Abstract
Seguindo um artigo anterior (cf. (Costa-Leite 2018)) no qual as oposições ló-gicas são definidas em um segmento de reta, este artigo vai um passo além e propõe um método para organizá-las usando um objeto de dimensão zero: um ponto.
Highlights
In the environment of a two-valued logic such as first-order logic, oppositions are regularly four: contradiction, contrariety, subcontrariety and subalternation
In (Costa-Leite 2018), it is argued that a line segment of integers is enough to organize logical oppositions in such a way that there is no need to use n-dimensional objects (n ≥ 2) to get representations of standard logical oppositions
The theory of logical oppositions, as it has been developed in the literature, uses n-dimensional diagrams (n ≥ 2) to represent contradiction, contrariety, subcontrariety and subalternation
Summary
In the environment of a two-valued logic such as first-order logic, (logical) oppositions are regularly four: contradiction, contrariety, subcontrariety and subalternation. In (Costa-Leite 2018), it is argued that a line segment of integers is enough to organize logical oppositions in such a way that there is no need to use n-dimensional objects (n ≥ 2) to get representations of standard logical oppositions.. Positions to be established in a line segment This produces, a conversion of the square and the hexagon of opposition into a line segment of opposition (for precision and details cf (Costa-Leite 2018)). The following strategy defines all four oppositions by means of a mathematical dot, a point, a fragment of zero-dimensional space: it does not work, for all points in general It works precisely for an unique and special point in the real line and the reasons for this fact will be clear in due time
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