Version 1
: Received: 13 February 2022 / Approved: 15 February 2022 / Online: 15 February 2022 (08:35:02 CET)
How to cite:
Skliar, O.; Gapper, S.; Monge, R. Using the Set Equality Method (SEM) to Determine the Validity of Categorical Syllogisms. Preprints2022, 2022020183. https://doi.org/10.20944/preprints202202.0183.v1
Skliar, O.; Gapper, S.; Monge, R. Using the Set Equality Method (SEM) to Determine the Validity of Categorical Syllogisms. Preprints 2022, 2022020183. https://doi.org/10.20944/preprints202202.0183.v1
Skliar, O.; Gapper, S.; Monge, R. Using the Set Equality Method (SEM) to Determine the Validity of Categorical Syllogisms. Preprints2022, 2022020183. https://doi.org/10.20944/preprints202202.0183.v1
APA Style
Skliar, O., Gapper, S., & Monge, R. (2022). Using the Set Equality Method (SEM) to Determine the Validity of Categorical Syllogisms. Preprints. https://doi.org/10.20944/preprints202202.0183.v1
Chicago/Turabian Style
Skliar, O., Sherry Gapper and Ricardo Monge. 2022 "Using the Set Equality Method (SEM) to Determine the Validity of Categorical Syllogisms" Preprints. https://doi.org/10.20944/preprints202202.0183.v1
Abstract
A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered -- that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In some cases, as will be specified, it is possible to provide a second test for the validity of a syllogism whose validity was already proven, thus providing information about the logical form of categorical syllogisms.
Keywords
categorical syllogisms; categorical propositions; set theory; set equalities
Subject
Computer Science and Mathematics, Logic
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
