Anti-Mormon critics argue from at least two different positions.
1)- asking Mormons to support their claims with evidence.
2)- proposing deductive arguments which ostensibly show that LDS beliefs or claims are false.
These positions are both fine on their own. The problem is, anti-Mormons conflate the two.
To illustrate with a fictitious example, an anti-Mormon might say, "we have proof Joseph Smith lied, because he told one person that he 'has never eaten fish,' but told another person that he 'has eaten fish.' These statements can't both be true!" That is a deductive argument, and is easily countered by observing that Joseph may have eaten fish between making the first and second statement. But if you point this out, the switch takes place. The anti-Mormon now says, "you don't have any evidence to support your claim that Joseph Smith ate fish. We have evidence for our claims, while the Mormons are making claims without evidence." Of course, we don't need any evidence that Joseph Smith ate fish, as we have already refuted their deductive argument - by presenting a plausible alternative to their argument's conclusion. In other words, their argument is now reduced to, "we think Joseph Smith lied, but we can't prove it."
Unfortunately, it seems to me that many LDS apologists don't realize the deductive nature of the anti-Mormon arguments, and therefore feel they must only "fight fact with fact," and never mention anything that isn't documented. For instance, in the fish illustration, an apologist might think, "well, they have documentation on their side, showing that Joseph did make those statements, so I must therefore find documentation that Joseph Smith ate fish." This is a fallacy.
Of course, LDS apologists can additionally provide evidence to support their points, and that evidence can demonstrate increased plausibility and likelihood. However that evidence is not necessary in order to demonstrate that an anti-Mormon argument is flawed. Unfortunately, when people see the apologist presenting evidence, they can get confused and think the apologist needs to prove his point is true in order to counter the anti-Mormon argument.
Moreover, anti-Mormons often invoke Occam's Razor - in an inapt defense of deductive argument. For instance, in the context of the fish fallacy illustration, they might say, "we already know Joseph Smith was a liar, so by using Occam's Razor we can confidently say he was lying about this too." If you disagree with their premise (i.e. that Joseph Smith was a liar), they often will try to prove that the premise is true by moving on to other examples of Joseph Smith allegedly lying - never returning to the original argument or admitting it was flawed.
Now let's look at a real example of a flawed anti-Mormon argument, and my response to it. Notice that I defend my point with evidence, which strengthens my point but which may lead some to the false belief that my point is only relevant if it is proven - when in fact my point exposes a flaw in the anti-Mormon argument, even without being proven and even while including speculation.
[2020 update: the following reflects my ideas on the subject as they existed a few years back. I have greatly updated the theory, and you can find a good starting point here]
Argument: Joseph Smith said that a roll, which we now refer to as the "Ta-sherit-min roll," contained the writings of Joseph of Egypt. We now know it does not contain any writings of the sort, so Joseph Smith was either deluded or lying.
Response: As my friends and readers know, I like to question things - exploring new ideas and trying not to take anything for granted.
One example is the belief that Joseph Smith said that his papyrus collection contained both a book of Abraham and a Book of Joseph.
The reason this sort of information is important is because it sets the tone for how we interpret other facts. For instance, the theory that Joseph Smith translated the Book of Abraham from papyrus which is now missing takes a hit if Joseph claimed there were two separate rolls for Abraham and Joseph - because that would mean two rolls are missing which need to be accounted for, not just one - which makes the theory less plausible.
Alternatively, the missing papyrus theory would be bolstered if Joseph Smith was referring to only one document. This would allow, for instance, for the possibility that Abraham had written a book and then Joseph of Egypt redacted a small part of Abraham's book, and the small redacted version is what ended up in Joseph Smith's papyri. From that small redacted version, Joseph Smith could then have restored the full Book of Abraham - the book written as Joseph Smith said, "by his own hand." That's just one possibility, but if that's what Joseph Smith was talking about, then it could go a long way toward solving the Book of Abraham puzzle. A small redacted excerpt could more easily have fit on the missing end of the Hor papyrus scroll.
So let's explore the possibility.
There is little evidence that Joseph Smith personally said that Abraham's writings were on one roll and Joseph's writings were on a separate roll. For one thing, Joseph Smith was not keeping a journal at the time of his alleged statement. It's easy to see how, if Joseph Smith said something about the papyri containing the writings of "Abraham and Joseph," people could assume he meant that the writings of the two Patriarchs were on separate rolls (since we tend to perhaps think of scripture in terms of each prophet having his own separate book).
In the context of my theory, one possibility is that Joseph of Egypt put together a few things Abraham had said about the Egyptians, for the purpose of talking with Pharaoh about Abraham's time in Egypt and about Egyptian history.
This would seem to square with a statement from Parley P. Pratt:
The record is now in course of translation by the means of the Urim and Thummim, and proves to be a record written partly by the father of the faithful, Abraham, and finished by Joseph when in Egypt.
Pratt is talking about a single record which both men (Abraham and Joseph of Egypt) contributed to, and the wording of Pratt's statement is consistent with the redaction idea. This would account for why Joseph Smith never really talked about the contribution from Joseph of Egypt, due to the fact that Joseph Smith restored the original Book of Abraham, the one written by Abraham's own hand, not the redacted excerpt passed down perhaps in the extra space on the Hor roll.
We only have one account of Joseph Smith mentioning a connection between Joseph of Egypt and the papyri, a statement allegedly made soon after the purchase of the papyri. This one statement attributed to Joseph Smith reads:
… with W. W. Phelps and Oliver Cowdery as scribes, I commenced the translation of some of the characters or hieroglyphics, and much to our joy found that one of the rolls contained the writings of Abraham, another the writings of Joseph of Egypt
This quote is from History of the Church, which was written in a first-person style as if Joseph was himself speaking, but was actually a compilation of statements which were primarily written by others.
Howard C. Searle explains:
Although little of the subsequent history was dictated or written by the Prophet himself, writers used his diaries where available and retained the first-person narrative style throughout.
Although unfamiliar to us today, this first-person editing practice for compiled materials was quite common and acceptable at the time. Historian Michael D. Quinn observes:
Our present standards concerning plagiarizing, footnoting, and editorial adherence to the original manuscript did not begin to penetrate even professional historical writing in American until nearly fifty years after the original composition and editing of Joseph Smith's history, and were not generally reflected in non-professional histories until long after B.H. Roberts prepared the second edition of that history in 1900.
So, the quote attributed to Joseph actually appears to have come years later from Willard Richards, who wasn't even there at the time of the alleged statement. Unfortunately, it was a complex situation. And Joseph's method of translation does not require us to assume that he was even looking at the rolls of papyrus or explaining to his scribes which roll(s) he was talking about when he identified that the papyrus contains the writings of Abraham and Joseph. Moreover, the account from Richards could also be tainted by the public perception about the rolls as it developed over the intervening years. In any event, Richards does not inform us of anything Joseph himself actually said, and instead gives his own account wherein he chooses to talk about the scribes, and takes liberties such as the phrase "much to our joy," etc.
In a non-extant letter to William Frye, Oliver Cowdery made a statement describing his understanding of the Book of Joseph. In the history of the Church, this statement was also wrongly attributed in first person to Joseph.
The letter written by Cowdery states in part:
The inner end of the same roll (Joseph's record) presents a representation of the judgment. At one view you behold the Savior seated upon His throne, crowned and holding the scepter of righteousness and power, before whom also, are assembled, the twelve tribes of Israel, the nations, languages and tongues of the earth, the kingdoms of the world over which Satan is represented as reigning, Michael the Archangel, holding the key of the bottomless pit, and at the same time the devil as being chained and shut up in the bottomless pit.
It's not surprising that Oliver took occasion to “study it out in his own mind,” in accordance with the commandment which had been given specifically to him in D&C 9:8. In no way does Oliver attribute this information to Joseph Smith, or claim that it was an actual translation. Rather, Cowdery states that it is self-evident: “The evidence is apparent upon the face, that they were written by persons acquainted with the history of the Creation, the fall of man, and more or less of the correct ideas of the notions of the Deity.”
Cowdery's letter was printed in The Messenger and Advocate, and, accordingly, I believe that's where the rumor of the roll of Joseph started. Cowdery plainly believed the Tshemmin roll was doctrinally significant, and since the writings of Abraham were being translated from the other roll, it would be reasonable to deduce (in Cowdery' s shoes) that the Tshemmin roll contained the “writings of Joseph” which Joseph Smith had evidently said something about. Again, I believe Joseph most likely said something about the papyri containing the writings of both Abraham and Joseph, but we have no way of knowing what his exact phraseology was.
Some people may still choose to assume that Joseph Smith said the Tshemmin roll contained the writings of Joseph of Egypt. But if Joseph Smith was on trial, there would be no direct evidence to make that case. The only people who are known to have claimed that the Tshemmin roll contained the writings of Joseph of Egypt are people who would have had no personal means of knowing.
These people can't be witnesses to any particular roll being the Book of Joseph, or being a record of anything else, unless they had the ability to translate. And the only one who did claim to have that ability, Joseph Smith, appears silent on the matter except for a quote which is attributed to him in a history known for routinely attributing statements to him which he did not make.
One might wonder, if a misconception existed then why didn't Joseph correct the misconception? Well, if he became aware of the problem, then perhaps he did correct it – at least to anyone asking him about it in person.. But the question is when or if he became aware of the problem. He had a lot happening in his life.
Did anyone ever ask him to clarify? I don't know that they saw any need. Once Joseph said something to the effect of finding the writings of Joseph and Abraham, and people could see for themselves that there were two rolls, the people could have seen that as sufficient grounds for their assumption, and then Oliver's publication of the letter, with those two words, “Joseph's record,” solidified the assumption.
But wouldn't it have come up frequently in conversation? Not if Joseph only talked about the Book of Abraham. It's easy to say that everyone should have gotten together and talked about every conceivable misunderstanding and gotten them all cleared up, but that's hindsight - how many misunderstandings took place which were in fact cleared up, but we don't know about because they were cleared up before anyone wrote about them?
Perhaps there is information of which I am unaware, but I see no reason to assume that Joseph Smith associated the Tshemmin roll with Joseph of Egypt.
Thus we see that a flawed anti-Mormon argument can be effectively refuted by pointing out plausible yet unproven possibilities which contradict the premises and/or conclusion of the anti-Mormon argument.