Heschmeyer has two similar experiments - in both cases an object is dropped and broken. Heschmeyer asks whether the object's owner can forgive the breaker of the object and still demand that the person who broke it clean up the consequent mess. Secondarily, Heschmeyer asks whether someone can pay for the value of the broken item and still demand that the person clean up the wreckage.
There a few critical problems with the experiment.
1) Fairness vs. Forgiveness
Heschmeyer relies throughout on what is "fair" but is simultaneously posing questions in which there is an assumption that forgiveness is taking place. Forgiveness is mercy - it runs in the opposite direction of "fair."
Even if the breaker is really sorry for having broken the item, fairness still demands that the breaker make the breakee whole, restoring what belonged to the breakee and cleaning up the mess resulting from the breakage.
2) Conflation of Dignity and Physical Categories
In fact, whether or not the breaker is really sorry is relevant only to the dignity offense against the breakee. If you spit on someone's shoe, you are doing more than ruining the leather, you are insulting the person. The same occurs (to a lesser extent) when one is negligent with the goods of another. One is showing that one lacks the proper regard for that person and also for God who set your duty to be careful of the goods of others.
When someone apologizes sincerely for harming another, he is attempting to terminate the offense against the dignity of the person whom he has offended. After all, if you break someone's car and then don't apologize, the dignity of the person continues to be harmed by your continued disdain for them as evidence by your lack of contrition.
Another reason to apologize is attempt to bring about reconciliation. In other words, we may apologize in order to attempt to restore friendship between us and the person whom we have offended. If they accept our apology, we can be friends again, otherwise they may continue to be aggrieved at us for the offense we caused.
3) Imposition of Divine Command for Forgiveness on Fairness Structure
We have a divine command that requires us to forgive others. That is our duty toward God, however, not our duty toward the person who has offended us. A person who offends us has no right to demand that we accept their apology. When we apologize to another person, we should do so not insisting that they accept our apology as a matter of our right.
Instead, we are commanded to forgive others as a duty toward God in gratitude of the forgiveness he has given to us. God does not have a similar reciprocal duty. God is not required by any higher power to forgive and man has no right to demand forgiveness from God for sin.
This actually gets us back to the fairness versus forgiveness issue that we started the article with. Heschmeyer's discussion seems to assume that fairness requires that we forgive those who apologize but that fairness also requires that the person who broke the item pay for it, clean up the mess, etc.
4) Human Friendship conflated with Divine Justice (or Full versus Partial Forgiveness)
Related to the above conflations, Heschmeyer appears to conflate the issues of human friendship with divine justice. When Hechmeyer speaks of a person accepting an apology he is speaking primarily in terms of the person no longer being angry at the breaker. The anger of the breakee has been set aside and, to some degree at least, human friendship has been restored.
Nevertheless, a person can stop being angry with the breakee and still expect payment for the item and a clean-up of the mess. Or can forgive payment but still expect clean-up of the mess.
Divine justice, however, is not satisfied when forgiveness is only partial. Being forgiven of part of your wrong-doing may lessen your guilt under divine justice, but it does not remove your guilt.
In terms of human friendship, we may view this sort of partial friendship as acceptable, but in terms of divine justice the same partial forgiveness is not enough. It is enough to have partial forgiveness from a friend because we can pay for the broken item and clean up the mess. It is not enough to have partial forgiveness from God because we cannot atone for our sins, even in part.
These mistakes seem to sum up the problems with Heschmeyer's thought experiments. But after the experiments he attempts to make an argument from Scripture. In doing so, he makes a further mistake.
5) Chastisement versus Penalty
Heschmeyer considers the account of David's sin against Uriah, his plotting the death of Uriah to cover the sin of David's adultery with Uriah's wife Bathsheba. Nathan the prophet comes to David and rebukes David for this sin, and David repents. God spares David's life but takes the life of David's son. Heschmeyer puts it this way:
David is forgiven. No matter how you read it. But his son still dies. Anti-Purgatory logic falls apart here: if he's forgiven, how can he still be penalized? If he's penalized, how can he be forgiven?But Heschmeyer has made a two very fundamental mistakes. The first mistake is the mistake of confusing chastisement with penalty. David is being disciplined in the eyes of the nations for his sin against God. It is a chastisement, not a punishment. It is discipline to help David learn, not punishment that expiates sin.
The second mistake is to overlook the typological significance of this event. David's son dies instead of David. For David's sin, David's son dies. Who bears the wrath of God for David's sin? Not principally David, though he feels great sorrow at the death of his son, but the son instead. This is an illustration for us of the Son of David who died for all of David's sins. Christ is the son of David, as the scribes testified:
Matthew 22:42 Saying, What think ye of Christ? whose son is he? They say unto him, The Son of David.
And not only do we have the genealogies of Jesus, but the very children of Jerusalem testified that Jesus was the Son of David:
Matthew 21:15 And when the chief priests and scribes saw the wonderful things that he did, and the children crying in the temple, and saying, Hosanna to the Son of David; they were sore displeased,
As did the Canaanite woman:
Matthew 15:22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil.
And the two blind men:
And, behold, two blind men sitting by the way side, when they heard that Jesus passed by, cried out, saying, Have mercy on us, O Lord, thou Son of David. And the multitude rebuked them, because they should hold their peace: but they cried the more, saying, Have mercy on us, O Lord, thou Son of David.
But the truly blind were those who did not see that the Son of David was the Lord of David:
He saith unto them, "How then doth David in spirit call him Lord, saying, 'The LORD said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool'? If David then call him Lord, how is he his son?" And no man was able to answer him a word, neither durst any man from that day forth ask him any more questions.
Christ took on himself the punishment not only for David's sins, not only for the sins of the Jewish believers, but for the sins of the whole world. David's bastard son by Bathsheba died on account of David's sins, and took the punishment for them in his person - much more so did Christ the double son of David: first legally through Solomon's line by Joseph's adoption (see Matthew 1:1-23) and second by blood through his mother Mary and grandfather Heli, by the line of David's immediate son Nathan (see Luke 3:23-38).
God forgave David but punished David's son instead. David received chastisement only, and not punishment.
There is certainly much more that could be said on the topic of purgatory, but this may serve to answer a few of the points raised by Heschmeyer's article.