How does a priest figure out whose confessions he has heard?
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Exactly. (Could there be something to the new fad of face-to-face "Reconciliation?")
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As regards past confessions to an invalidly ordained priest, so long as the same penitent made a good confession to a validly ordained priest later, it is not necessary to revisit the previous matter from the invalid confessions ("ego te absolvo a peccatis tuis...").
But, think of the rock and a hard place one would be in [between] who mistakenly confesses to an imposter, then dies:
Supplied jurisdiction only covers jurisdiction, not orders (i.e., that person's sins would not be absolved); perfect contrition would have been their only hope.
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Making a good confession to a validly ordained priest later is nice, but what about the mortal sins confessed to the impostor without perfect contrition and not repeated later to a real priest?
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That's why it's incuмbent on the conditionally re-ordained priest to at least attempt to go out and make known to everyone who might have confessed to him before he was re-ordained that they should recall the serious sins they had thought were absolved and confess them again to a good priest. It's always a good idea to recall past sins that you think were absolved and confess them again, anyway.
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In the end, perfect contrition covers a wide swath of problems, but perfect contrition is far from a simple matter.
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It is a principle that ought to be the focus of every catechism class, to make your entire life a continuous effort to attain perfect contrition. Some students might think the confessor would be bored with penitents who have perfect contrition, but that's not so. Every priest would very much love to have a line-up of penitents at his confessional all of whom could go straight to heaven without confessing their sins to him! Perfect contrition is what we ought to be striving for every day. It is a great goal and an enormous challenge.
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There are books to read to help one learn how to achieve perfect contrition. They are great reading material, and it's really simple to get a firm grip of the state of your soul by seeing if you would dare take the book off the shelf and read it --- again!
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St. Alfonse de Liguori's
Preparation for Death is a good example, and Fr. Schouppe's
Purgatory is another.
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Fr. Martin von Cochem's
Death, Judgment, Heaven, Hell.