bookmark_borderIndex: Draper’s Evidential Argument from Pain and Pleasure

The purpose of this page is to provide an index for my blog series on Paul Draper’s classic 1989 article defending an evidential argument from evil which focuses on the biological role (and apparent moral randomness) of pain and pleasure.

  • Part 1: summarizes key terminology for the argument, as well as the argument itself.
  • Part 2: summarizes the first part of Draper’s argument, which purports to show that facts about pain and pleasure are more probable on the hypothesis of indifference (HI) than on theism (T).
  • Part 3: summarizes Draper’s refutation of three theodicies which might be used to defeat the first half of his argument
  • Part 4: summarizes Draper’s own views on the evidential significance of his argument, as well as reasons for thinking it will be very difficult for theists to offset the evidence about pain and pleasure.

See also:

bookmark_borderDraper on Pain and Pleasure: Part 4

This post is part of a series on Paul Draper’s classic version of the evidential argument from evil. In the previous entry, I summarized Draper’s refutation of three theodicies which might be used as an objection to the claim that HI explains the facts about the biological role of pain and pleasure much better than T does. In this post, I’m going to review the final section of Draper’s classic 1989 article on the evidential argument from evil.
1. Darwin’s Argument from Evil
In the final section of his paper, Draper sets up an analogy between Darwin’s evidential argument against special creationism and Draper’s evidential argument against theism. It is worth quoting Draper’s remarks about Darwin’s argument in full.

“Darwin argued that his theory of the evolution of species by means of natural selection explains numerous facts (e.g., the geographical distribution of species and the existence of atrophied organs in animals) much better than the alternative hypothesis that each species of plant and animal was independently created by God. (Let us call this latter hypothesis “special creationism.”) Darwin’s results were significant partly because special creationists at Darwin’s time did not have nor were they able to obtain evidence favoring special creationism over evolution theory that outweighed or at least offset Darwin’s evidence favoring evolution theory over special creationism. For this reason, many theists, while continuing to believe in creationism, which is consistent with Darwin’s theory, rejected special creationism. And those theists who were familiar with Darwin’s arguments and yet remained special creationists did so at a cost: their belief in special creationism was no longer an epistemically rational one.”

Draper says that the significance of his evidential argument from evil is to be determined in an analogous way, viz., it depends upon whether theists have evidence favoring T over HI, evidence which could offset his evidence O favoring HI over T. (N.B. Draper points out this evidence could be propositional evidence, non-propositional evidence, or both.) If a theist confronted with his argument lacks and cannot find such offsetting evidence, Draper argues, the theist “cannot rationally continue to believe that theism is true.”
2. Prospects for Theistic Offsetting Evidence
Draper then offers four reasons for doubting the theist will be able to find such offsetting evidence. It is interesting to compare those reasons (offered in 1989) with the positions Draper has adopted later in his career.
(1) In his 1989 paper, Draper claims that it is “doubtful that it could be shown that HI is ad hoc or that T is intrinsically more probable than HI.” It is noteworthy that, long after his 1989 paper, Draper finally started developing his new theory of epistemic probability. When that theory of epistemic probability is applied to HI and T, it yields the result that the intrinsic probability of HI is significantly greater than T.
(2) Next, Draper argued in 1989 that “Traditional and contemporary arguments for theism are far from compelling.” Since 1989, Draper has gone on record as stating that several facts are evidence favoring T over naturalism (which entails HI). Indeed, he even published a paper arguing that the argument from moral agency is “in the same league” as his evidential argument from evil. But Draper also usefully identified a new fallacy of inductive reasoning he calls the “fallacy of understated evidence.” According to Draper, many (most?) evidential arguments for theism, including his own argument from moral agency, commit the fallacy of understated evidence.
(3) Draper’s third reason (in 1989) for thinking that the theist’s search for offsetting evidence will be difficult is this.

Many traditional and contemporary arguments for theism … may not solve the theist’s position even if they are sound and recognized by the theist to be so. For they at most purport to show that an omnipotent and omniscient being exists–not that the being is morally perfect.”

This point seems (to this writer) as true in 2014 as it was in 1989.
(4) Finally, Draper argues (in 1989) that religious experience doesn’t solve the problem identified in (3): “Religious experience is ambiguous with respect to the moral attributes of the creator.” Furthermore, he notes that theistic justification derived from theistic experiences is offset by atheistic justification derived from “experiences of indifference.” Not only is this yet another example of the fallacy of understated evidence, but Draper wrote an article in 1992 on the evidential value of religious experience. In that article, Draper concluded that three specific facts about religious experience favor atheism over T.

bookmark_borderDraper on Pain and Pleasure: Part 3

This post is part of a series on Paul Draper’s classic version of the evidential argument from evil. In the previous entry, I summarized Draper’s first argument, which attempts to show that certain facts about the types, quantity, and distribution of pain and pleasure (P&P) are much more probable on the hypothesis of indifference (HI) than on theism (T), and so constitute strong evidence against T and for HI. In this entry, I summarize Draper’s discussion of theistic explanations for those facts.

I apologize for the size of the text in my graphics. If you find it hard to read, you should be able to see the graphics at “full size” by clicking on them one-at-a-time in your browser window.
1. “Theodicies” and Theistic Explanations for Facts about Good and Evil
As Draper observes, “Explaining some phenomenon in terms of a statement usually involves adding other statements to that statement.” The relevance to the problem of evil is obvious: people who offer a theistic explanation for facts about good and evil add to T (the proposition that God exists) some additional statement Tn (the proposition that God must allow certain evils in order to achieve some goal).In the philosophy of religion, such additional statements are called “theodicies.” In inductive logic, additional statements of this sort are generically called ‘auxiliary hypotheses.’ In Draper’s terminology, he refers to them as “expansions.”

expansion statement: “a statement h* is an ‘expansion’ of a statement h just in case h* is known to entail h. (Notice that h* can be an expansion of h even if it is logically equivalent to h.)”

With this in mind, consider’s the second part of Draper’s evidential argument from evil again.

A. O is known to be true.
B. T is not much more probable intrinsically than HI.
C. Pr(O/HI) >! Pr(O/T).
So, D. Other evidence held equal, T is probably false.

Draper argues that if a theodicy is to successfully defeat an argument from evil against theism, it must somehow undermine premise (C) by raising the value of Pr(O / T). In order to evaluate whether an expansion Tn of theism raises Pr(O / T) enough to defeat (C), Draper proposes that we use the “Weighted Average Principle” (WAP):
Pr(O / T) = Pr(O / Tn) x Pr(Tn / T) + Pr(O / ~Tn) x Pr(~Tn / T).
As Draper points out, this formula is an average because Pr(Tn / T) + Pr(~Tn / T) = 1. It is not a simple straight average, however, since those two values may not equal 1/2; that is why it is a weighted average. The higher Pr(Tn / T), the closer Pr(O / T) will be to Pr(O / Tn & T); similarly, the higher Pr(~Tn / T), the closer Pr(O / T) will be to Pr(O / T & ~Tn).
Draper states that the second part of his evidential argument from evil assumes that theodicies do not “significantly raise” Pr(O / T) and so the argument effectively treats Pr(O / T) as roughly equal with Pr(O / T & ~Tn). In order to show that this assumption is justified, he says he needs to show that Pr(O / Tn) is “not significantly greater” than Pr(O / T & ~Tn). As he puts it:

In other words, I would need to show that, independent of the observations and testimony O reports, we have little or no more reason on Tn than we have on theism ~Tn to believe that O is true.

In his 1989 article, Draper considers three theodicies:
T1: The Free Will Theodicy, version 1;
T2: The Free Will Theodicy, version 2; and
T3: The Human Ignorance Theodicy.
(Note that while the T1 – T3 notation is Draper’s, the titles of T1 – T3 are mine.)
Before we can discuss T1 and T2, we first need to define a key term:

freedom*: “An action is free* only if
(i) it is free in an incompatibilist sense–that is, in a sense incompatible with its being determined by antecedent conditions outside the agent’s control–and
(ii) if it is morally right, then at least one alternative action that is open in an incompatibilist sense to the agent is such that it would be morally wrong for the agent to perform that alternative action.”

Both T1 and T2 agree that God endows humans with freedom*. They offer contradictory explanations for the existence of pain, however. According to T1, “God permits pain in order to advance morality.” In contrast, T2 explains pain by adding to T a statement about how one of God’s goals is to “increase the responsibility humans have for their own well-being and the well-being of others and thereby increase the importance of the moral decisions humans make.”
Let’s turn to Draper’s objections to each of these expansions of T.
2. “Free Will and the Advancement of Morality”
Let T1 stand for the following expansion of T:

God exists, and one of his final ends is a favorable balance of freely* performed right actions over wrong actions.

Draper begins his response to T1 by making a very charitable concession to the theodicist. He grants, for the sake of argument, that Pr(T1 / T) is high. In order to defend (C) against T1, his strategy instead is to show that:

Pr(T1 / T) is not much greater than Pr(O / T & ~T1).

I interpret Draper’s 1989 article as offering two reasons to believe that.
First, Draper argues that T1 provides a reason we do not have on T & ~T1 to expect that “the world will contain both pain that influences humans to perfom morally right action and pain that is logically necessary for some of the right actions humans perform.” As Draper points out, “O reports the existence of pain of both these sorts,” so those predictions of T1 are confirmed.
But O also reports other facts which T1 predicts should not be true. O also reports both:
(a) that pain often influences humans to perform morally wrong actions; and
(b) that pain is logically necessary for many of the wrong actions humans perform.
Draper concludes that the combination of (a) & (b) is more surprising on the assumption that T1 is true than on the assumption that T is true and T1 is false.
Second, Draper argues that “the world does not contain a very impressive balance of right over wrong actions performed by humans and that this is due in part both to a variety of demoralizing conditions like illness, poverty, and ignorance, and to the absence of conditions that tend to promote morality.” He concludes, accordingly, that this (balance of right over wrong actions) is more surprising on the assumption that T1 is true than on the assumption that T is true and T1 is false.
APP-T1
3. “Free Will and Responsibility”
Let T2 stand for the following expansion of T:

T2: God exists, and one of His final ends is for humans to have the freedom* to make very important moral decisions.

Again, Draper assumes for the sake of argument that the antecedent probability of this theodicy is high, viz., Pr(T2 / T) is high. Again, his strategy is to show:

Pr(O / T2) is not >! Pr(O / T & ~T2)

Draper points out that, “assuming there is no better way,” T2 may provide us with a reason that we do not have on T & ~T2 to expect “the existence of pain for which humans are morally responsible.” But, he argues, Pr(O / T2) is not >! Pr(O / T & ~T2) since other facts O reports are even more surprising on T2 than they are on T & ~T2.
First, “Many humans are plainly not worthy of the freedom* to do serious evils.” On the assumption that T2 is true, however, we would predict that humans would only be given great responsibility when they are worthy of it.
Second, “Nor is the human race making any significant amount of moral progress.” If T2 were true, however, we would expect that humans would be “benefitted by having such responsibility.”
Third, there have been (and are) humans who had (or have) great responsibility, who have abused that responsibility, and did not have their responsibility decreased by God “until they are worthy of a second chance.” But if T2 were true, that is what we would expect.
Draper concludes, accordingly, that Pr(O / T2) is not significantly greater than Pr(O / T & ~T2).
APP-T2
4. The Human Ignorance Theodicy
Here is T3:

T3: God exists and has a vast amount of knowledge about good and evil and how they are related that humans do not have.

Unlike T1 and T2 where Draper granted for the sake of argument that they were antecedently very probable on T, Draper does not make such a concession for T3. It isn’t necessary. As Draper correctly states, Pr(T3 / T) = 1. This, in turn, entails that Pr(O / T) = Pr(O / T3).
But, as Draper argues, T3 fails to defeat O because

We have no more antecedent reason to expect that [God’s additional knowledge is such that he would permit any of the facts O reports to obtain], than to expect that God would have unknown reasons for preventing evil.

Observant readers will notice that the sentence just quoted just is an application of WAP to the idea that God has unknown reasons for his actions.
Furthermore, however much reason we might have on T3 to expect humans would be “unable to product a plausible theistic explanation” for the facts O reports, we have “even more reason” on  HI to expect this. Thus, T3 does not significantly raise the value of Pr(O / T).
APP-T3

bookmark_borderDraper on Pain and Pleasure: Part 2

This post is part of a series on Paul Draper’s classic version of the evidential argument from evil. In the previous entry, I explained Draper’s terminology and summarized the logical form of Draper’s two arguments. In this entry, I focus on Draper’s first argument, which attempts to show that known facts about the biological role of pain and pleasure are much more probable on the hypothesis of indifference than on the hypothesis of theism.
1. Background Knowledge
Like all abductive arguments, background knowledge plays a crucial role in Draper’s evidential argument from evil. Draper’s formulation suppresses reference to background knowledge, i.e., his probability notation does not explicitly contain a symbol to represent the propositions which constitute the relevant background knowledge. In the interest of clarity, however, I’m going to reformulate Draper’s argument so as to explicitly identify the role of those propositions. If we let “B” stand for our background knowledge, then Draper’s first argument may be restated as follows.

(1′) Pr(O1/HI & B) >! Pr(O1/T & B)
(2′) Pr(O2/HI & O1 & B) > Pr(O2/T & O1 & B)
(3′) Pr(O3/HI & O1 & O2 & B) >! Pr(O3/T & O1 & O2 & B)
————————————————————————-
(4′) Therefore, Pr(O/HI & B) >! Pr(O/T & B). (from 1, 2, and 3)

As I interpret him, the following propositions constitute the relevant background knowledge B.
B1: Pain and pleasure, if they exist, have intrinsic moral value.
B2: A physical universe–which operates according to natural laws, is intelligible, and which supports the possibility of intelligent life–exists.
B3: Living things, including sentient beings, exist on Earth. These sentient beings include, but are not limited to, human beings.
B4: Some (Earthly) sentient beings are not moral agents but are biologically very similar to embodied moral agents.
B5: Humans are goal-directed organic systems, composed of parts that systematically contribute to the biological goals of these systems.
2. Draper’s Defense of Premise (1′): Pr(O1 / HI & B) !> Pr(O1 / T & B)
B5 gives us some antecedent reason to expect that pain and pleasure (P&P), if they exist, will also systematically contribute to those goals, just as O1 reports. But, as B1 reports, notice that, unlike other parts of organic systems, P&P have intrinsic moral value: “pain is intrinsically bad and pleasure is intrinsic good.” This difference (hereafter, “moral difference”) between P&P and other organic systems is crucial to Draper’s argument.
First. consider HI. On HI & B, Draper argues this moral difference gives us no reason at all to be surprised by O1. HI entails that, if P&P exist, then they are not the result of “malevolent or benevolent” supernatural persons. Therefore, on HI, the moral difference between P&P and other parts of organic systems provides no reason whatsoever to predict that P&P “will not play the same biological role that other parts of organic systems play.” In other words, blind nature is indifferent to moral value.
Second, consider T. On T & B, Draper argues this moral difference does gives us good reason to predict that O1 is false. T entails that, if P&P exist, God is responsible for their existence. Since God is morally perfect, He would have good reasons for producing pleasure even if it is never biologically useful, and He would not permit pain unless He had, not just a biological reason, but also a morally sufficient reason to do so. Furthermore, since God is omnipotent and omniscient, He could create goal-directed organic systems (including humans) without biologically useful P&P. So T entails both:
(a) that “God does not need biologically useful P&P to produce human goal-directed organic systems;” and
(b) “that, if human P&P exist, then God has good moral reasons for producing them, reasons that … might be inconsistent with P&P contributing to the biological goals of those systems.”
Thus, we have much less antecedent reason on T & B than on HI & B “to be surprised if it turned out that human P&P differed from other parts of organic systems by not systematically contributing to the biological goals of those systems.” In other words, Pr(O1 / HI & B) !> Pr(O1 / T & B).
APP-arg2-1
3. Draper’s Defense of Premise (2′): Pr(O2 / HI & O1 & B) > Pr(O2 / T & O1 & B)
Here is Draper on O2:

O2 reports the observations and testimony reported by O about sentient beings that are not moral agents (e.g., young human children and nonhuman animals) experiencing pain or pleasure that we know to be biologically useful.

Draper’s defense of (2′) is based upon the insight of B4. For the convenience of the reader, I’ll state it again:
B4: Some (Earthly) sentient beings are not moral agents but are biologically very similar to embodied moral agents.
Since O1 implies that moral agents experience biologically useful P&P, HI & O1 & B makes it likely that some sentient beings that are not moral agents will also experience biologically useful P&P. But the corresponding, parallel claim about T is not true: T & O1 & B do not make O2 just as likely HI & O1 & B do. Given T & O1, “we have reasons to believe that God permits the pain O1 reports because it plays some sort of (presently indiscernible) moral role in the lives of the humans that experience it. But the pain O2 reports cannot play such a role, since the subjects of it [hereafter, ‘moral patients’] are not moral agents.”
The distinction between moral agents and moral patients isn’t relevant to Pr(O2 / HI & O1 & B), but it is relevant to Pr(O1 / T & O1 & B). This distinction gives us some reason on T & O1 & B to expect that “the good reasons God has for permitting moral agents to experience pain and pleasure do not apply to moral patients.” This, in turn, gives us some reason to believe that God will not permit such beings to experience pain.
APP-arg2-2
4. Draper’s Defense of Premise (3′): Pr(O3 / HI & O1 & O2 & B) !> Pr(O3 / T & O1 & & O2 & B)
Finally, let’s turn to (3′). Let’s begin by quoting what Draper has to say about O3 and then introduce some more terminology. Here is Draper on O3:

O3 reports facts about sentient beings experiencing pain or pleasure that we do not know to be biologically useful. This includes much pain and pleasure that we know to be biologically gratuitous, as well as some that is not known to be useful and is also not known to be gratuitous.

And here is the terminology.

pathological P&P: P&P that results from the failure of some organic system to function properly, i.e., pain caused by terminal cancer.
biologically appropriate P&P: P&P that occurs in a situation which is such that it is biologically useful that pain or pleasure is felt in situations of that sort.
biologically gratuitous P&P: P&P that occurs in a situation which is such that it is biologically useful that pain or pleasure is felt in situations of this sort, i.e., pain felt by a person killed in a fire is not biologically useful, but it is biologically appropriate because it is biologically useful that humans feel pain when they come in contact with fire.

Let’s move onto Draper’s defense of (3′). He offers a two-part argument in support.
First, he argues, we have much more reason to expect sentient beings, especially nonhuman animals, to be happy given T & O1 & O2 & B than given HI & O1 & O2 & B. Why? We find that many humans and animals experience prolonged and intense suffering and a much greater number are far from happy. Also, we have more reason on T & O1 & O2 & B than on HI & O1 & O2 & B to expect a close connection between moral goods and biologically gratuitous P&P. But we discover no such connection.
Second, Draper observes that we have much more reason on HI & O1 & O2 & B than on T & O1 & O2 & B to believe that the fundamental role of pain and pleasure is biological and that biologically gratuitous P&P is “a biological accident resulting from nature’s or an indifferent creator’s failure to ‘fine tune’ organic systems.” This is supported by O3: much of the P&P reported by O3 is “either pathological or biologically appropriate, while very little is known to be both non-pathological and biologically inappropriate.” “This is exactly what we would expect if P&P are fundamentally biological rather than moral phenomena.”

APP-arg2-3

5. The Deduction of (4′) from (1′) – (3′)
I have saved this section for last since it is uncontroversial. Why is it uncontroversial? Because if (1′) – (3′) are true, (4′) has to be true. This is easier to see graphically, so I’ll start with a graphic and then prove the result.

APP-arg2-5

Here is the proof:
Pr(O / h) = P(O1 & O2 & O3 / h) [logical equivalence]
By the chain rule, we know that Pr(O / h) = Pr(O1 / h) x Pr(O2 / O1 & h) x Pr(O3 / O2 & O1 & h). But, just for fun, let’s derive the chain result anyway.
Let X = O2 & O3 and let Y = O1
Pr(O / h) = Pr(X & Y/ h) [definition of X and Y]
Pr(O / h) = Pr(X / Y & h) x Pr(Y / h) [product rule]
Pr(O / h) = Pr(X / O1 & h) x Pr(O1 / h) [definition of Y]
Pr(O / h) = Pr(O2 & O3 / O1 & h) x Pr(O1 / h) [ definition of X]
Let D = O3 and E = O2
Pr(O / h) = Pr(E & D / O1 & h) x Pr(O1 / h) [definition of D and E]
Pr(O / h) = Pr(D / E & O1 & h) x Pr (E / O1 & h) x Pr(O1 / h) [definition of conditional probability]
Pr(O / h) = Pr (O3 / O2 & O1 & h) x Pr(O2 / O1 & h) x Pr(O1 / h) [definition of D and E]
Pr(O / h) = Pr(O1 / h) x Pr(O2 / O1 & h) x Pr(O3 / O2 & O1 & h)
Using this application of the chain rule, we get:
Pr(O/HI) = Pr(O1/HI) x Pr(O2/O1 & HI) x Pr(O3/O1 & O2 & HI)
Pr(O/T) = Pr(O1/T) x Pr(O2/O1 & T) x Pr(O3/O1 & O2 & T)
At this point it follows axiomatically that Pr(O / HI) >! Pr (O / T) just in case the ratio of each multiplicand on the right-hand side of the equation is greater than one and at least one of those ratios is much greater than one. That is exactly what (1′) – (3′) show:

  • (1′) shows that the first multiplicand for HI is much greater than the first multiplicand for T;
  • (2′) shows that the second multiplicand for HI is greater than the second multiplicand for T; and
  • (3′) shows that the third multiplicand for HI is much greater than the third multiplicand for T.

Thus, if (1′) – (3′) are true, (4′) must be true: Pr(O / HI) must be much greater than Pr(O / T).
 

bookmark_borderDraper on Pain and Pleasure: Part One

The academic journal Nous published an article by Paul Draper in 1989 on the evidential argument from evil. (The article used to be available online for free but is now only available behind a paywall at JSTOR.) The article is now widely regarded as a ‘classic’ in the contemporary literature on the problem of evil; it has been republished in numerous anthologies and readers.
In this part, I’ll summarize the terminology he uses and provide a basic overview of the argument’s logical structure or form. Note that, unless otherwise indicated, all quotations inside quotation marks (“) are quotations of Draper’s article.
1. Terminology, Symbols, and Key Concepts
Before we begin, we need to be clear on how Draper uses the key terminology in his argument.

hypothesis: a proposition which we do not know with certainty to be true or false
theism (T): the hypothesis that “there exists an omnipotent, omniscient, and morally perfect person who created the Universe.”
hypothesis of indifference (HI): the proposition that neither the nature nor the condition of sentient beings on earth results from benevolent or malevolent actions performed by supernatural persons.” Note that HI is logically consistent with both supernaturalism and naturalism. Furthermore, note that HI is logically incompatible with T.
goal-directed: “a system S is ‘goal-directed’ just in case some property G that S has exhibited or will exhibit, a broad range of potential environmental changes are such that:
(i) if they occurred at a time when S is exhibiting G and no compensating changes took place in the parts of S, then S would cease to exhibit G and never exhibit G again,
(ii) if they occurred at t a time when S is exhibiting G, then compensating changes would take place in the parts of S, resulting in either S’s continuing to exhibit G or in S’s exhibiting G once again.”
biological goals: “the goals to which organic systems are directed.”
biologically useful: “a part of some goal-directed organic system S is ‘biologically useful’ just in case:
(i) it causally contributes to one of S’s biological goals (or to one of the biological goals of some other goal-directed organic system of which it is a part), and
(ii) its doing so is not biologically accidental.”
biologically gratuitous: pain and pleasure that is not biologically useful.
O: a statement about “the kinds, amounts, and distribution of pain and pleasure in the world.” O is the conjunction (combination) of the following statements:
O1: a statement about facts about “moral agents experiencing pain or pleasure that we know to be biologically useful;”
O2: a statement about facts about “sentient beings that are not moral agents experiencing pain or pleasure that we know to be biologically useful;” and
O3: a statement about facts about “sentient beings experiencing pain or pleasure that we do not know to be biologically useful.”
“>!”: much greater than
epistemic probability: “Relative to K, p is epistemically more probable than Q, where K is an epistemic situation and p and q are propositions, just in case any fully rational person in K would have a higher degree of belief in p than in q.” Note that epistemic probabilities can “vary from person to person and from time to time, since different persons can be in different epistemic situations at the same time and the same person can be in different epistemic situations at different times.”
Pr(x): the epistemic probability of X.
Pr(x | y): the epistemic probability of x conditional upon y, viz., the epistemic probability that proposition X is true, on the assumption that proposition y is true.

2. The Argument’s Logical Structure 
Draper’s 1989 classic article really has two arguments, which I will summarize in reverse order. The second argument is his evidential argument from evil. That argument is the argument where he argues that the biological role of pain and pleasure is prima facie evidence against theism. Draper did not explicitly state the logical form of his argument in his 1989 article, but he did in a later article. He states the argument as follows.

A. O is known to be true.
B. T is not much more probable intrinsically than HI.
C. Pr(O/HI) >! Pr(O/T).
So, D. Other evidence held equal, T is probably false.

APP-arg2
Note that while the above argument implies that we have a good prima facie reason to believe that T is probably false (since T and HI are incompatible), it does not imply that we have a good prima facie reason to believe that HI is true (since T and HI are not jointly exhaustive and so both could be improbable). So the argument from the biological role of pain and pleasure could be more accurately described as an argument against T than as an argument for HI, though of course in some sense it is both.
Let’s turn, then, to Draper’s first argument. Draper’s first argument, which was the focus of his 1989 article, is his argument for the truth of C. Since O is logically equivalent to O1 & O2 & O3, Draper observes that we can use the chain rule to measure the evidential impact of O upon any generic hypothesis h:
Pr(O/h) = Pr(O1 & O2 & O3/h)= Pr(O1/h) x Pr(O2/O1 & h) x Pr(O3/O1 & O2 & h)
By substituting h with “HI” and “T” we get the following statements, respectively:
(a) Pr(O/HI) = Pr(O1/HI) x Pr(O2/O1 & HI) x Pr(O3/O1 & O2 & HI)
(b) Pr(O/T) = Pr(O1/T) x Pr(O2/O1 & T) x Pr(O3/O1 & O2 & T)
Draper’s strategy for showing that Pr(O / HI) is much greater than Pr(O / T) is to show that “each of the multiplicands” on the right-hand side of (a) is “either greater or much greater than the corresponding multiplicand” of (b). Thus, his first argument goes like this.

(1) Pr(O1/HI) >! Pr(O1/T)
(2) Pr(O2/HI & O1) > Pr(O2/T & O1)
(3) Pr(O3/HI & O1 & O2) >! Pr(O3/T & O1 & O2)
————————————————————————-
(4) Therefore, Pr(O/HI) >! Pr(O/T). (from 1, 2, and 3)

APP-arg1
Obviously, to make both arguments in any way compelling, Draper needs to support the premises of both arguments. We’ll look at the support for those premises in future posts.