Abstract
This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives:
- O T A :
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Talmudic obligation
- F T A :
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Talmudic prohibition
- F D A :
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Standard deontic prohibition
- O D A :
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Standard deontic obligation.
In classical logic one would have expected that deontic obligation O D is definable by
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\(O_DA \equiv F_D\neg A\)
and that O T and F T are connected by
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\(O_TA \equiv F_T\neg A\)
This is not the case in the Talmud for the T (Talmudic) operators, though it does hold for the D operators. We must change our underlying logic. We have to regard {O T , F T } and {O D , F D } as two sets of operators, where O T and F T are independent of one another and where we have some connections between the two sets. We shall list the types of obligation patterns appearing in the Talmud and develop an intuitionistic deontic logic to accommodate them. We shall compare Talmudic deontic logic with modern deontic logic.
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Notes
The translation of (1)–(4) must give four consistent and logically independent sentences adequately representing the linguistic text.
In Talmudic logic we have that \(\neg \neg F_T(A)\) is not equivalent to F T (A). The first is only a weak prohibition, a recommendation for good behaviour in the eyes of God, while the second is a full fledged strong prohibition. This is reflected in our use of intuitionistic logic as a basis.
The perceptive reader might say that perhaps we could obtain a similar result without the use of intuitionistic logic, by considering explicit permissions which are distinct from the negation of a prohibition.
More specifically, we introduce an additional modal operator P, with the axiom \(F \to \neg P\), but without the axiom \(\neg P \to F\). In that case, the negation of permission may correspond to a weak prohibition, but without requiring intuitionistic logic for this purpose.
However introducing another independent operator is too strong and does not manifest the intention that \(\neg \neg F_T(A)\) is only a recommendation of F T (A). Furthermore the idea of explicit permissions is not compatible with Talmudic thinking. God never said in the Bible “you are allowed to do this”. He only delivered to us Obligations and Prohibitions. See Sect. 5.1 for further discussion.
A main difference between biblical obligation and prohibition and ordinary traditional deontic obligation and prohibition is that violation of a biblical prohibition would imply a sanction whereas fulfilment of the corresponding biblical obligation implies a reward. This in an important dimension, and will be further discussed in Sect. 5.1.
The Talmud interprets the Bible. So when we say Talmudic logic, this includes Biblical logic.
Assuming she is not married. If she is married, the guy is in really serious trouble! If she is not married but does not want to marry the guy, he has to pay compensation only.
The following is the labelled history of actions violations. “+” means obeyance, “−” means violation.
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(s1)
label [(−b)]
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(s2)
label [(−b), (+c), (−a)]
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(s3)
label [(−b), (+c), (−a), (−d)].
If he makes the fence low we will get also (+f) and (−e), and if he makes the fence high we will also have (−f) and (+e).
On the basis of the above history of labels we make a decision.
Controlled revision applies when we start with a theory \(\Updelta_0\) and have a series of inputs \(A_1, A_2, A_3\ldots\). At stage n we have \(\Updelta_n\), and when we revise to accommodate A n+1 we must remember the entire history of revisions and revise accordingly.
So, for example, if \(\Updelta_0 =\{A, A\to B\}\) and we get \(\neg B\), we revise and get \(\Updelta_1 =\{\neg B, A\to B\}\). If we now get input B, we ordinarily may revise and get \(\Updelta_2 =\{B, A\to B\}\). But in controlled revision we remember the history, so we know that we took out A and hence we bring it back and revise to \(\Updelta_2^{\rm controlled}=\{A, A\to B\}\).
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(s1)
For a discussion of why it is necessary to use 613 labelled modalities, see Sect. 5.2.
To give an example, suppose I find a lost item in the street, say a handkerchief. There are two possibilities to consider.
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1.
The owner does not bother to come back looking for it.
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2.
The owner will not give up and come back for it (monogrammed handkerchief).
Legally in case 1 my obligation to seek the owner does not exist since the owner has given up. In comparison in the second case I must pick up the handkerchief and find the owner or give it to the police.
However, even in the first case, it is recommended and even legislated that I try and find the owner (e.g. give it to the police), even though the owner has abandoned the handkerchief, i. e. there is no O T obligation to return the handkerchief, but nevertheless the Talmud recommends that I return the handkerchief. Our notation for this is \(\neg\neg O_T\).
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1.
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Acknowledgments
We are grateful to the Deon 2010 referees for valuable comments, and to the Deon 2010 participants for penetrating discussion during the presentation lecture, and to the referees of Deon 2010 special issue.
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Abraham, M., Gabbay, D.M. & Schild, U. Obligations and prohibitions in Talmudic deontic logic. Artif Intell Law 19, 117 (2011). https://doi.org/10.1007/s10506-011-9109-0
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DOI: https://doi.org/10.1007/s10506-011-9109-0