The Argument from the Biological Role of Pain and Pleasure

Here is a formal statement of the "argument from the biological role of pain and pleasure," as formulated by agnostic philosopher Paul Draper.

Let ">!" to mean "is much greater than"

HT = hypothesis of theism

HI = hypothesis of indifference: 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 consistent with both metaphysical naturalism and supernaturalism

-- Note that HI and HT are mutually exclusive

Let O = observations of humans and animals experiencing pain and pleasure. O can be broken down into three specific observations:

O1 = moral agents experiencing pain or pleasure we know to be biologically useful

O2 = sentient beings that are not moral agents experiencing pain or pleasure that we know to be biologically useful

O3 = sentient beings experiencing pain or pleasure that we do not know to be biologically useful

O is equivalent to O1 &  O2 & O3.

Let h refer to any generic hypothesis.

Pr(O/h) = Pr(O1 & O2 & O3/h)= Pr(O1/h) x Pr(O2/O1 & h) x Pr(O3/O1 & O2 & h)

So, it follows that:

Pr(O/HI) = Pr(O1/HI) x Pr(O2/O1 & HI) x Pr(O3/O1 & O2 & HI)
Pr(O/HT) = Pr(O1/HT) x Pr(O2/O1 & HT) x Pr(O3/O1 & O2 & HT)

In order to show that Pr(O/HI) >! Pr(O/HT), we can show that each of the terms on the right hand side of equation A is greater or even much greater than each of the corresponding terms on the right hand side of equation B.

(1) Pr(O1/HI) >! Pr(O1/HT)
(2) Pr(O2/HI & O1) > Pr(O2/HT & O1)
(3) Pr(O3/HI & O1 & O2) >! Pr(O3/HT & O1 & O2)
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(4) Therefore, Pr(O/HI) >! Pr(O/HT). (from 1, 2, and 3)
(5) O is known to be true.
(6) HT is not much more probably intrinsically than HI.
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(7) Therefore, other evidence held equal, HT is probably false.

Note that while the above argument implies that we have a good prima facie reason to believe that HT is probably false (since HT and HI are incompatible), it does not imply that we have a good prima facie reason to believe that HI is true (since HT and HI are not jointly exhaustive and so could both be improbable). So the argument from the biological role of pain and pleasure could be more accurately described as an argument against HT than as an argument for HI, though of course in some sense it is both.