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Contrary to time conditionals in Talmudic logic

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Abstract

We consider conditionals of the form A ⇒ B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.

Three main aspects will be investigated:

  1. 1.

    Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality).

  2. 2.

    Comparison with similar features in modern law.

  3. 3.

    New types of temporal logics arising from modelling the Talmudic examples.

We shall see that we need a new temporal logic,which we call Talmudic temporal logic with linear open advancing future and parallel changing past, based on two parameters for time.

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Notes

  1. In practice such condition is not allowed because it looks like legalised wife swapping.

  2. c may have been b’s “friend”, and the husband insisted on this condition.

  3. We can formulate a formal language for the Iota based on the temporal logic of the current paper enriched with the Iota symbol. We shall have to allow for \((\iota x)\phi(t,x)\) and for \((\iota t)\phi(t,x)\) to be formed independently of any semantical condition. This means that we have to give denotation to these expressions also in the case where there exists more than one element satisfying ϕ and for the case where there exists no element satisfying ϕ.

    There are several options in the literature of what to assign to the Iota expression in such cases, but as far as we know, there is no discussion in the context of temporal logic. The classical options are to make the Iota expression undefined or to assign an arbitrary element to it. In temporal logic it is better to view the Iota elements as a non existent free element which may come into existence, should a unique element show up.

    There is no need for us to pursue this course of action. It is too complex. Our paper (Abraham et al.) avoids the use of the Iota by using quantum superposition models.

  4. According to British law m, by making the offer to g is already giving him permission to hack into the laptop.

    We can change the example a bit. m sells the laptop to a. a makes the condition that if anyone hacks into it between 18.00 and 18.30 then the deal is off. Now m gives the laptop to g under the condition that g hacks into it between 18.00 and 18.30. Now g would commit a crime.

  5. Rabbi Shlomo Fisher, 1932–.

  6. Rabbi Shimon Shkop, 1869–1939.

  7. At τ = 30 there is a discontinuous jump from t = 18.30 back to t = 18.00.

  8. Note that what we call τ2 here is called τ in Example 13, it is the τ of action a′ at that example.

  9. Note that in the case that one of them dies exactly at 18.30, this still counts as “existing” at 18.30, for the purpose of the model. This follows from Talmudic rulings in such cases. So, according to Shkop, the Talmud requires them to exist at all moments of time up to but not necessarily including the end time 18.30.

References

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Acknowledgments

We are grateful to A. Avron and N. Dershowitz for critical comments, and to the referees for penetrating analysis and criticism.

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Authors and Affiliations

  1. Bar-Ilan University, Ramat-Gan, Israel

    M. Abraham, D. M. Gabbay & U. Schild

  2. King’s College, London, UK

    D. M. Gabbay

  3. University of Luxembourg, Luxembourg, Luxembourg

    D. M. Gabbay

Authors
  1. M. Abraham
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  2. D. M. Gabbay
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  3. U. Schild
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Correspondence to D. M. Gabbay.

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Abraham, M., Gabbay, D.M. & Schild, U. Contrary to time conditionals in Talmudic logic. Artif Intell Law 20, 145–179 (2012). https://doi.org/10.1007/s10506-012-9123-x

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