Logicometry: Graphical Representations of Logical Space Interrelations

Abstract

The graphical approaches associated with the philosophy of mind and logic have been underused so far in the visual literacy. This paper aims to extend the graphical methods of logical analysis, by constructing a multi-dimensional geometric model, using differential geometry concepts. The model features two qualitatively different representations of logical space, based on Wittgenstein’s Tractatus, where one is graphed on the Cartesian and the other on the polar coordinate system. Each representation comes with its own spatio-temporal structure of contained modalities, that Wittgenstein calls propositions. These propositions, geometrically translated as variables, form every line of reasoning in space, and provide pictures of the case reality. According to Wittgenstein, every form of reality is composed of space, time and color (meaning) and only through this configuration its picture is complete. In the geometrical model, for every point in space, the temporal character is specified by its positional declination, and the potential variability of its meaning is depicted with a color map. For example, if white and black represent a certain “p” or “~p” attribute, then a proposition’s light or dark tonality specify its logical tendency. This mathematically underpinned composition of entities forms a complete geometrical structure with analogically measurable units that can shed some light on forms of causality between the mental phenomena. The structure operates as a function and provides a graphical representation of logic in terms of space. Consequently, the model’s ability to graphically plot logical interrelations may introduce a new methodology of modeling phenomena and processes which can be applied in theoretical studies and combined with the natural sciences. As an instrument of direct assessment and suggestion, it can strongly contribute to logical analysis. This is notably important in regard to the modern-day philosophy of mind, which has a tendency towards fragmentariness as it separates the metaphysical qualities from the scientific knowledge.