I see that Plantinga’s skeptical argument refers to “Dwindling Probabilities” rather than “Dwindling Probability”. Sorry about my failure to get the name of this topic quite right.

I should mention that I did not learn about this sort of skeptical argument from the Christian philosopher Alvin Plantinga. I learned about the *Multiplication Rule* of probablity in high school math, and then again in one of many courses on logic and critical thinking that I took in college and as a graduate student of philosophy.

Although I enjoyed learning about basic probability calculations in a Critical Thinking class at UCSB (esp. from *The Elements of Logic* by Stephen Barker, Chapter 7, 5th edition), the significance of the *Multiplication Rule* did not fully register with me until (I think) I read a skeptical argument by a Christian bible scholar: Robert Stein.

In his book *Jesus the Messiah*, Stein makes a skeptical argument about scholarly attempts to reconstruct the historical development of Q, a hypothetical source that most N.T. scholars believe was used by the authors of the Gospel of Luke and of the Gospel of Matthew. Stein notes eight different hypotheses required in order to arrive at such a reconstruction of the history of Q. Then Stein suggests estimated probabilities for each of the first five of the eight hypotheses, and argues that the probability that all five of those hypotheses is true is equal to the multiplication of the probabilities of those five hypotheses:

**In other words, if the probability of the first five hypotheses were (1) 90 percent, (2) 80 percent, (3) 60 percent, (4) 50 percent, (5) 40 percent, the possibility of the fifth being true is .90 x .80 x .60 x .50 x .40, or a little more than 8 percent! **(*Jesus the Messiah*, p. 40)

Stein is a little sloppy here, and he appears to contradict himself. He seems to be saying that the probability of the fifth hypothesis being true is 40 percent and also saying that the probability of this hypothesis being true is a little more than 8 percent. But I think what he means is that the probabilty of the fifth hypothesis being true GIVEN the relevant facts AND *the truth of the previous four hypotheses* is 40 percent, and I think what he means is that the probability of the fifth hypothesis being true GIVEN only the relevant factual data is a little more than 8 percent (because the truth of the conjunction of the previous four hypotheses is NOT certain, but is actually somewhat improbable).

In any case, this skeptical argument presented by Stein inspired me to make use of the Multiplication Rule of probability in constructing skeptical arguments.

Richard Swinburne has raised some objections to Plantinga’s “Dwindling Probabilities” argument, and I am going to state and clarify those objections, and respond to each objection in relation to my example of “Dwindling Probabilities” presented in Part 1 of this series of posts.

Swinburne presents one primary objection, and then presents two more objections. Swinburne’s primary objection is stated early in his essay on this issue:

**Now, strictly speaking – as Plantinga acknowledges, but takes no further – P(G/K) is the sum ****of the probabilities of the different routes to it. ****G might be true without some of these intermediate ****propositions being true. **

First, let me explain the meaning of P(G/K). Read this as “The probability of G given K.”

G means:

**The central elements of Christian doctrine are true. **

(e.g. God exists; Jesus rose from the dead; Jesus’ death on the cross atoned for our sins; etc.).

K refers to:

**The totality of what we know apart from theism.**

So P(G/K) means:

**The probability that the central elements of Christian doctrine are true GIVEN the totality of what we know apart from theism.**

One “route” to G is to establish the authority of the teachings of Jesus, and the reliability of the Gospel accounts of the teachings of Jesus. If one could show that the teachings of Jesus are a reliable source of theological truths, and that the Gospel accounts of the teachings of Jesus are accurate and reliable, then one could establish the probable truth of many or most Christian doctrines on the basis of the teachings of Jesus as presented in the Gospels.

So, one could break this line of reasoning down into various components, assign probabilities to each of the components, and then multiply the probabilities to arrive at a probability for G, for it being the case that the central elements of Christian doctrine are true:

**1. God exists.**

**2. Jesus existed.**

**3. Jesus was crucified in Jerusalem about 30 CE, assuming that Jesus existed.**

**4. Jesus rose from the dead, assuming that God exists, and that Jesus existed, and that Jesus was crucified in Jerusalem about 30 CE.**

**5. God showed approval for Jesus’ claims about himself by raising Jesus from the dead, assuming that God exists and that Jesus rose from the dead.**

**6. The Gospel accounts of the words and teachings of Jesus are accurate and reliable accounts, assuming that Jesus existed.**

**7. Jesus claimed to be a prophet who was a reliable source of truth about God and theological matters, assuming that Jesus existed and assuming that the Gospel accounts of the words and teachings of Jesus are accurate and reliable accounts.**

**8. Jesus’ teachings about God and theological matters are a reliable source of truth, assuming that God showed approval for Jesus’ claims about himself by raising Jesus from the dead and assuming that Jesus claimed to be a prophet who was a reliable source of truth about God and theological matters.**

**9. The central elements of Christian doctrine are true, assuming that Jesus’ teachings about God and theological matters are a reliable source of truth and assuming that the Gospel accounts of the words and teachings of Jesus are accurate and reliable accounts.**

None of these claims is certain.

A careful and rational evaluation of this line of reasoning would require assigning probabilities to each of these claims. There is some probability that God exists, and some probability that Jesus existed, and some probability that Jesus was crucified (given that he existed), and some probability that Jesus rose from the dead (given that he existed and was crucified), etc.

Even if we assign a high probability to each of these claims (such as .8 or .9), when we use the *Multiplication Rule* of probability to determine the probability of G, the claim that the central elements of Christian doctrine are true, the probability will be fairly low. For example, suppose that we assign a probability of .9 to each of the first four claims. In that case the probability of the conjunction of these four claims would be: .9 x .9 x .9 x .9 = .81 x .81 = .6561 or about .7 which is not exactly a high probability.

If we assigned a probability of .8 to each of the first four claims, then the probability of the conjunction of those claims would be:

.8 x .8 x .8 x .8 = .64 x .64 = .4096 or about .4 which is clearly NOT a high probability.

Swinburne’s objection is that there may be other “routes” to the ultimate conclusion that G is the case, and if this is so, then we have to add the probability of arriving at G from other routes to the probabilty of G based on the particular route described above.

Let’s consider a simpler example to make Swinburne’s point more clearly:

**1. It will (probably) rain this afternoon.**

**2. If it rains this afternoon, then your lawn will (probably) be wet this evening.**

**Therefore:**

**3. Your lawn will (probably) be wet this evening.**

Neither premise of this argument is certain. We coud assign a probability to each premise and use that to calculate the probability of the conclusion. Supose that there is an 80% chance of rain this afternoon, and if it rains this afternoon, there is a 90% chance that your lawn will be wet this evening. We could calculate the probability of the conclusion (3) by multiplying .8 x .9 to get: .72. Thus, the probability of (3) appears to be about .7 based on these assumptions about the probability of the premises.

However, there could be other “routes” or ways that your lawn could become wet:

**4. Your lawn sprinkler system will (probably) turn on and water the lawn for an hour this afternoon.**

**5. If your lawn sprinkler system turns on and waters the lawn for an hour this afternoon, then your lawn will (probably) be wet this evening.**

**Therefore:**

**3. Your lawn will (probably) be wet this evening.**

We could assign probabilities to each of the premises in this argument to arrive at a probability for the conclusion. Suppose that the sprinkler system is fairly reliable, and has been set to water the lawn for an hour each afternoon. In that case, we might assign a high probabililty of .9 to premise (4), and a probability of .9 to premise (5). We could calculate the probability of conclusion (3) by multiplying .9 x .9 to get: .81. Thus, the probabilty of (3) appears to be about .8 based on these assumptions. But this is a different probability than what we arrived at based on the previous argument. Which probability is correct? .7 or .8?

If both arguments apply *on the same day to the same lawn*, then NEITHER estimate is correct, because the probabilty that (3) will be true would be higher than either estimate, since there are TWO DIFFERENT WAYS, each of which has a significant probability, that your lawn could become wet this afternoon.

Presumably the operation of the sprinkler system would NOT affect the weather, and thus NOT affect the chance of rain. However, if it rains, that could affect the operation of the sprinkler system. Some sprinkler systems can detect rain or detect moisture in the soil and adjust the watering schedule based on that data. A sprinkler system might be designed to cancel the scheduled watering for the afternoon if it starts to rain early in the afternoon. So, with some sprinkler systems, rain in the early afternoon would reduce the probability of the scheduled afternoon watering to nearly ZERO. But if the scheduled watering begins early in the afternoon, that would have no impact on whether it would rain later that afternoon.

But suppose the sprinkler system has a simple timer and no mechanism for detecting rain. In this case the sprinkler system which is set to water the lawn each afternoon, will turn the sprinklers on whether it rains that afternoon or not. In that case, we could reasonably assume that these two different ways of making your lawn wet, operate INDEPENDENTLY of each other, and thus both of the above calculations of the probability of (3) would be too low, because each calculation assumes that there is only ONE WAY for your lawn to become wet, when there are actually (at least) TWO WAYS for this to occur. Rain is one ROUTE for making your lawn wet, but a sprinkler system is another different ROUTE for making your lawn wet.

One ROUTE for showing central Christian doctrines to be true, is through the resurrection of Jesus as evidence for the authority (reliability) of the teachings of Jesus about God and theological matters. But other ROUTES are possible, as Swinburne points out, so the probability of the truth of central Christian doctrines does NOT rest exclusively on the ROUTE through the resurrection of Jesus as evidence for the authority (reliability) of the teachings of Jesus. In order to arrive at an accurate probabilty of G, one must take into account any and every ROUTE that contributes some degree of probability to G.

**My response to this objection** in relation to my example of dwindling probabilities in the previous post is that there is ONLY ONE ROUTE (that has a probability higher than ZERO) to the claim “Jesus died on the same day he was crucified” in my probability tree diagram. So, although I agree with Swinburne’s point and his logic, this point has NO RELEVANCE in relation to my particular example of dwindling probabilities.

There is some relevance to Swinburne’s point, however, if one uses my example probability tree diagram as *part of one’s thinking about the resurrection* of Jesus. The claim “Jesus died on the same day he was crucified” reflects the standard Christian view or scenario about the death of Jesus. According to the Gospels, Jesus died on the cross on the same day that he was crucified (which is somewhat unusual – crucifixion was intended to be a slow, long, drawn-out, and painful death). But it is possible that Jesus rose from the dead, even if he did not die on the day that he was crucified.

Jesus might have been *barely alive* when removed from the cross, the soldiers mistakenly believing that he was already dead, and Jesus might have been placed in a nearby tomb, again by someone who mistakenly believed he was already dead, and then Jesus might have survived that Friday night and died in the cold, dark tomb *early on Saturday morning*, but came back to life on Sunday morning about 24 hours later.

This would still count as *rising from the dead*, and would still be more-or-less in line with Christian belief and doctrine. Therefore, it is not absolutely required that “Jesus died on the same day he was crucified” in order for it to be the case that “Jesus rose from the dead”. So, there is this alternative ROUTE or WAY that the resurrection could have occured, and in order to accurately assess the probability of the resurrection of Jesus, the probability of this alternative ROUTE must be added to the probability of the standard ROUTE, where Jesus dies on the same day that he was crucified.

To be continued…

# Tag: conditional probability

*bookmark_border*One Problem with Swinburne’s Case for God

In *The Existence of God* (2nd edition, hereafter: EOG), Richard Swinburne lays out a systematic cumulative case for the claim that it is more likely than not that God exists.

I have a specific objection to the third argument in this case, but I believe this objection throws a monkey wrench into the works, and creates a serious problem for the case as a whole.

To understand my objection, it is important to understand the general logical structure of Swinburne’s case for the existence of God. It is always natural and tempting to immediately focus in on the question of the truth of the premises of an argument for God, so in order to get a clear grasp on the logical structure of Swinburne’s case, it may be best to FIRST consider that structure apart from the specific content of the premises of the arguments in his case. The content of the premises will be important to make my objection, so we will get to the specific content at a later point.

One key idea in Swinburne’s logic is that we begin from a state of ignorance in which we are to imagine that we know ZERO empirical claims (both facts and theories). Swinburne thus controls the flow of empirical data, introducing one fact at a time, and arguing that in each case (with the exception of the problem of evil) that the added fact increases the probability of the hypothesis that God exists.

The basic strategy is to (1) put forward an empirical fact, (2) show that the empirical fact is more likely to be the case if God were to exist than if there were no God, (3) conclude that the fact increases the probability of the hypothesis that God exists above the *a priori* probability that God exists (i.e. the probability based on ZERO empirical facts), then (4) introduce a second fact, (5) show that the second fact is more likely to be the case if God exists (and the first fact is the case) than if God does not exist (and the first fact is the case), (6) conclude that the second fact in conjunction with the first fact increases the probability that God exists above the probability based on the first fact by itself, (7) put forward a third fact, (8) show that the third fact is more likely to be the case if God exists (and the first two facts are the case) than if God does not exist (and the first two facts are the case), (9) conclude that the third fact in conjunction with the previous two facts increases the probability of the hypothesis that God exists above the probability based on just the previous two facts, and so on…slowly increasing the probability of God’s existence with each new fact.

Swinburne changes the strategy a bit when he gets to the argument from religious experience (in Chapter 13 of EOG), but the above pattern of reasoning is supposed to hold up until that point, and the above pattern of reasoning, filled in with the empirical facts that Swinburne has selected, is supposed to get us to the point where the probability of the existence of God is about .5 (meaning there is about a 50/50 chance that God exists).

Swinburne uses Bayes’ theorem to justify key inferences in his reasoning, so I will reformulate the above description of the logical structure of Swinburne’s case in terms of conditional probability statements. Let’s use the letter **e** for evidence, plus a number to indicate which empirical claim we are talking about in the sequence of empirical claims introduced by Swinburne. Thus, **e1** represents the first empirical claim in Swinburne’s case, and **e2** the second empirical claim, and so on.

**g: God exists.**

**k: [tautological background knowledge – analytic truths, truths of logic, math, and conceptual truths]**

The probability of **e1** being the case *given that God exists* is written this way:

**P(e1|g & k) **

Here is how we represent the idea that the first factual claim is more likely to be the case if God exists (and we have only tautological truths as background knowledge) than if God does not exist (and we have only tautological truths as background knowledge):

**P(e1|g & k) > P(e1|~g & k)**

From this Swinburne makes use of Bayes’ theorem and infers that **e1** provides evidence that increases the probability that God exists, over the *a priori* probability that God exists (the probability based on ZERO empirical facts):

**P(g| e1 & k) > P(g| k)**

Then Swinburne introduces a second factual claim **e2**. Again Swinburne argues that this factual claim is more likely to be the case if God exists than if God does not exist (now assuming e1 as part of our background knowledge, for after consideration of the first argument we are no longer completely ignorant of all empirical facts):

**P(e2|g & e1 & k) > P(e2|~g & e1 & k)**

From this Swinburne makes use of Bayes’ theorem and infers that the addition of this second empirical fact to the first empirical fact has again increased the probability of the existence of God, over what it was based on just the first fact by itself:

**P(g| e2 & e1 & k) > P(g| e1 & k)**

Then Swinburne introduces a third factual claim: **e3**. Again Swinburne argues that this factual claim is more likely to be the case if God exists than if God does not exist (now assuming both e1 and e2 as part of our background knowledge):

**P(e3|g & e2 & e1 & k) > P(e3|~g & e2 & e1 & k)**

From this Swinburne makes use of Bayes’ theorem and infers that the addition of this third empirical fact to the first empirical fact has yet again increased the probability of the existence of God, over what it was based on just the first two facts:

**P(g| e3 & e2 & e1 & k) > P(g| e2 & e1 & k)**

There are problems and objections that can be raised against each of the particular arguments that Swinburne uses to get up to the point where the probability of the existence of God supposedly reaches the halfway mark, but this post will focus on the third argument in the systematic cumulative case that Swinburne presents: The Teleological Argument from Spatial Order (hereafter: TASO).

TASO can be stated fairly briefly:

**(e3) There is a complex physical universe that is governed by simple natural laws and the values of the constants of the laws and of the variables of the universe’s initial conditions make it probable that human bodies will evolve in that universe.**

**Therefore:**

**(g) God exists.**

Remember, this is NOT a deductive proof for the existence of God. (e3) is put forward NOT as a conclusive reason for (g), but merely as evidence for (g); (e3) is an empirical claim that is supposed to *increase the probability* of (g) relative to the probability of (g) based on just the two previous empirical claims:

**(e1) There is a complex physical universe.**

**(e2) There is a complex physical universe that is governed by simple natural laws.**

One problem is that it is not clear to me that (e3) is in fact true. The fact that human bodies evolved once in this universe does NOT imply (by itself) that it was *probable* that human bodies would evolve in this universe. I think a good deal of argumentation and evidence would be required to establish the truth of (e3).

Another more important problem with (e3) is one that Swinburne himself mentions and briefly discusses: “What reason would God have for taking an evolutionary route?” (EOG, p.188). Swinburne goes on to talk about the beauty of the long cosmological “evolution” of the universe, and the beauty of plants and animals that resulted from the long history of biological evolution. But this is all beside the point. God, being omnipotent and omniscient, could have brought about all of the beautiful plants and animals on earth including human beings in the blink of an eye.

God had no need to use the natural biological process of evolution, and no need to build such a process into the fabric of the universe. The story in Genesis makes much more sense than evolution as the way that God would create animals and humans. If there really was an omnipotent and omniscient person, then that person could have brought about all life on earth in an instant. Most importantly, doing so would have bypassed hundreds of millions of years of animals suffering and dying from disease and parasites and predation and injury. A huge amount of animal suffering was involved in the natural process of evolution, so a perfectly morally good person clearly would NOT have used evolution to produce human bodies when there was a much better solution ready at hand: create plants, animals, and humans instantly, as in the book of Genesis. So, it seems clear to me that contrary to Swinburne’s view, (e3) does not provide evidence in support of the existence of God, even assuming (e3) to be true.

But there is a deeper problem here than just the inductive inference from (e3) to (g). What do we need to know in order to determine that (e3) is true? I think we have to know, or have good reasons to believe, that the theory of evolution is true, and I think we have to know, or have good reasons to believe that the Big Bang theory of the universe is true. What do we need to know in order to determine that the theory of evolution is true and that the Big Bang theory is true? I think we need to know at least a little about: chemistry, biology, physics, paleontology, geology, cosmology, and astronomy. We might not need to be experts in any of these scientific fields, but we need to have some grasp of some key facts, concepts, and theories in these areas of knowledge.

Furthermore, since the theory of evolution has been generally opposed by many Christian and Muslim religious believers, we need to have given some consideration to the problem of the apparent conflict between science and religion. For example, if the Pope were to declare that evolution is a false theory, would that be a sufficient reason to reject this theory, even given all of the scientific evidence we have supports the theory? What if the Bible clearly teaches that God created the world 6,000 years ago, is that sufficient reason to reject the theories and findings of geology and astronomy that indicate the age of the earth to be billions of years? Unless one has done some thinking about science vs. religion, I don’t see how one can be fully justified in believing the theory of evolution. In sum, to have a justified belief in the theory of evolution and the Big Bang theory, one must have a bit of knowledge about the history and philosophy of science, in addition to knowing a good deal of scientific facts, concepts, and theories from several scientific disciplines.

OK. Here is the big problem. In order to know that (e3) is true, one must have a good deal of knowledge about science and about a number of important scientific disciplines, including a good deal of basic facts, concepts, and theories from a variety of scientific disciplines. This means that the background knowledge that is in play in evaluating this third argument has grown exponentially. A large portion of human knowledge has been pulled back into the picture, and Swinbure has *completely lost control of the flow of data*. Because of the significant amount of empirical facts, concepts, and theories that are required to determine whether (e3) is true, it is difficult to distinguish between such a sizable collection of information and knowledge and our normal everyday background knowledge.

One very important implication of this is that the problem of evil has itself been pulled back into the picture. Knowing that the theory of evolution is true involves knowing that there has been hundreds of millions of years of animal suffering from disease, injury, parasites, and predation. Swinburne’s strategy was to put off the problem of evil until after several empirical facts that favor the existence of God had been put forward one at a time, and the probability of the existence of God had been bumped upward several times. But since the problem of evil has come rushing back in with just the third argument, it is no longer clear whether his logical strategy can work. At any rate, the problem of evil cannot be dealt with after three or four more factual claims have been put forward in support of God’s existence. The problem of evil must be faced as part of the consideration of the significance of (e3).

*bookmark_border*The Carrier-Barnes Exchange on Fine-Tuning

Reader GGDFan77 asked me for my thoughts on the exchange between Dr. Richard Carrier, who I respect and consider a friend, and Dr. Luke Barnes regarding fine-tuning arguments. I initially responded in a series of comments in the combox for my post about Hugh Ross’s estimates for the probability of life-permitting prebiotic conditions. But those turned out to be so lengthy that I think the topic deserves its own dedicated post.

Here’s some brief context for readers not familiar with the exchanges between Dr. Richard Carrier and Dr. Luke Barnes:

* Dr. Carrier wrote an essay, “Neither Life Nor the Universe Appear Intelligently Designed,” in *The End of Christianity* (ed. John Loftus, Buffalo: Prometheus Books, 2011), pp. 279-304.

* Dr. Barnes wrote a four part series on his blog critiquing that essay by Carrier.

* Dr. Carrier and Dr. Barnes had an extensive back-and-forth exchange in the combox on Carrier’s blog.

Let me preface my comments by saying that I have a lot of empathy for any writer, including Dr. Carrier, who is trying to use the formal apparatus of Bayes’ theorem in a way that is accessible to a beginning-to-intermediate audience, which I take to be the target audience of *The End of Christianity.* If you go for too much precision and formalism, you risk losing your audience. If you focus too much on accessibility, you risk misunderstandings, oversimplifications, and outright errors. Finding the right balance isn’t easy.

## Part 1

With all due respect to Dr. Carrier, I find part 1 of Dr. Barnes’ critique to be very persuasive and, in fact, to be a prima facie *devastating* critique. (I quickly skimmed the combox on Dr. Carrier’s site to see if they debated anything relevant to part 1, but I didn’t find anything, so it appears that the points in part 1 of Dr. Barnes’ series have gone unchallenged by Dr. Carrier.)

In particular, I agree with the following points by Dr. Barnes.

- “Bayes’ theorem, as the name suggests, is a theorem, not an argument, and certainly not a definition.”
- “Also, Carrier seems to be saying that P(h|b), P(~h|b), P(e|h.b), and P(e|~h.b) are the premises from which one formally proves Bayes’ theorem. This fails to understand the difference between the derivation of a theorem and the terms in an equation.”
- “Crucial to this approach is the idea of a reference class – exactly what things should we group together as A-like? This is the Achilles heel of finite frequentism.”
- “It gets even worse if our reference class is too narrow.”
- “This is related to the ‘problem of the single case’. The restriction to known, actual events creates an obvious problem for the study of unique events.”
- “Carrier completely abandons finite frequentism when he comes to discuss the multiverse.”
- “Whatever interpretation of probability that Carrier is applying to the multiverse, it isn’t the same one that he applies to fine-tuning.”
- “If we are using Bayes’ theorem, the likelihood of each hypothesis is extremely relevant.”

In addition, I would add the following comment.

- In his essay, Carrier writes: “Probability measures frequency (whether of things happening or of things being true).” Not exactly. The
*frequentist interpretation of probability*measures relative frequency, but the*frequentist interpretation of**probability*isn’t the only interpretation of probability. There are “many other games in town” besides that one; there is also the*epistemic interpretation of probability*(aka “subjective” aka “personal” aka “Bayesian”), which measures degree of belief. Thus, to say that probability just is relative frequency is to beg the question against all the rival interpretations of probability. (And, for the record, I’m actually a pluralist when it comes to probability; following Gillies, I think different interpretations can be used in different situations.)

## Part 2

Here are my thoughts on Part 2 of Dr. Barnes’ reply.

This simulation tells us nothing about how actual cars are produced.

I strongly agree.

The fact that we can imagine every possible arrangement of metal and plastic does not mean that every actual car is constructed merely at random.

I agree.

Note a few leaps that Carrier makes. He leaps from bits in a computer to actual universes that contain conscious observers. He leaps from simulating every possible universe to producing universes “merely at random”.

I agree.

This is a textbook example of affirming the consequent, a “training wheels” level logical fallacy.”

I think this is an uncharitable interpretation of Carrier’s statements by Barnes.

False. Obviously False.

I disagree with Barnes. Here is the passage by Carrier which Barnes is referring to.

It simply follows that if we exist and the universe is entirely a product of random chance (and not NID), then the probability that we would observe the kind of universe we do is 100 percent expected.

Let’s abbreviate the statement “we exist” as B (for our background knowledge); the statement “the universe is entirely a product of random chance (and not NID)” as C (for chance); and the statement “we observe the kind of universe we do” as E (for evidence). Then we can abbreviate the paragraph just quoted as:

Pr-L(E | B & C) = 1, where Pr-L represents a

logicalprobability.

It seems to me that Carrier is correct. Contrary to what Barnes writes, however, it doesn’t follow that we can’t conclude it is highly probable someone was cheating in a game of poker. It just means that the correct way to show that cheating took place is not to use an argument analogous to the argument Carrier is refuting.

Aside: Reading the exchange between Carrier and Barnes reminds me of one of my wishes for people who use Bayes’ Theorem in this way: I really wish people would explicitly state the propositions they are including in their background knowledge. It avoids misunderstandings and misinterpretations.

Carrier says that “if the evidence looks exactly the same on either hypothesis, there is no logical sense in which we can say the evidence is more likely on either hypothesis”. Nope. Repeat after me: the probability of what is observed varies as a function of the hypothesis. That’s the whole point of Bayes theorem.”

I think Barnes is being uncharitable to Carrier. When Carrier writes, “the evidence looks the same,” I interpret him to mean “when the evidence is *equally likely* on either hypothesis.”

All that follows from the anthropic principle…

I need to study this section in detail, but I think agree with Barnes.

I would add the following. In his essay, Carrier writes this:

Would any of those conscious observers be right in concluding that their universe was intelligently designed to produce them? No. Not even one of them would be.

It would be most helpful if Carrier would explicitly defend this statement: “No. Not even one of them would be.” Unless I’ve misunderstood his argument, I think this is false. If we include in our background knowledge the fact that Carrier’s hypothetical conscious observers exist in a universe we know is the result of a random simulation, then we already know their universe is the result of a random simulation. Facts about the relative frequency aren’t even needed: we know the universe is the result of a random simulation.

If, however, we exclude that from our background knowledge, so that we are in the same epistemic situation as the hypothetical observers, then things are not so easy. Again, it would be helpful if Carrier could spell out his reasoning here.

## Part 3

Let’s move onto Part 3 of Barnes’s reply.

“Refuted by scientists again and again”. What, in the peer-reviewed scientific literature? I’ve published a review of the scientific literature, 200+ papers, and I can only think of a handful that oppose this conclusion, and piles and piles that support it.

I think Dr. Carrier absolutely has to respond to this point by Dr. Barnes or publicly issue a retraction.

With regards to the claim that “the fundamental constants and quantities of nature must fall into an incomprehensibly narrow life-permitting range”, the weight of the peer-reviewed scientific literature is overwhelmingly with Craig. (If you disagree, start citing papers).

This strikes me as a *devastating* reply. Like the last point, I think Dr. Carrier absolutely has to respond or else issue a retraction.

He can only get his “narrow range” by varying one single constant”. Wrong. The very thing that got this field started was physicists noting coincidences between a number of constants and the requirements of life. Only a handful of the 200+ scientific papers in this field vary only one variable. Read this.

Ouch. Same as the last two points.

“1 in 8 and 1 in 4: see Victor Stenger”. If Carrier is referring to Stenger’s program MonkeyGod, then he’s kidding himself.

I haven’t studied MonkeyGod enough to have an opinion, so I have no comment on this one.

In all the possible universes we have explored, we have found that a tiny fraction would permit the existence of intelligent life. There are other possible universes,that we haven’t explored. This is only relevant if we have some reason to believe that the trend we have observed until now will be miraculously reversed just beyond the horizon of what we have explored.

If I understand Dr. Barnes’ point correctly here, then I think he is making a simple appeal to *induction by enumeration* and I think his argument is logically correct.

In fact, by beginning in our universe, known to be life-permitting, we have biased our search in favour of finding life-permitting universes.

I find this point very interesting. I hadn’t even thought of it that way, but I think he’s right.

Nope. For a given possible universe, we specify the physics. So we know that there are no other constants and variables. A universe with other constants would be a different universe.

I *think* I agree with this.

How does a historian come to think that he can crown a theory “the most popular going theory in cosmological physics today” without giving a reference? He has no authority on cosmology – no training, to expertise, no publications, and a growing pile of physics blunders.

Ouch.

In any case, the claim is wrong…

I don’t have the physics expertise to evaluate this paragraph.

By what criteria is that the simplest entity imaginable? If the point is lawless, why does it evolve into something else? How does it evolve? What evolves? What defines the state space? If it is a singular point, how are there now many spacetime points? Why are they arranged in a smooth manifold? Why spacetime? What if space and time aren’t fundamental? It’s not clear that a lawless physical state makes any sense. Even if it does, if it’s lawless, why do we observe a law-like universe?

Good questions.

Fine-tuning doesn’t claim that this universe has the maximum amount of life per unit volume (or baryon, or whatever). So this argument is irrelevant.

Dr. Barnes is, of course, correct that fine-tuning doesn’t *logically entail* that this universe has the maximum amount of life per unit volume, in the sense that “fine-tuning” is logically compatible with “the universe NOT having the maximum amount of life per unit volume.” But I disagree with Dr. Barnes that the hostility of life is irrelevant. In fact, as I’ve argued before, focusing only on facts about “fine-tuning” while ignoring facts about “course-tuning” (i.e., the hostility of the universe to life) commits the logical fallacy of understated evidence.

## Part 4

Let’s move onto part 4 of Dr. Barnes’ reply. Barnes writes:

What is Carrier’s main argument in response to fine-tuning, in his article “Neither Life nor the Universe Appear Intelligently Designed”? He kept accusing me of misrepresenting him, but never clarified his argument.

I agree.

Bayes’ theorem follows from Cox’s theorem, which assumes only some reasonable desiderata of reasoning.

I haven’t studied Cox’s theorem, so I can’t comment on that directly. Instead, I want to point out that Bayes’s theorem *also* follows from the Kolmogorov axioms of the probability calculus plus the definition of conditional probability.

A given proposition

can play the role of “background” or “evidence”, depending on the term.K_{i}

I agree.

Talking about “

theprior” or “thelikelihood” in such a context is ambiguous. Better to use notation.

I strongly agree.

Look closely at p(o | ~NID.b’). This is the probability that a universe with intelligent observers exists, given that there is no intelligent cause of their universe, and given background information b’ that does

notimply o. This is exactly the probability that Carrier is afraid of, the one that could equal an “” (pg. 293). It is the probability that “the universe we observe would exist by chance” (pg. 293). Carrier argues that this term is irrelevant because ignores o. It does, butungodly percentage. The posterior does not ignore o. Look at Bayes’ theorem: p(H|EB) = p(E|HB) p(H|B) /p(E|B). Both E and B are known, and yet the likelihood p(E|HB) just ignores the fact that we know E! Rightly so! This is the whole point of Bayes’ theorem.rightly so

1. Here I think Dr. Barnes is being just a tad snarky (“This is exactly the probability that Carrier is afraid of”).

2. This may be a nitpick, but I wouldn’t word things the way Dr. Barnes does, when he writes that p(o | ~NID.b’) is “the probability that ‘the universe we observe would exist by chance.'” Instead, I would define that probability in plain English as “the probability that intelligent observers exist conditional upon our background knowledge conjoined with the hypothesis that a non-terrestrial intelligent designer did NOT design the universe.” The key difference here is that the latter phrasing keeps the distinction between “the universe we observe” and “intelligent observers exist.”

3. I *strongly* agree with this: “Carrier argues that this term is irrelevant because ignores o. It does, but * rightly so*. The posterior does not ignore o. Look at Bayes’ theorem: p(H|EB) = p(E|HB) p(H|B) /p(E|B). Both E and B are known, and yet the likelihood p(E|HB) just ignores the fact that we know E! Rightly so! “

4. Again, this may be another nitpick but I agree and disagree with this statement: “This is the whole point of Bayes’ theorem.” Not exactly; here I think Dr. Barnes is unwittingly presupposing the epistemic interpretation of Bayes’s theorem. Based on that interpretation, he’s correct. On rival interpretations–such as the frequency interpretation–we wouldn’t talk about knowledge at all, but the relative frequency among some reference class.

Here’s the problem with the argument above. What (3) shows is that, since f follows from o, I need not condition the posterior on f. There is a redundancy in our description of what we know. But that does not mean that the posterior p(NID|f.b) is independent of the “ungodly percentage” p(o | ~NID.b’). The surprising fact on ~NID, that a life-permitting universe universe exists

, cannot hide in the background. We can draw it out. It’s right there in equation (7).at all

I agree. Dr. Barnes is making a very similar point to the one I make below, where I talk about pushing the problem back a step.

There a couple of different versions of NID floating around Carrier’s essay….

I agree with pretty much this entire section of Dr. Barnes’s essay.

Question 5:What mathematician should I read to learn about reference classes and why probabilities measure frequencies? Is Carrier a frequentist or a Bayesian?

Actually, this is a question not best suited for a mathematician, but a *philosopher.* In my opinion, the “go-to” reference books for this question are (1) *Choice & Chance *by Brian Skyrms and (2) *Philosophical Interpretations of Probability* by Gillies.

Question 9:Moving on to Carrier’s scientific claims, there’s some explaining to do.

I think Dr. Carrier must directly answer the questions in the bulleted list that follows.

This time could have been spent

that I am wrong. More time is spent attacking me than defending, or even explaining, his case. Take the comment on January 7, 2014 at 8:43 am. Of 14 sentences: 1 clarification of a previous comment, 2 repetitions of points from his article that I agreed with, 2 claims contrary to mine (hurray! interaction!), and 9 that merely accuse of error and incompetence.showing

I *strongly* agree. I hope that Dr. Carrier will directly respond to Dr. Barnes without the personal attacks.

## Carrier’s Endnote 23

GGDFan777 also asked me to parse endnote 23 of Dr. Carrier’s essay. Unless otherwise indicated, the quotations are from that endnote.

This is undeniable: if only a finely tuned universe can produce life, then by defintion P(FINELY TUNED UNIVERSE | INTELLIGENT OBSERVERS EXIST) = 1, because of (a) the logical fact that “if and only if A, then B” entails “if B, then A” (hence (“if and only if a finely tuned universe, then intelligent observers” entails “if intelligent observers, then a finely tuned universe,” which is strict entailment, hence true regardless of how that fine-tuning came about; by analogy with “if and only if colors exist, then orange is a color” entails “if orange is a color, then colors exist”; note that this is not the fallacy of affirming the consequent because it properly derives from a biconditional), and because of (b) the fact in conditional probability that P(INTELLIGENT OBSERVERS EXIST)=1 (the probability that we are mistaken about intelligent observers existing is zero, a la Descartes, therefore the probability that they exist is 100 percent) and P(A and B) = P(A|B) x Pr(B), and 1 x 1 =1.

I agree.

Collins concedes that if we include in b “everything we know about the world, including our existence,” then P(L | ~God & A LIFE-BEARING UNIVERSE IS OBSERVED) = 100 percent (Collins, “The Teleological Argument,” 207).

I don’t have access to the material by Collins, but I don’t have any reason to doubt that what Carrier says here is correct.

He thus desperately needs to somehow “not count” such known facts. That’s irrational, and he ought to know it’s irrational.

Sigh. I think the statement “desperately needs” is snarky and off-putting. I think these two sentences are uncharitable to Collins, for reasons I will explain below.

He tries anyway (e.g., 241-44), by putting “a life-bearing universe is observed” (his LPU) in e instead of b. But then b still contains “observers exist,” which still entails “a life-bearing universe exists,” and anything entailed by a 100 percent probability has itself a probability of 100 percent (as proven above). In other words, since the probability of observing ~LPU if ~LPU is zero (since if ~LPU, observers won’t exist), it can never be the case that P(LPU|~God.b) < 100 percent as Collins claims (on 207), because if the probability of ~LPU is zero the probability of LPU is 1 (being the converse), and b contains “observers exist,” which entails the probability of ~LPU is zero.

I agree with his analysis, but — you knew there was a “but” coming — I think this misses the point, which seems to be a restatement of the anthropic principle dressed up in the formalism of probability notation. Yes, if we include “(embodied) intelligent observers exist” in our background knowledge (B), then it follows that a life-permitting universe (LPU) exists. But that isn’t very interesting. In one sense, this move simply pushes the problem back a step.

To see why, we can (in a sense) do a Bayesian analysis in reverse. Abstract away everything we know, *including our own existence,* and include in our background knowledge *only* the fact that our universe exists. Based on that fact *alone,* the prior (epistemic) probability of “(embodied) intelligent observers exist” is not 1 on naturalism and it is not 1 on theism.

In the jargon of academic philosophy of religion, the proponent of a fine-tuning argument for theism is asking us to compare the *epistemic* probability–not relative frequency–of a life-existing universe conditional upon theism to the epistemic probability of a life-existing universe conditional upon naturalism. To respond to that argument with “But we exist” misses the point.

The proponent of the fine-tuning argument can, should, and will respond, “No shit, Sherlock. Everyone agrees that we exist. The question is whether the life-permitting preconditions of our universe is evidence relevant to theism and naturalism.”

If (in even

greaterdesperation) Collins tried putting “I think, therefore I am” in e, his conclusion would only be true for people who aren’t observers (since b then contains no observers), and since the probability of there being people who aren’t observers is zero, his calculation would be irrelevant

Again, I find the snark (“*greater* desperation”) off-putting, but let’s put that aside. At the risk of repeating myself, the fact that each of us knows that we exist doesn’t make fine-tuning arguments go away. Yes, we know that our universe is life-permitting *because* we know that we exist. But *why* is our universe life-permitting? Some philosophers (including both theists *and* atheists like Paul Draper) argue that that is evidence favoring theism over naturalism. If they are right, then so be it. But if they are wrong, they are NOT wrong because we exist. That objection just doesn’t work.

(it would be true only for people who don’t exist, i.e., any conclusion that is conditional on “there are no observers” is of no interest to observers).

Dr. Carrier doesn’t speak for all observers. I’m an observer and find the question of interest. So does Paul Draper. So do many atheist philosophers who don’t think fine-tuning arguments work, including Bradley Monton, Keith Parsons, Graham Oppy, Quentin Smith, and so forth. So do many (but not all) theist philosophers. So do many non-philosophers of all stripes. If he doesn’t find the question of interest, that’s fine. But, at risk of stating the obvious, his lack of interest in the argument isn’t a *defeater* for the argument.

*bookmark_border*Swinburne’s Cosmological & Teleological Arguments

I’m not going to try to fully explain and evaluate Swinburne’s Cosmological and Teleological arguments for God here. That would be way too much to tackle in one or two blog posts. There are just a couple of doubts or concerns about these arguments that I would like to express and explore.

Swinburne’s inductive cosmological argument for God has just one premise:

**e. A complex physical universe exists (over a period of time).**

**Therefore:
g. God exists.**

Swinburne argues that e is more likely to be the case if God exists, than if God does NOT exist. From this he concludes that the e represents legitimate inductive evidence for the existence of God; that is to say, the truth of e increases the probability that God exists relative to the

*a priori*probability that God exists, relative to the probability that God exist given only tautological truths (truths of logic and math and analytic conceptual truths) as background knowledge.

If g represents the hypothesis that God exists, and k represents background knowledge consisting only of tautological truths, then Swinburne argues for the following claim:

**1. P(e|g & k) > P(e|k)**

(Read this as asserting: “The probability of e given g and k is GREATER THAN the probability of e given only k.”)

From premise (1), Swinburne infers the following:

**2. P(g|e & k) > P(g|k)**

(Read this as asserting: “The probability of g given e and k is GREATER THAN the probability of g given only k.”)

One objection that has been raised against this argument is that it is not clear that a probability can be reasonably or justifiably assigned to a factual hypothesis given background knowledge consisting in only tautological truths. If “The probability of e given only k” cannot be reasonably or justifiably determined (or estimated), then we are in no position assert that some other probability is greater than (or less than, or equivalent to) “The probability of e given only k”.

The same issue arises with claim (2) that Swinburne infers from claim (1). If “The probability of g given only k” cannot be reasonably or justifiably determined, then we are in no position to assert that some other probability is greater than (or less than, or equivalent to) “The probability of g given only k”.

But this issue with the idea of a probability given only background knowledge consisting of tautological truths is not the concern I wish to explore here. My concern is with the other conditional probabilities in these equations:

**P(e| g & k)**

**P(g| e & k)**

I’m not sure that these probabilities make sense either. My concern is this: Is it possible to know just one contingent fact? Is it possible to know that ‘God exists’ without knowing any other contingent facts? Is it possible to know that ‘A complex physical universe exists (for a period of time)’ without knowing any other contingent facts? If it is not possible to know just one contingent fact, or if it is not possible to know only the contingent fact that ‘God exists’ or to know only the contingent fact that ‘A complex physical universe exists (for a period of time)’, then it appears that we are being asked to conceive of a set of circumstances that is logically impossible.

If it is not possible for a human being to know just one contingent fact, these expressions might still be meaningful and useful as abstractions, as tools of hypothetical reasoning. Arguments typically have just a few premises, and we evaluate arguments by focusing in on these questions: Are each of the premises clear and unambiguous? Are each of the premises true? If all of the premises were true, would the conclusion follow logically? or would the conclusion be made probable assuming the premises were true? Does any of the premises beg the question at issue?

However, if knowing that g is true requires that one knows some other things as well, if knowing g presupposes knowing q, then objections to the knowability of q also work as objections to the knowability of g. So, the epistemological presuppositions of knowing g or of knowing e are relevant to evaluating Swinburne’s cosmological argument.

Suppose I know the fact that I am 5 feet 8 inches tall. Suppose I know that ‘Brad Bowen is 5 feet 8 inches tall’. Can I know just this contingent fact and no other contingent facts? Let’s think about this for a bit. I must understand that the name ‘Brad Bowen’ refers to a specific person, a specific human being, and that the measurement here relates to the size of the human body that belongs to a specific human being. I suppose that all of this could be taken as conceptual knowledge, as knowledge involved in simply understanding the meanings of the words and phrases in the sentence ‘Brad Bowen is 5 feet 8 inches tall’.

To have a clear and correct understanding of this sentence, I must also know that while many animals walk on four legs, human beings walk on two legs and use their arms for other purposes. Thus, the height of a human being is not measured when the person is on his or her hands and knees. Also, height at least for human beings, is measured when the person is standing, not when the person is horizontal, as when the person is sleeping. I should also know that rulers or yardsticks or measuring tapes are used for measuring the height of humans. This assumes that there are physical substances that are fairly stable in their length. Rulers and yardsticks don’t generally grow or shrink large amounts in short periods of time. A ruler that is 12 inches this morning is not likely to be 24 inches this evening. A yardstick that is 36 inches today is not likely to be 25 feet tomorrow. Furthermore, human height is significant and relevant in part because it is relatively stable, at least for periods of days and weeks. I was only about two feet tall when I was born, was about four feet tall when in elementary school, and was over five feet tall in high school. People usually get taller rapidly as young children and teenagers, and then their growth in height slows, and height is stable for many years.

As you can see, there is a fair amount of background knowledge involved in knowing the fact that ‘Brad Bowen is 5 feet 8 inches tall’. Some of that knowledge is conceptual/linguistic knowledge, but some of the knowledge mentioned above is contingent factual knowledge about the world and about human beings. If such an apparently simple and innocuous fact as this requires a good deal of background knowledge in order to clearly and fully understand and know the fact to be true, then I suspect that a deep philosophical claim like ‘God exists’ or ‘A complex physical universe exists’ also requires a significant amount of background knowledge to clearly and fully understand that claim.

To be continued…