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The RaM"a (Y"D 87:6) cites an opinion that one may shouldn't stoke a flame beneath a non-Jew's pot, for fear that there's some milk and meat residue in it, and you might come to cook said milk and meat residue.

R' Akiva Eiger there asks why this should be forbidden considering that there's really a doubt if there is any residue and you don't intend to cook it if it's there. He answers that it's a Pesik Resheih (inevitable consequence), and the doubt relates to the past (whether the pot has milk and meat residue from previous cooking), not purely to the present/future (whether your action will cook meat and milk together), and in that case a simple Safek (doubt) isn't enough to overcome the defining characteristic of a Pesik Resheih, which is its inevitability.

(Pesik Resheih is confusing enough without adding DeLa'Avar to it, so I hope the above was clear.)

If this is so, are there other cases like this in which a Safek DeLa'Avar is deemed inconsequential, and a Pesik Resheih is declared and said action is forbidden? Are there any cases that contradict this (either within R' 'Akiva Eiger's own writings or just in rulings by others who don't hold this opinion)?

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@doubleAA New Pesik Resheih (or Psik Reisha or P'sik Reishe) tag? –  Seth J Sep 21 '12 at 14:00
    
I'm not sure it's necessary, but if you make it I'll be sure to link all those synonyms to each other. –  Double AA Sep 21 '12 at 16:56
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The Achronim (Shulchan Aruch OC 316:3) deal with the case of closing a box on Shabbos when there might be fly in it: Safek if there will be a definite Melacha of trapping. I believe there is a large Machloket there between the Achronim, with the Taz famously permitting closing the box.

See also the Gemoro in Shabbos 41b about allowing someone to put cold water in a pot that might cause the pot to become stronger and you will be Mechuyv in Meleches MeTzaref. The Gemoro says Rabbi Shimon is Matir because it is a Davar Sheeina Miskaven. Tosfos there says that is therefore not a Psik Reshe becuase if it were Davar Sheeina Miskaven would not help. Rabbi Moshe Feinstein on his Peirush on Maseches Shabbos says that the reason why it is not a Psik Reshe is because it is doubtful whether the pot really reached a hot enough heat for cold water to soldify it. Rabbi Moshe says that we see from here that even though the Melacha in the Safek is only in the past, it is still good enough not to be considered a Psik Reshe.

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I believe the Ta"Z Matirs closing the box (I think it's more of a cupboard, but that doesn't make much of a difference) because of a Sefek Sefeka, which makes that a different case. Your second point is a great example, though. Do you have more information or a citation to look up how he reaches this conclusion? I'm interested to know if this is the same type of situation or something a little bit different. –  Seth J Sep 21 '12 at 12:23
    
(By "he", of course, I'm referring to R' Moshe.) –  Seth J Sep 21 '12 at 12:30
    
@SethJ will check up over Shabbos the location of Reb Moshe. And the Taz and co are specifically talking about Psik Reshe Sheleovar. Perhaps the Sefak Sefeka is an extra part to the Shtickel –  yehuda Sep 21 '12 at 12:37
    
Regarding the Ta"Z, right, that's what I meant - it's talking about LeShe'Avar, but the extra Safek removes the Pesik Reisheih aspect to it. I believe this is within the רע"ק, but I could be wrong. I was listening to an old Shi'ur and didn't have it in front of me when I wrote my question. –  Seth J Sep 21 '12 at 13:10
    
So my question re: R' Moshe, if you get a chance to look it up, is, is R' Moshe arguing with רע"ק, or is he saying that in R' Moshe's case, the construct doesn't apply for some reason or another? –  Seth J Sep 21 '12 at 14:02
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