Abstract
In this paper, a new kind of opposition relations is presented. Taking privation as a main negative operation on predicates, in this paper is presented a relative opposition theory, i.e., a sub-theory of oppositions.
Supported by ANID-Chile. Special thanks to the reviewers, without their valuable comments this work would not have been possible.
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Notes
- 1.
“The range \(\hat{P}\) of a predicate P can be seen as the range of applicability of P, denoting things that may be meaningfully– even if not truly–described by P”. [19, pp. 266].
- 2.
This characterization is close to the one proposed by Seuren & Jaspers in [20], specifically related to the concept of morphological negation that they develop. In addition, Seuren & Jaspers’ approach can be compared with many-valued analysis of privation in [13]. Due to lack of space, more in-depth comparisons are not elaborated here, but this will be left for future work.
- 3.
This definition is a variation of the notion of range of applicability defined in [19, 271].
- 4.
In Spanish: “?‘Es lo mismo ser no-justo que ser injusto? Aristóteles y sus comentaristas”.
- 5.
It is worth mentioning that Aristotle’s formulation only included contradiction, contrariety and subcontrariety; subalternation was added by the commentators.
- 6.
In Spanish: Puesto que la afirmación privativa es equivalente con la afirmación indefinida y, en la otra columna, la negación privativa es equivalente con la negación indefinida, y ello no ocurre con las respectivas afirmación simple y negación simple, se tiene que: “dos proposiciones” (a saber: la afirmativa y la negativa con predicado indefinido), “se relacionan, en orden de secuencia (sc. son similares), según la afirmación y la negación, del modo como las privaciones se relacionan, mientras que dos no” (a saber, la afirmación y la negación simples).
- 7.
(Met. 1055 a 34 – 1055 b 10).
- 8.
This definition may seem very redundant, and can possibly be omitted. It is explicitly included here only to keep us aligned to Proto-exposition.
- 9.
All these relations are valid by Definition 9.
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García Cruz, J.D. (2021). What Kind of Opposition-Forming Operator is Privation?. 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_11
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