the realist must find some way to reconcile the fact that human cognitive faculties have evolved and developed in a complex and messy fashion with their own claim that these faculties can pick out mind-independent moral truths.

Street takes it that the coincidence of our evolved faculties with the mind-independent realm of values is, at the very least, "puzzling". This does not mean that the coincidence is improbable. For all we know it might be highly probable. Nonetheless, Street thinks that some kind of explanation is needed.


3. Possible Solutions
Street then proceeds to survey three possible solutions to the problem.

The first is the antirealist solution. For the antirealist, the coincidence is irrelevant. They maintain that normative reasons arise from the practical standpoint. That is, from the standpoint of agents with evaluative attitudes. So our moral faculties are not picking out or intuiting mind-independent moral truths. This position has been covered at length in my other entries on Street's work.

The second solution is to provide a causal explanation of the coincidence. The analogy here would be with how our non-moral cognition evolved. If we could expect our cognitive faculties to evolve and track the truth of propositions about the external world (e.g. the world of trees, stones, rivers, predators and food), then perhaps we could expect our moral faculties to do the same?

Whatever the merits of causal explanations in the non-moral domain, Street thinks there is a significant disanalogy when it comes to the moral domain: our evolutionary ancestors would actually have causal interact with the external world; they could not have causal interactions with moral properties. This is because realists like Dworkin do not think moral properties are causal in nature. They think they are abstract in nature.

The third solution is the brute fact explanation. This argues that the puzzling coincidence is just a brute fact. That our moral faculties just happen to tell us the truth about moral facts. This, surprisingly, is the view defended by Dworkin. We will look into it in more depth in the next part.





* There is also a position known as moral particularism which holds that our moral lives are sustained without support from principles. One proponent of this view is Jonathan Dancy.

Teehan on the Moral Function of God

John Teehan's book In the Name of God is a must-read for anyone who is interested in the relationship between moral psychology and religious ethics.

The opening two chapters cover the evidence and theory surrounding the evolutionary origins of moral and religious beliefs and practices. They are worth the price of admission alone, providing a wonderful survey and synthesis of a diverse range of studies and theoretical concepts. The evolutionary perspective adopted is a marriage between traditional evolutionary psychology, cultural evolutionary theory and cognitive science. The end result is, I think, impressive.

The remaining chapters use the theoretical framework from the opening chapters as the basis for a textual analysis of the three main religions-of-the-book: Judaism, Christianity, Islam. Teehan shows how the beliefs and practices of the evolved mind are reflected in these texts.

I have only managed to get through the chapter on Judaism so far so I won't comment on the remainder of the book. My only observation would be that, because the Hebrew bible is such a large, sprawling and multi-vocal text, the analysis is necessarily limited and focused in what it can do.

Anyway, I thought I might share one of the core ideas of the book. It comes from Chapter 2 and it deals with the putative moral function of belief in God (or gods).


1. The Problem of Cooperation
To understand the moral function of God-belief, we must go back for a moment and consider some of the practical social problems that evolutionary theorists suppose gives rise to our moral and religious beliefs.

These problems tend to stem from the oft-times troubling results of the interactions between self-interested actors. One such problem is that of cooperation: how do we get self-interested actors to cooperate in order to enhance overall welfare?

The problem of cooperation is well-illustrated by a famous social game: the tragedy of the commons (TOC). I use "game" here in the sense employed in game theory to cover any social interaction with actors, choices, outcomes (payoffs) and information.

A simple story can help to illustrate the TOC. Imagine two firms (A and B), each producing the same product and competing in the same market. Suppose their product relies ultimately on having a clean, unpolluted environment, but that their production process leads to increased levels of pollution. They would both be better off if they internalised the costs of this pollution and changed their production process. However, if  one factory does this on its own, the other factory can gain a short-term competitive advantage and drive the other out of the market.

As described, the game has two actors, two choices (stop polluting or continue to pollute) and common information (i.e. both sides have access to the same information). The game also has four outcomes or payoffs. We will rank these outcomes from best to worst from the perspective of firm A. The exact same ranking, only reversed, applies to firm B. The outcomes and rankings are as follows:

• Firm A pollutes, but Firm B does not. (Payoff = 4)
• Firm A and Firm B do not pollute. (Payoff = 3)
• Both firms continue to pollute (Payoff = 2)
• Firm A stops polluting, but firm B does not (Payoff = 1)

A standard game-theoretic analysis predicts that, although it puts them both in a worse position, the firms will continue to pollute. This is because the prospect of gaining a competitive advantage provides a temptation to pollute, while the prospect of being driven out of the market prevents the unilateral cessation of polluting. More formally, this strategy is a Nash equilibrium

The basic dynamic of the TOC crops up in many situations, e.g. overgrazing of common pastures, overfishing, global warming and so on. The TOC is also structurally equivalent to the more famous Prisoners' Dilemma.

The resolution of the TOC and the PD is cooperation. In other words, if people can cooperate they can achieve the more mutually advantageous outcome. But how do you get them to cooperate? This will require some sort of system for inspecting and punishing those who fail to cooperate. Examples are given in the diagram.

Evolution-oriented psychologists will also argue that we have evolved a set of moral instincts and biases that encourage cooperation. These can help ease the difficulties with policing cooperation. However, our brains are a tangled web of competing instincts, some of which are disinclined to cooperation. Thus, continued cooperation is a perpetual problem. Eternal vigilance seems to be the only solution.


2. The Moral Function of God
This brings us face-to-face with God. Teehan, among others, argues that one of the core moral functions of God is to help solve the problem of cooperation. To see how this might work, we need to first consider the content of God-belief.

Teehan follows the work of Scott Atran in seeing God as a minimally counter-intuitive concept (MCI). God, as conceptualised by major world religions, is a person. As a person he has a mind. This mind thinks, feels, and has beliefs and desires just like the rest of us. However, he is not "just like the rest of us": he has something more.

Specifically, he has far greater cognitive and perceptual faculties. Some even go so far as to say he is omniscient and omnipresent. These capacities are what make the personhood of god minimally counter-intuitive.

Conceptualised as such, God can help to resolve the problem of cooperation. You see, the temptation to defect in the TOC stems largely from the belief that we won't get caught, i.e. that we can "free-ride" on the good will of others. Human invigilators are, after all, fallible mortals. They cannot be everywhere at once. They won't know -- will they? -- if I catch more fish than my quota?

God is not like that. God knows all and sees all. He is the perfect, eternal invigilator we need to ensure stable, lasting cooperation.

3. Commitment
Interesting things can follow from this basic idea. One of which tells us something about public affirmations or signals of religious belief.

Although belief in God can help to solve the problem of cooperation, it does have one obvious shortcoming: you have to actually believe in God. If I live in a populous society and must cooperate with many people on a daily basis, it would benefit me if I could distinguish the trustworthy from the duplicitous. And if God-belief makes people more trustworthy, it would be good if I could tell the believers from the non-believers.

How might this be done? One way is to have hard-to-fake public signals of religious commitment. The complex and time-consuming rituals that are so typical of religions may function as these hard-to-fake signals. They allow members to constantly monitor and convince one another of their trustworthiness.


4. Conclusion
Teehan backs-up a lot of this theoretical sketch with empirical evidence. Unfortunately, you'll have to read the book to chase down the relevant references.

I will conclude simply by noting that, although God-belief can help to encourage cooperation, it is not necessary for it. Secular beliefs, rituals and practices can have similar effects. For example, citizenship tests might function as a signal of commitment to the laws and values of a particular country.

Furthermore, the above theory does not rule out the potential negative impact of religious belief on moral behaviour. For example, the desire to develop well-defined group boundaries can lead to harsh or discriminatory treatment of "outsiders".

See the five features of fundamentalism for more.