The Blot

P. 225–238.

Pietarinen A., Bellucci F., Bobrova A., Haydon N., Shafiei M.

TheblotisasigninPeirce’sdiagrammaticsyntaxofexistentialgraphs that has hitherto been neglected in the literature on logical graphs. It is needed in order to trigger the cut-as-negation to come out from the scroll, namely from the implicational sign of a positive implicational (paradisiacal) logic. Since the cut-as-negation presupposes the blot and the scroll, what does the blot represent? On the one hand, it stands for constant absurdity, but on the other hand, Peirce takes it to be an affirmative sign. This paper explores the blot and its logical and conceptual properties from the multiple perspectives of notation, rules of transformation, icons, and scriptibility of graphs. It explains the apparent conflict in the blot’s meaning in its capacity of giving rise to the pseudo-graph that exploits positive character of absurdity. In effect, the blot is the mirror image of the sheet of assertion, not its complementation. On the sheet, it acts as a non-juxtaposable singularity.

Keywords: Blot, Existential Craphs

In book

Diagrammatic Representation and Inference. 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings

Vol. 12169 : Diagrammic Representation and Inference. , Cham: Springer, 2020.