This talk, presented to the Oxford Communist Corresponding Society on Jan 26th 2024, examines the relationship between Zeno’s ancient argument of the paradox of the arrow, which seems to demonstrates that motion is logically impossible, and the mathematical calculus, our most successful formal theory of change and motion. I argue that the calculus, when properly interpreted, does indeed solve Zeno’s paradox by pointing to the necessity to understand reality as not only composed of what is, but also composed what isn’t (i.e. absence or “negativity”), in the sense that motion (and change in general) is driven by “real contradictions”, or causal structures that form closed-loops, such that (i) a component A represents the non-existence of the state of another component B, and (ii) the causal structure of the loop is such that the state of B becomes that which A represents. In other words, the mathematical calculus is remarkably consistent with the Hegelian theory of change.

First 48 mins: main talk. 48 mins to 1 hour 12 mins: discussion by participants. Last 10 mins: my response.