René Descartes (1596-1650): Probably one of the most influential philosophers and scientists, whose contribution, at a time of change and definition, marked Western civilization in many ways. The Cartesian dualism he developed ascertains a physical (res extensa) and a thinking (res cogitans) substance. The first is extended, can be measured and divided; the second is indivisible. The body is part of res extensa, the mind (including thoughts, desires, volition) is res cogitans. His rules for the Direction of the Understanding (1628), influenced by his mathematical concerns, submitted a model for the acquisition of knowledge. The method of doubt, i.e., rejection of everything not certain, expressed in the famous Discourse on Method (1637), together with the foundation of a model of science that combines a mechanic image of the universe described mathematically, are part of his legacy.
Edwin A. Abbot. Flatland. A Romance of Many Dimensions. By a
Square.
A broad-minded square guides the reader through a 2-dimensional space. High priests (circular figures) forbid discussing a third dimension. Abruptly, the square is transported into spaceland and peers astonished into his 2-dimensional homeland.
Spatial reasoning: a type of reasoning that incorporates the experience of space either in direct forms (geometric reasoning) or indirectly (through terms such as close, remote, among others).
Linearity: relation among dependent phenomena that can be described through a linear function.
Non-linearity: relations among dependent phenomena that cannot be described through a linear function, but through exponential and logarithmic functions, among others.
Jackson E. Atlee. Perspectives of Non-Linear Dynamics.
Cambridge/New York: Cambridge University Press, 1990.
S. Neil Rasband. Chaotic Dynamics of Non-Linear Systems. New
York: Wiley, 1990.
Coherence: the notion that reflects interest in how parts of a whole are connected. Of special interest is the coherence of knowledge.
Ralph C.S. Walker. The Coherence Theory of Truth: Realism,
Anti-Realism, Idealism. London/New York: Routledge, 1989.