Abstract
In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT.
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DOI 10.1093/jigpal/jzaa026
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Asymmetries in Time.Paul Horwich - 1990 - Noûs 24 (5):804-806.
The Problem of Counterfactual Conditionals.Nelson Goodman - 1947 - Journal of Philosophy 44 (5):113-128.
Machines, Logic and Quantum Physics.David Deutsch, Artur Ekert & Rossella Lupacchini - 2000 - Bulletin of Symbolic Logic 6 (3):265-283.
Questions and Answers in an Orthoalgebraic Approach.Reinhard Blutner - 2012 - Journal of Logic, Language and Information 21 (3):237-277.

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