The hallmark of philosophical acuity is the ability to explain in rich detail and flawless clarity humanity's most commonly made logical errors. It requires philosophical genius to make these errors obvious to the lowest common denominator in any society. Thankfully, genius does not need to be housed within one individual, but can often result from the collective and faithful efforts of many individuals, accrued over centuries of recorded thought. However, many errors, once made obvious, are often easily passed over among later generations of thinkers, and are thus left without a decent explanation that may be vital to the philosophically apathetic.
One such easily ignored error of reasoning comes up easily among theological speculation, expressed always with some variant of the cliché question: "Can God make a burrito so hot, that He Himself cannot eat it?" (I much prefer this version to the agonizingly mindless one involving God lifting rocks; credit goes to Homer Simpson for posing it). Any student of first-order logic should be capable of answering the "Burrito Challenge", but too often the subtlety of the answer and its sweeping implications are beyond a student's explanatory power and beneath the dignity of a real scholar.
By the grace of God, burritos and all, I am neither of these. My goal is not only to fully explain the answer to the Burrito Challenge, but to make it possible for you, the reader, to do so as well. In actuality, that is a lie; my true goal is to further reduce, by every possible degree, the great cranial silences that afflict most representatives of humanity. Hopefully you, dear reader, will join me in this effort, and when confronted by this or similar challenges, you will dutifully roll your eyes and proceed to once again explain what should be collectively obvious: the answer is No.
1. Load The Question
First take note of the question itself; most people pose it in one of three general flavors. Because of the challenge's stock-in-trade use as a riddle designed to trip up the thoughtlessly faithful, it's most common appearance is as a weapon that neither party truly wishes answered. People otherwise reasonable in other discussions tend to throw out this challenge as an all-purpose 'get out of jail free' card when solicitors of faith come knocking on the door. The unfortunate fact is that most of the people posing the question rarely know the answer themselves, relying instead on the solicitor's own deficit of logic. In turn, these same solicitors who come to ignore the question by tacitly repeating that God can do anything, only reveal to their would-be converts the utter thoughtlessness of their own faith.
On the other hand, years of this kind of willful ignorance to the Burrito Challenge lead both the honestly religious and genuinely curious to pose the question in good faith to their teachers, parents, or peers, most of whom have no better explanation than that the challenge itself is simply wrong. Although this is true, once again the subtlety of the proper answer is lost, allowing the cycle to continue unabated. Normally I wouldn't consider this to be much of a problem, but I've come to believe that by letting such an obvious point of reason slide, we stunt the growth of human progress. There is simply no excuse for allowing this kind of easily-avoided stupidity to perpetuate itself.
2. Tacit Agreements (The Short Answer)
The Burrito Challenge includes in itself an implicit assumption: that the 'God' which it specifies is omnipotent, or simply all-powerful. The challenge rather loses its punch if this assumption is left out. Thus, anyone in their right mind will agree that we can rewrite the challenge to read: "Can He-who-can-do-anything (God) make a burrito so hot, that He Himself cannot eat it?" Even those without a degree in logic or philosophy should already begin to see that, phrased this way, though obviously identical to the original question, the challenge is a wee bit more specious.
That done, the harder part follows. We must ignore the first part of the question, in order to clearly rewrite its end in the same manner. It seems uneccessary, but often people are still hung up on the thought that God can do or make anything, which clouds reasoning through the second half. Instead, simply ask, "is there a burrito so hot that God cannot eat it?" Do not play the game of trying to answer this, because all it really asks is, "is there something that God cannot do?" We can rewrite this again, as we did the first half, replacing 'God' with 'He-who-can-do-anything'. What it becomes is: "is there something that He-who-can-do-anything cannot do?"
Strangely enough, there is a clear answer to this reformed question; something that an all-powerful being cannot do is, clearly, something that cannot be done. In the end, this is what a burrito-so-hot-that-God-Himself-cannot-eat-it is; something that cannot be done. It follows that what the Burrito Challenge is really asking is this: "Can He, who can do anything, do that which cannot be done?"
The answer, obviously, is "No".
3. Categorically Wrong (The Long Answer)
Don't be fooled into thinking that this is the end of the story. Those of you reading this, who think that this explanation serves to better support the Burrito Challenge as a valid weapon against avid monotheists have, once again, missed the subtlety in the argument. Feel free to blame me if you have, but let me be clear. The fault expressed in the Burrito Challenge has nothing to do with any imaginable limitations on divine power, but instead picks out a problem of vagueness in human language. Just because our language allows us to put together these words, which in turn refer to more complicated ideas, we will always have the ability to assign incompatible ideas together in grammatically correct statements.
Years ago a former teacher summed up this kind of fault in a simple, beautifully useless question: "why is a duck?"
The answer is, of course, that there is no answer; the question itself was simply formed wrong, a practice that first-year philosophy students learn to call 'categorical mistakes'. The Burrito Challenge is simply one of many examples of these, but like other questions that fall under this label, the flaw isn't readily apparent until the logical reasoning is followed up on. Thus a more religiously-minded thinker might like to point out that the true answer to the Burrito Challenge is: "No, God cannot make a burrito that hot.. but that's your problem, not His".
Once the two parties have managed to clear this little matter up, they can finally move on to far more interesting theological questions, like why bad things happen to good people, or why Christians, Jews, and Muslims all say they worship the same deity but still think everyone else is a heretic.
Now go convert some infidels!