Imagine a round square

Amirouche Moktefi and Jelena Družinina


There is growing interest in the logic of imagination. A widespread position holds that all that is imagined is conceived and all that is conceived is possible. Hence, (logical) impossibilities such as ‘round squares’ cannot be imagined. Yet, during a tutorial at the Diagrams 2018 conference, we asked participants to undertake this impossible task: to imagine a round square, and we collected their drawings. Should we then dismiss the collected round squares on the ground that they cannot be? We present the outcomes of this experiment and explore what it teaches us on imagination, impossible objects and diagrams. In particular, we argue that there is no need to draw an object that is actually round and square in order to visualise an object that is round and square. All that is needed is to visualise the possession of those properties of round-ness and square-ness. Diagrams help considerably.

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