Why the Transitivity of Perceptual Simultaneity Should be Taken Seriously

A relation is transitive if and only if from the fact that A has a relation to B, and B has a relation C, it necessarily follows that A also has a relation to C. As a relation fulfilling this requirement, consider simultaneity understood as two events occurring at the same time and only at the same time (thus this is not a case of mere partial temporal overlap): If A and B share all the same temporal properties, and B and C share them too, then it is impossible for A and C not to share them too. Accordingly, the simultaneity of the time of events is a transitive relation. On the other hand, “to be non-simultaneous (asynchronous)” is not a transitive relation because A and C can be simultaneous although both of them are non-simultaneous with B. Perceptual simultaneity refers to our perception or judgment that two or more things are simultaneous (or at least that we cannot tell their temporal order). While the transitivity of the simultaneity of time of events is virtually always accepted, philosopher Kelly (2005) has argued that perceptual simultaneity is an intransitive relation. If successful, and the conclusions drawn from this claim were sound, Kelly’s (2005) argument would pose a serious challenge to certain theories of consciousness and views on neural synchrony (Elliott et al., 2006). Instead of elaborating on these consequences, and how they follow from the possible intransitivity of perceptual simultaneity, I will argue that the argument itself rests on an assumption that requires justification. Accordingly, it should remain an open question whether perceptual simultaneity is a transitive or intransitive relation, and addressing this question would be a fruitful empirical endeavor. Kelly’s argument takes the imprecision of perceptual simultaneity as its starting point. It is indeed a well-known fact that when two stimuli are presented in a short temporal asynchrony, we judge them to be simultaneous. Depending on the nature of the stimuli, this window of simultaneity – temporal extension during which we cannot tell the temporal order of asynchronous stimuli – can range from few milliseconds to tens of milliseconds. Based on this imperfection of our perceptual processes, Kelly’s argument focuses on situations where subjects are shown three or more asynchronous stimuli. One way to present it goes as follows. Let us assume that a subject is shown three brief asynchronous stimuli (A, B, and C) such that the onset asynchrony between A and B is three quarters of the temporal window of simultaneity, and that this holds for B and C too. Accordingly, A and B, and B and C are judged to be simultaneous. But the onset asynchrony between A and C is 50% longer than the window of simultaneity. Hence, A and C are not perceptually simultaneous. Given that the relation of perceptual simultaneity holds between A and B, and between B and C, but not between A and C, perceptual simultaneity turns out to be an intransitive relation. To make this more concrete, let us assume that the temporal window of simultaneity is 40 ms (although the exact number has no bearing on the success of the argument, this is close the lower limit of the estimations for visual simultaneity threshold). In this case A and B, and B and C could be presented 30 ms apart, and they are perceptually simultaneous. Nevertheless, A and C appear 60 ms apart, which makes them perceptually asynchronous. The previous line of reasoning rests, however, on (at least thus far unjustified) assumption because the intransitivity of perceptual simultaneity does not follow by logical necessity from the imperfection of our perceptual processes to determine temporal relations between stimuli. To see this, consider Kelly’s argument again. In order for the argument to get off the ground, three comparisons need to be established: while we perceive A and B as simultaneous, we also perceive B and C as simultaneous and A and C as non-simultaneous. For this to take place, the argument needs to entail that we can successfully make a number of simultaneity comparison that cover the same episodes of experiencing. If it turned out, for example, that the episode of experiencing B cannot be part of two simultaneity comparisons, one for A and B and the other for B and C, then the simultaneity of one of them cannot be established and at least one of the premises of the argument for intransitivity would lose its grounding. Kelly’s argument is therefore based on a hidden assumption of parallelity according to which two or more simultaneity comparisons can partly cover the same moments of experiencing. (Because the simultaneity comparisons are done based on the information still lingering in our consciousness rather than, say, based on our memory of yesterday’s events, the assumption of parallelity amounts roughly to the idea that we can do more than one simultaneity comparison before the information disappears.) If one holds the assumption opposite to the one that Kelly is making – the assumption of seriality according to which simultaneity comparisons cannot cover the same moments of experiencing – then there is no argument for the intransitivity. It thus remains an open question whether perceptual simultaneity is transitive or not. Nevertheless, in addition to the general principle that one should not adopt any assumptions – especially those that may have significant consequences – without testing them, two experiments suggest that the assumption of parallelity along with the intransitivity of perceptual simultaneity may not hold. It is worth noticing that the following cases concern only visual modalities, and whether they can be extended to apply to other sensory modalities as well as to crossmodal simultaneity is an open question. First, the issue whether the visual judgments of simultaneity are transitive or not has been explicitly tested by Corwin and Boynton (1968). Based on their results, they concluded that “[w]ithin the experimental