Equivalence of Grandfather and Information Antinomy Under Intervention

Causal loops, e.g., in time travel, come with two main problems. Most prominently, the grandfather antinomy describes the potentiality to inconsistencies: a problem of logical nature. The other problem is called information antinomy and is lesser known. Yet, it describes a variant of the former: There are not too few consistent solutions—namely none—but too many. At a first glance, the information antinomy does not seem as problematic as the grandfather antinomy, because there is no apparent logical contradiction. In this work we show that, however, both problems are equivalent under interventions: If parties can intervene in such a way that the information antinomy arises, then they can also intervene to generate a contradiction, and vice versa.