Abstract
Charles S. Peirce achieved, by the line of identity, a rich and useful analysis of quantification in the Beta Graphs that can be easily translated into the standard existential quantifier of First Order Logic. In this paper I claim that the way the line of identity expresses identity relation does not correspond to the usual understanding in the standard classical First Order Language with identity (FOL=). It will be argued that the line of identity cannot be used to express equations as in FOL=, but it expresses individual identity (in an ontological sense).
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1. References
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Acknowledgements
The author wishes to thank the anonymous referees for their valuable criticism to a previous draft of this paper. This work was supported by the research projects PIP 11220170100463CO (CONICET, Argentina), PICT 2017 0506 (ANPCyT, Argentina) and UBACYT 20020170100684BA (University of Buenos Aires).
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Legris, J. (2021). On Identity in Peirce’s Beta Graphs. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_22
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DOI: https://doi.org/10.1007/978-3-030-86062-2_22
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