http://en.wikipedia.org/wiki/Reductio_ad_absurdum
There is no such Latin word as "miseratum" -- there's miser, -a, -um (adjective), misere (adverb), miseratio (noun), miserandus, -a, -um (adjective), miserabilis (adjective), misereo (verb), and others -- but no "miseratum" anywhere in ancient Latin.
If you want to use that noun to complete your invented phrase, then use "miserationem."
Short form of the question: is "reductio ad miseratum" correct Latin?
But if you're interested, here's the whole story:
"Reductio ad absurdum" is a logical argument where you use the premise to deduce an absurd conclusion-- since the conclusion is so absurd it can't possibly be true, you can reject the premise.
In a similar vein, I've noticed that people sometimes argue that a given course of action would have horrible consequences, and therefore the action under consideration cannot possibly by entertained. Colloquially, I have called this sort of argument "reductio ad miseratum", which is my own way of trying to say "reduced to misery" or something similar.
Unfortunately, I've never had a day of latin class, and am now about to write a little article about "reductio ad miseratum". So if I'm going to correct any grammatical errors, now is the time. Help!
2 answers
"Reducio ad miserationem" is precisely what I was looking for-- thank you.