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Volume 12
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10.3390/axioms12030236
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Peer-Review Record

Aristotelian Diagrams for the Proportional Quantifier ‘Most’

Axioms 2023, 12(3), 236; https://doi.org/10.3390/axioms12030236
by Hans Smessaert 1,* and Lorenz Demey 2,3
Reviewer 1:
Harrie De Swart
Reviewer 2: Anonymous
Axioms 2023, 12(3), 236; https://doi.org/10.3390/axioms12030236
Submission received: 31 January 2023 / Revised: 21 February 2023 / Accepted: 22 February 2023 / Published: 24 February 2023
(This article belongs to the Special Issue Modal Logic and Logical Geometry)

Round 1

Reviewer 1 Report

An elegant exposition about combinations of Aristotelian diagrams. The authors combine Aristotelian diagrams for "for all" and for "most", and they do so in a clear and coherent way.

To the best of my knowledge their contribution is new, although it builds (of course) on earlier work by the same authors. I simply have no suggestions for improvement, I find the paper interesting, elegant, well written and relevant.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

This is a very well-written article. It is properly developed containing an original research on a issue which has attracted the attention of a great audience.  The paper deals with the Square of Opposition and its possible decorations  and extensions provided by the logic of modulated quantifies. These are are logics to study mathematically concepts such as "most", "generally", "rarely", "almost all" etc. In this sense, I think that some connections with issues on the logics of modulated quantifiers are missing. For instance, the paper

 

Veloso, S. R. M; Veloso, P. A. S. On Modulated Logics for "Generally": Some Metamathematics Issues. In: Béziau, Costa-Leite, Facchini (editors) Aspects of Universal Logic, Travaux de Logique, 17, 2004

 

contains some decorations on the interactions of oppositions and the logic of modulated quantifiers (p.156-157).  A reference and a brief discussion of this work should appear in the final version of the paper.

 

Moreover, nothing is said on the current debate on the end of the square and its extensions (Schang, Fabien. End of the Square?  South American Journal of Logic 4 (2), pp. 485-505, 2018). It is argued that there is no need to construct two-dimensional (square, octagons etc) to define and decorate oppositional concepts. A mere line segment is enough. Indeed, even a point can be used (cf. Costa-Leite, A. Oppositions in a line segment.  South American Journal of Logic, 4(1), pp.185-193, 2018 and Costa-Leite, A. Oppositions in a point. Perspectiva Filosófica, 47(2), pp.113-119, 2020.

 

 So, why should we go towards octagon if the constructions suggested can be done in a line segment? Just food for thought.

 

I recommend the current paper for publication after a very minor revision, especially adding a discussion on Veloso's idea.

 

 

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

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