Abstract
The question is posed: in which respects and to what extent are logical systems which employ diagrammatic representations “formal”? I propose to characterize “formal” rules to be those which are reducible to simple constructive operations on the representations themselves. Formal systems, then, are those which employ such formal rules. It is argued that “formality” thus characterized underlies a particular strategy for meeting a certain epistemological challenge. Some diagrammatic and heterogeneous logical systems are tested for formality, and it is suggested that any robust heterogeneous system is unlikely to be formal. The analysis of this paper, then, provides a principled account of how some diagrammatic systems differ significantly from linguistic ones.
The author would like to thank Johan van Benthem, John Etchemendy, Krista Lawlor, Keith Stenning, and two anonymous referees for helpful comments on an earlier draft. The author also gratefully acknowledges the financial assistance of the Social Sciences and Humanities Research Council of Canada.
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di Luzio, P.S. (2000). Logical Systems and Formality. In: Anderson, M., Cheng, P., Haarslev, V. (eds) Theory and Application of Diagrams. Diagrams 2000. Lecture Notes in Computer Science(), vol 1889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44590-0_14
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DOI: https://doi.org/10.1007/3-540-44590-0_14
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