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Note that C-Trans can be false for some e, p and q because there are probability distributions that verify its antecedent while falsifying its consequent for any chosen t ∈ [0, 1). Thus C-Trans makes room for non-transmissivity of justification. C-Trans and C-Fail actually capture some feature of Wright's informal framework (cf. Chandler 2010, 338).
A Set-Set sequent Γ≻ Δ holds on a valuation v if and only if it is not the case that v verifies every formula in Γ while falsifying every formula in Δ; note that this coincides with the definition of "holding on v" given for Set-Fmla in the case in which Δ = for some ψ.
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We therefore see that abduction is the fruit of the scientist's inventive, creative moment, of the fortunate instant of scientific inventiveness that formulates generalised explicative hypotheses, which, if confirmed, become scientific laws (though still able to be corrected and substituted) while, if falsified, are rejected.
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