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Tarot Divination using Boolean Logic

NB: I am not a practitioner of the Tarot, and I make no claims as to the divinatory power of the Tarot. I am just an interested layperson.

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There are two parts to my system. The first part is an algorithm that uses the Tarot cards to generate a sentence in propositional logic, the second part is a method for divining from that sentence using the Tarot. The second part is simpler to explain, so I will explain that first.

Divining from a sentence of propositional logic

In Tarot readings, typically the practitioner will make use of a spread, a certain layout of cards on the table, where the placement of a card signifies what that card means in relation to the question given. In my system, a sentence of propositional logic provides the spread to be used. A Tarot card is drawn for each of the atomic subsentences (those which are individual characters) in a sentence of propositional logic, and from the connectives of the sentence and the Tarot cards selected, the practitioner can divine meaning.

Here is an example. Take the following sentence of propositional logic:

 ((A ∨ B) ∧ (C ↔ ¬B))

There are only 3 atomic sentences present here: A, B and C. So, three Tarot cards are selected, corresponding to the atomic sentences A, B and C. Depending on your Tarot deck, you can reduce this to only cards from the Major Arcana, or if your Tarot is fully illustrated, you can select from the whole Arcana.

Here is one selection you might have made:

The next step is interpretation. The Boolean connectives should not here be understood in their truth-functional sense, so here is a key for how to understand each of the 5 Boolean connectives:

I hope it is now clearer how, when accompanied with a question, which my example was not, a Tarot reading can be performed from a given sentence in propositional logic once the connectives are given these deviant interpretations.

Generating a sentence of propositional logic using the Tarot

Now, the first part of my system, requiring a full 78-card Tarot. This involves continually picking a card from the deck without replacement and generate a sentence until you eventually pick up a termination card.

I have reduced the number of available atomic sentences to only seven: A, B, C, D, E, F and G. I did this because there are 14 cards for every suit in the Minor Arcana, and 21 cards of the Major Arcana (excluding the Fool), and these are both numbers divisible by 7. Every card (except the Fool) is associated with exactly one of these atomic letters. Here is a table to show which atomic sentence every card is associated with.

The algorithm works by using a stack data structure. Sentences of propositional logic are added (pushed) onto the stack and sentences are taken from the top of the stack to apply connectives.

Here are the rules for what to perform upon drawing a card:

1. All Kings and the Fool: Terminate the algorithm. Take the sentence at the top of the stack as the generated sentence.
2. Minor Arcana card from Ace to 7: Add the associated atomic sentence to the top of the stack.
3. Major Arcana: take the top sentence of the stack and apply negation to it. (Append ‘¬’ to the front of the top sentence). If the stack is empty, add on the associated atomic sentence to the stack and then negate it.
4. Pentacles card from 8 to Queen: Apply conjunction to the top two sentences on the stack taking the topmost sentence for the left side of the conjunction, and the sentence beneath it for the right side of the conjunction and add the result to the stack. If there are less than two sentences on the stack, push the associated atomic sentence onto the stack until there are at least two sentences on the stack, and apply conjunction.
5. Wands card from 8 to Queen: Same as in 4, but with disjunction.
6. Swords card from 8 to Queen: Same as in 4, but with the conditional.
7. Cups card from 8 to Queen: Same as in 4, but with the biconditional.

I realise that still, it might be opaque how this algorithm works, so I will go through a demonstration to show how it will generate a sentence.

Demonstration

The first card drawn is the 3 of Wands. Its associated atomic sentence is C, so C is pushed onto the stack.

The second card drawn is 6 the Lovers. As there is already a sentence on the stack, there is no need to work out this card’s associated atomic sentence. Instead, we take the top of the stack and negate it.

The third card drawn is the 5 of Swords. This adds onto the stack. Its associated atomic sentence is E, so that is pushed to the stop of the stack.

The fourth card drawn is the 8 of Pentacles. This applies conjunction to the top two sentences of the stack, and pushes the result onto the stack.

The fifth card drawn is the 10 of Cups. This applies the biconditional to the stack. However, there is only one item on the stack, so before this is applied, the atomic sentence associated with this card is pushed onto the stack. That atomic sentence is C. Now the stack has two elements, and this can be combined to form the biconditional and the stack is reduced again to only having one element.

The sixth card drawn is the 8 of Wands. This applies disjunction. Just as before, however, there is only one element on the stack. So, the associated atomic sentence must first be pushed onto the stack. That atomic sentence is A. Now disjunction can be applied.

The seventh card drawn is the King of Wands which terminates the algorithm. The top element of the stack is returned as the generated sentence of propositional logic. Our final sentence is:

 (A ∨ (C ↔ (E ∧ ¬C)))

Now a reading can be performed on this generated sentence in the manner described in the first section. This sentence is particularly interesting because one of its disjuncts contains a contradiction.

 (C ↔ (E ∧ ¬C))

This is false on every attribution of truth values to the atomic sentences. Given that this is one of the disjuncts of a disjunction, the other disjunct (in this case, A) must be true. The contradiction can be read as significant in relation to the question asked.

One interesting feature of my algorithm is that it is possible for it to terminate without generating a sentence, if the Fool or a King is drawn first from the deck. If this happens, then the practitioner should read whatever significance this holds in relation to the question. Perhaps it indicates that in some way the question is defective, or misleading.

Conclusion

Possibly, there is room for expansion of this system using modal operators, but I don't have anything interesting to say about that.

Finally, I would like to recommend a few websites. First, I used and slightly edited some images from the British Museum, here is their credit:

© The Trustees of the British Museum. Shared under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) licence.

Here is an interesting website discussing Tarot history with a focus on the Marseilles Tarot:

https://tarot-history.com/

Finally, this website has quite a few high quality scans of various Tarot decks:

https://hermes-thot-archives.blogspot.com/p/tarots_9.html