Abstract
An incessant debate that history of syllogistic reasoning has witnessed is on the status of fourth figure after its alleged invention. Commentators on Aristotle and several other logicians have advocated various approaches to include or abandon this last figure. However, in the middle of last century, the debate seemed to have reached quiescence with fifteen valid syllogisms present in four figures. Among this, some moods are distinct, i.e. they are valid in one figure whereas others are non-distinct as they are valid in multiple figures. In this paper, the notion of diagrammatic congruence for non-distinct syllogisms using Venn-Peirce diagrams is introduced. Consequently, we establish the equivalence of moods that are diagrammatically congruent. Furthermore, it is argued that the presence of a distinct mood is pivotal to recognize an arrangement as a separate figure, which is evident in Aristotle’s own treatment of figures. With this, the redundancy of fourth figure is demonstrated.
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Notes
- 1.
Adapted and redrawn from Kneale and Kneale [8].
- 2.
A similar approach is also found in Peterson [12].
- 3.
‘Aristotelian’ here refers to both Aristotle’s and his commentators.
- 4.
A particular conclusion does not follow from two universal premises.
- 5.
The notion of ‘Equivalence’ is discussed in Richman [15].
- 6.
A diagrammatic justification of perfect syllogisms is demonstrated in Sharma [20].
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Acknowledgment
This paper has substantially benefited from the discussions with Prof. A.V.J. Pietarinen, Dr. G. Stapleton, Dr. J. Burton, Dr. F. Bellucci, Prof. M. Chakraborty and Prof. L. Choudhury, on an earlier draft. I also thank anonymous reviewers for their comments and suggestions.
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Sarathi Sharma, S. (2018). Depicting the Redundancy of Fourth Figure Using Venn-Peirce Framework. In: Chapman, P., Stapleton, G., Moktefi, A., Perez-Kriz, S., Bellucci, F. (eds) Diagrammatic Representation and Inference. Diagrams 2018. Lecture Notes in Computer Science(), vol 10871. Springer, Cham. https://doi.org/10.1007/978-3-319-91376-6_61
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