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In this paper, I investigate the purported dilemma between a symmetrical conception of time and the denial of what I call Universal Logical Determinateness (ULD). According to the dilemma, the timeless and universal application of logical laws to all propositions necessitates either the view that the past and future are both open, or that they are both closed. My investigation proceeds by way of an assessment of Taylor’s argument for fatalism, then of Dummet’s presentation and refutation of the fatalistic argument, and finally of Dummet’s analogous argument which attempts to prove the possibility of an open past. In all cases, we find that the arguments implicitly rely upon the assumption that there exists a necessary connection between the truth aptness of propositions and the fixity (or non-fixity) of events. I question this assumption and conclude that any argument for the symmetry of time which relies upon it begs the question against the asymmetry of time.