# abstract Ian Lyons

**Ian Lyons** (University of Western Ontario, Canada)

### Ordinality and the Nature of Symbolic Numbers

Number symbols (e.g., 1, 2, 3…etc.) are a fundamental building block of mathematics – and by extension, much of our modern world. Taking number symbols as a focal point, one can ask what cognitive processes underpin number symbols. For instance, from where or what do these symbols derive their meaning? Turning in the opposite direction, one can also ask what other processes number symbols themselves underpin. For instance, how do number symbols contribute to more sophisticated forms of mathematical cognition? First, I will present neural and behavioral evidence that contradicts the – until recently, rather dominant – view that the meaning of number symbols is closely tied to how we process perceptual magnitudes. Instead, I will argue that number symbols act primarily as abstract entities, and so derive their meaning largely via how they relate to other abstract entities, namely, other number symbols. In particular, I argue that ordinality – a relatively overlooked property of numerical processing – is one of the fundamental relations that bind number symbols to one another. As such, examining how we process the relative order of numbers may help answer both questions posed above: what underpins a number symbol, and what do number symbols underpin? I will explore recent work – neural, behavioral, in children and in adults – that both supports and capitalizes on the insight that ordinality may be key to understanding the nature of symbolic numbers.