Mather’s (2019) provocative claim that octopuses have a mind hinges on the inference that their striking behavioural flexibility is evidence of “complex” cognitive abilities. I discuss alternative explanations -- not to deny the possibility of complexity but to point out that current evidence does not allow us to draw firm conclusions. Only an agnostic approach will lead to the systematic investigation of octopus behaviour and ultimately, greater insights into the cognitive capacities of these fascinating creatures.