Comunicação e Ética: O sistema semiótico de Charles ... - Ubi Thesis

✐✐✐✐356 Anabela GradimDepois de conceber e definir o contínuo matemático com recurso aos infinitesimais,definição essa que aglomera as propriedades atribuídas ao contínuopor Kant e Aristóteles, 44 sendo verdadeiro contínuo “algo cujas possibilidadesde determinação nenhuma multitude de indivíduos pode exaurir” de formaque “nenhuma colecção de pontos colocada numa linha contínua pode preencheressa linha, não deixando espaço para outros”. 45 O que significa que umalinha, ao contrário da visão habitual, não contém pontos, e quando estes nelasão marcados, a continuidade é quebrada: “o contínuo, onde é contínuo, semquebra, não contém partes definidas; as suas partes são criadas no acto de asdefinir, e a sua definição precisa quebra a continuidade”. 46be, not merely an indefinite succession, but a continuous flow of inference through a finite time,and the result will be a mediate objective consciousness of the whole time in the last moment.In this last moment, the whole series will be recognized, or known as known before, exceptonly the last moment, which of course will be absolutely unrecognizable to itself”, CollectedPapers, 6.111.44 . Não pertence a The Law of Mind este excerto algo extenso sobre o contínuo em Kant,Aristóteles e Cantor, que Peirce critica, mas é imprescindível ao estudo que temos em apreço:“The old definitions - the fact that adjacent parts have their limits in common (Aristotle), infinitedivisibility (Kant), the fact that between any two points there is a third (which is true ofthe system of rational numbers) - are inadequate.The less unsatisfactory definition is that of G.Cantor, that continuity is the perfect concatenation of a system of points - words which mustbe understood in special senses. Cantor calls a system of points concatenated when any twoof them being given, and also any finite distance, however small, it is always possible to find afinite number of other points of the system through which by successive steps, each less thanthe given distance, it would be possible to proceed from one of the given points to the other.He terms a system of points perfect when, whatever point belonging to the system be given, itis not possible to find a finite distance so small that there are not an infinite number of pointsof the system within that distance of the given point. As examples of a concatenated systemnot perfect, Cantor gives the rational and also the irrational numbers in any interval. As anexample of a perfect system not concatenated, he gives all the numbers whose expression indecimals, however far carried out, would contain no figures except 0 and 9. Cantor’s definitionof continuity is unsatisfactory as involving a vague reference to all the points, and one knowsnot what that may mean. It seems to me to point to this: that it is impossible to get the ideaof continuity without two dimensions. An oval line is continuous, because it is impossible topass from the inside to the outside without passing a point of the curve. Subsequent to writingthe above [164] I made a new definition, according to which continuity consists in Kanticityand Aristotelicity.The Kanticity is having a point between any two points. The Aristotelicityis having every point that is a limit to an infinite series of points that belong to the system”,Collected Papers, 6.164-6.166.45 . Collected Papers, 6.170.46 . Collected Papers, 6.168.www.labcom.pt✐✐✐✐