This is a short essay on how I look at tarot origin theories and how I assess their merits or shortcomings. Others may have different criteria. I invite others to share their own perspective or to comment on this one.
First, what is the material we have to work with? What is the evidence? I categorize the available information as follows:
1. The cards themselves (surviving early tarot decks and uncut sheets)
2. Early sources that refer directly to tarot cards (Steele sermon, Visconti letters, gambling edicts, etc.)
3. Quasi-tarots and sources that refer directly to them (Tarocchi of Mantegna, Sola Busca, Minchiate)
4. Non-tarot sources in which subjects depicted on the tarot cards are encountered (e.g., Petrarch's "I Trionfi", other depictions of Wheel of Fortune, Justice, tetramorph, etc., astrological illustrations of the Moon and Sun, etc.)
5. Sources not meeting the criteria for 1-4, but which are thought by some to be pertinent (the various philosophical schools and religious sects, medieval prophecies, apocalypse illustrations, alchemy, the Bible, classical mythology, etc.)
As we move down the list, we move farther from the cards themselves. This is both good and bad. It is good because it brings the possibility of connecting the tarot with something that is not tarot, hence "explaining" the cards in terms of something that is hopefully less of a mystery. It is bad because it is less certain that the more remote sources actually pertain to the tarot; we might be misled by coincidental resemblence or wishful thinking. Evidence in category 5 must be evaluated in a probabilistic fashion, and there is an inherent subjectivity to that. One person may see "obvious parallels" between tarot and alchemy, say, whereas another person would feel that those parallels are forced. How, then, are we to judge which of these "level 5" theories is compelling, or whether perhaps there is no compelling theory of that level at present?
For me, an important consideration is how each theory handles the lower levels of evidence. Here's what I think we learn from each of these levels:
1. (The cards). We see the actual pictures from a variety of decks, both hand-painted and printed. We know the trumps were integrated with the suit cards into decks. In some cases, the cards have numbers indicating their order. We don't have titles on 15th-century cards, but we see some from the 16th century.
2. (The direct references). We have card titles from the fifteenth century, we know the cards were used to play a trick-taking game (and have an incomplete description of the rules of the game). We know the earliest name for the tarot cards: Triumph cards.
1 and 2 together give a pretty clear picture of timing: tarot cards first appeared in the first half of the 15th century.
3. (Quasi-tarots). We know that other tarot-like sets of picture cards were made: the Tarocchi of Mantegna, with no suit cards but 50 trump-like cards of allegorical figures arranged in a hierarchy made explicit by a numbering and lettering scheme; the Sola-Busca, in which the subjects of the trump cards are completely changed, but the deck otherwise retains its structure, and (later), the Minchiate, which expands the trumps by the addition of signs of the zodiac, four elements, and missing virtues. We know Minchiate was a popular trick-taking game, very similar to tarot, for several centuries. We have no direct references on what the Mantegna was used for.
4. (Appearance of tarot subjects elsewhere). Many of the tarot card subjects (the Emperor and Pope, cardinal virtues, Death, Wheel of Fortune, etc.) were frequently employed elsewhere in the art and literature of the time, and by the same name as the subjects are given in the tarot. In some cases (Bagatto, Papess, Tower...) it is not clear that the tarot subjects are actually used elsewhere, although there are often similar subjects to be found. Petrarch's "I Trionfi" is important because it makes literary use of a significant number of tarot subjects in an order reminiscent of the tarot ordering.
I would certainly rule out any theory that was completely inconsistent with the direct evidence of the cards and early references to the cards. Someone whose theory implied, for example, that tarot cards were not used for playing a card game until the 1700s, would have to be rejected out of hand, and so on.
In addition, a theory should give a plausible account of the known subjects, titles, and ordering sequences of the cards. If a theory claims, for example, that the card called "The Emperor" represents the element sulfur, then the theory has a burden to explain why it would depict a man in imperial regalia and be referred to consistently as "The Emperor", never as "sulfur". That's not an impossible burden, but it is a heavy one.
A good theory should also give a satisfactory account of quasi-tarots, even if it is just to say they were designed with no concern whatsoever for whatever motivated the design of the tarot. But theories that do offer a positive explanation of the relationship between the tarots and quasi-tarots have greater explanatory power, and are to be preferred.
Since the use of tarot subjects in other contexts gives strong evidence for the meanings the culture attached to the subjects, a theory which claims that the designer meant something else by them bears a heavy burden. This is a second-order version of the requirement to explain subjects, titles, and ordering, discussed above. To continue the Emperor example, a depiction of a man with scepter, crown, eagle insignia, and called "Emperor" would probably suggest, to most 15th century Italians, the Holy Roman Emperor, either a specific one or the office. A theory that claims it represents the Emperor Marcus Aurelius, for example, would require much stronger support than a Holy Roman Emperor theory.
I tend to evaluate a theory's plausibility by how smoothly it accomodates the low-level (i.e., directly tarot-related) evidence of the first four categories, particulary the first two. Conversely, I evaluate its depth by how far it reaches (level 5) to connect tarot with some other facet of culture. It is certainly a distinct possibility that the "truth" about tarot may not be very deep! This is Dummett's contention. Given that two theories are comparably plausible, though, a deep theory is to be preferred because it has more explanatory power.
The merit of the cosmograph model as I presented it exploits the only unambiguous connection we have between the tarot cards (level 1 and 2) and the remote cultural sources of level 5: The tarot is unambiguously related to the Tarocchi of Mantegna, and the Tarocchi of Mantegna is unambiguously a cosmograph. The only danger I see in following such a course is if it is an assault on plausibility. At first, it seemed like this might be the case, because there are many differences between the tarot and the Tarocchi of Mantegna, differences that seemed like they would require either a great many changes in the identification of the card subjects or else a great many changes in the concept of the cosmograph. Now, though, I think that the differences between the two can be accounted for very efficiently, giving a theory that is both plausible and deep.
Here are my impressions of tarot origin theories currently "on the market" (ordered chronologically).
Moakley: moderate to good plausibility (many cards accounted for without stretch, but some failures), but only moderate depth; begs the question "What are the deeper cultural sources behind Petrarch's poem and the processions, and might the tarot designers be tapping in to those directly?"
Dummett: good plausibility, although I think he is so conservative (aversion to depth) that the theory actually loses some plausibility. He keeps to level 1 and 2 evidence, and by avoiding even the rather uncontroversial evidence of levels 3 and 4, ends up with an improbably truncated view of how a game designer might think.
O'Neill: excellent depth and range (many alternative "deep" theories considered), plausibility moderate. I'd say he's trying to get the most plausible of the deep theories, not the deepest of the plausible theories, if you follow me.
Williams: good use of level 4 evidence and good attention to plausibility concerns. Plausibility high, depth moderate.
Betts: deep, and very original. Loses a lot in plausibility, though, by requiring frequent departures from direct evidence regarding card titles and subjects, and level 4 evidence.
This perhaps reveals part of the reason why different folks have strong preferences for different theories: we may each place different value on depth and plausibility, and prefer to see those considerations balanced in different fashions. Personally, I find my preferences vary somewhat depending on what train of thought I'm engaged in and what I'm hoping to get out of considering the subject. As a card user, I'm very interested in deep theories for the interpretive insights they might offer. But there's also a side of me that's rather perfectionistic about plausibility. It makes me antsy to work with a theory that I feel like I need to make frequent apologies for.