Peter van Inwagen claims that some versions of the problem of evil rely on the claim that either every evil is necessary for God's purposes or God does not exist. Let's call this the standard claim.Footnote ¹ This claim assumes that there must be some minimum amount of evil sufficient for God's purposes. Peter van Inwagen rejects this assumption and argues for what has been called the no-minimum claim.

• The no-minimum claim

• For any amount of pain and suffering which serves God's purposes there is some lesser amount of pain and suffering that also would serve God's purposes.Footnote ²

Jeff Jordan argues that the no-minimum claim is either false or implausible depending on how we choose to quantify over pain and suffering.Footnote ³ Jordan presents a trilemma that begins by identifying the three ways in which we might quantify over pain and suffering. Jordan defines those ways as follows:

• The Benthamite assumption

• Pain and suffering can be individuated into units measurable by the whole numbers.

• The eleatic assumption

• Pain and suffering can be individuated into units measurable by the real numbers.

• The ordinal assumption

• Pain and suffering comes not in discreet units but in unindividuated amounts, that only an ordinal scale and not an interval scale is possible with pain and suffering.Footnote ⁴

We can formalize Jordan's argument using these three assumptions as follows:

1. (1) The no-minimum claim can only quantify evil according to, either:

   1. (i) The Benthamite assumption,

   2. (ii) The eleatic assumption, or

   3. (iii) The ordinal assumption.

2. (2) If the no-minimum claim quantifies evil according to the Benthamite assumption, then the no-minimum principle is false.

3. (3) If the no-minimum claim quantifies evil according to the eleatic assumption, then it is implausible.

4. (4) If the no-minimum claim quanitifies over evil according to the ordinal assumption, then it is implausible.

5. (5) Therefore, the no-minimum claim is either false, or implausible.

I concede that premise (1) and (2) are true. However, I think we have good reason to reject premises (3) and (4). In the remainder of this paper, I will consider Jordan's defence of premises (3) and (4).

Jordan notes that if the no-minimum claim quantifies over evil according to the eleatic assumption or the ordinal assumption, then the no minimum claim entails that pain and suffering can be divided into smaller and smaller units ad infinitum.Footnote ⁵ Jordan might be willing to concede that we could divide units of pain and suffering in this fashion, however, he argues that it is implausible to suppose that we could do so in a manner that would be detectable by human beings. At some point the changes in the amount of pain and suffering would not be detectable by human beings.

Jordan presents his argument for (3) and (4) quite nicely as follows:

This seems very reasonable. However, the capacity we have for detecting various quantities of pain is a contingent fact about us. Presumably, God could have created us with more fine-grained capacities for detecting quantities of pain and suffering.

However coarse we think the human sensory apparatus is for detecting differences between various quantities of pain and suffering, we could have had a less coarse sensory apparatus. There is no minimum limit to how fine-grained God could have made our apparatus.

If this is true, then we do not yet have good reason to accept premise (3) or (4) of Jordan's argument. When Jordan considers the series of possible worlds where the pain and suffering occurs in lesser degrees, he holds our actual cognitive faculties fixed. However, it seems that in the possible worlds where God creates lesser degrees of evil that suffice for His purposes, He could have given the humans in that world more sensitive cognitive faculties, faculties that could detect these lesser degrees of pain.

It seems that the no-minimum claim is still a viable solution to some versions of the problem of evil.